BIBLIOGRAPHY CRISANTA P. APIT, MARIFEE K.LOGRO,...
BIBLIOGRAPHY
CRISANTA P. APIT, MARIFEE K.LOGRO, NOEMI S. PALUBOS. April 2008.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006.Benguet State University, La Trinidad
Benguet.
Adviser: Maria Azucena B. Lubrica, Ph.D
ABSTRACT
Correspondence Analysis is a multivariate method for exploring cross-tabular
data by converting such tables into graphical displays, called maps,” and related
numerical statistics. It is a tool commonly used in many disciplines to identify and
visualize the association between two categorical variables.
The technique was applied to the contingency table on the number of births in the
six provinces of the Cordillera Administrative Region during the Calendar years 2000-
2006. The row variable consists of the six provinces of Cordillera Administrative Region
namely: Abra, Apayao, Benguet, Kalinga, Mt. Province, Ifugao and in the City of
Baguio. The column variable consists of the calendar year categories, namely: 2000,
2001, 2002, 2003, 2004, 2005 and 2006.
Correspondence Analysis was used to analyze the 7x7 ( 7 rows by 7 columns)
contingency table on the number of births in the six provinces of CAR during the years
2000-2006. It also intended to determine the weights (masses), quality and variance
(inertia) of the six provinces and Baguio City, and calendar year points.
Results of inertia and chi-square decomposition explained 77.44 cumulative
percent of variance in the first two dimensions. The root of the total inertia 0.0311154
equals 0.1764 as the eigen value. This suggested that the first two dimensions appear to
be satisfactory in representing the CAR provinces and calendar year profiles.
The Cordillera Administrative Region which was highly explained in the graph
were Benguet and Mt. Province. The rest of the provinces were quite well represented by
the dimensions, except Baguio which was poorly explained. The calendar year profile
points were well represented, except the calendar year 2002 in the two-dimensional map.
However, only the CY 2000 and 2004 were highly explained.
In the two-dimensional map, dimension 1 was defined by three provinces of CAR,
namely: Benguet, Kalinga, and Mt. Province and the CY 2003, 2005 and 2006 defined
the second dimension.
The categories with large mass meant high frequency and low mass implied low
frequency with respect to the entire data set. A dimension with high contribution to point
indicates that the dimension represents well the point in the dimensional map while the
low contribution of a dimension to point shows that the dimension explains poorly the
point in the map.
ii
TABLE OF CONTENTS
Page
Bibliography…………………………………………………………………….....i
Abstract……………………………………………………………………………i
Table of Contents………………………………………….……………………..iii
INTRODUCTION
Background of the Study………………………………………………….1
Objective of the Study…………………………………………………….3
Importance of the Study…………………………………………………...3
Scope and Delimitation……………………………………………............4
REVIEW OF RELATED LITERATURE
Correspondence
Analysis………………………………………………….5
Definition of Terms………………………………………………………..8
THEORETICAL FRAMEWORK……………………………..………………...11
METHODOLOGY
Location of the Study…………………………………………………….16
Data Gathering Procedure………………………………………………..17
Data Analysis…………………………………………………………………….18
RESULTS AND DISCUSSION
Contingency Table and Correspondence Matrix………………………………...19
Quality, Mass and Inertia of CAR Provinces……………………………………27
Row Coordinates.................…………………………….….……………………29
Quality, Mass and Inertia of the Calendar Year Points….………………………30
iii
Correspondence Map …………………………....................................................37
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
Summary…………………………………………………………………38
Conclusions………………………………………………………………39
Recommendations…………………………………………………..........41
LITERATURE CITED…………………………………...…………………..….43
APPENDICES
A. Letter of request to the National Statistics Office……………………44
Letter of request to the National Statistics Coordination Board ….... .45
B. Number of Registered births by month and Provinces……………….46
C. Inertia and Chi-square Output………………………………...………52
D.
STATA
Output…………………………………………………….….54
E. Plot of Correspondence Solution………………………………..….…56
iv
1
INTRODUCTION
Background of the Study
Cordillera Administrative Region (CAR) is at the central part of northern
Luzon. This Region is a land-locked region, consisting of six provinces: Abra,
Apayao, Benguet, Ifugao, Kalinga, Mountain Province, and Baguio City, a first
class, highly urbanized city, which is the regional center. Cordillera encompasses
most of the areas within the Cordillera Central mountain ranges of Luzon, the
largest ranges in the country. This Region is home to numerous indigenous tribes
collectively called Igorots.
CAR is more heavily populated compared to other mountainous areas of
the Philippines. Based on the 2000 census, its six provinces and one city have a
total population of 1,365,220 people. With a land area of 18,294 square
kilometers, the population density is 75 per square kilometer.
Among the six provinces of CAR, Benguet ranked first in terms of
population size with 1,365,220 people in the 2000 census, its population density is
275 people per square kilometer. This province contributed 24.2% of the
population in the region, and 0.43% to the Philippine population of 76.5 million.
From 1995 to 2000, its annual growth rate is 1.0990, which is much lower than
the national average of 2.43%. The average household is 5.2 persons, a little
higher than the national average of 4.99. Benguet, with La Trinidad as its capital,
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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it is often called the Salad Bowl of the Philippines, It has agriculture, mining and
tourism as major industries..
Abra has a rugged terrain, with mountains and hills rising along its
perimeter and interior. This basin-like province is drained by the Abra River. Its
population of 20,491 is the 12th smallest in the country with a density of 53 people
per square kilometer. Abra’s economy is agriculture. With its capital in Bangued.
Ifugao with Lagawe as its capital is also a landlocked mountainous region
characterized by rugged terrain, river valleys, and massive forests. Its population
of 161,623 is the 9th smallest in the country, with a density of 64 people per
square kilometer. The 2000 year old Banaue Rice Terraces is the main tourist
attraction of the province.
Kalinga is rugged and sloping with mountain peaks. Its population of
174,023 is the 11th smallest and its density of 56 people per square kilometer is
the 6th lowest. The people of Kalinga are the most extensive rice farmers among
the Cordillerans. Founded in 1995, its capital is Tabuk City.
Apayao become a province when it was separated from Kalinga in 1995.
Kabugao became its capital. Its population is 97,129, which is the 4th smallest
and it has the lowest density of 25 people per square kilometer.
Mountain Province was named as such because it is found in the
Cordillera mountain range. Prior to 1966, Mountain Province included Benguet,
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Kalinga-Apayao and Ifugao. Its population of 140,349 is the 6th smallest and its
density of 67 people per square kilometer is the 10th lowest.
Objectives of the Study
The general objective of the study is to apply correspondence analysis to
the number of births in the six provinces of CAR, including Baguio City, during
the calendar years 2000-2006.Specifically, the study aimed to determine the
association of the six provinces and calendar years on the number of births in the
correspondence map.
Importance of the Study
The findings of the study would provide a comprehensive understanding on the
distribution of the number of births when taking into consideration the six
provinces of CAR including Baguio City and the seven calendar year period.
This study would also be a way of presenting graphically these CAR
provinces in relation to the distribution on the number of births. Such information
would be useful in the fiscal management of the Region since appropriate
budgetary allocation could be given based on the groupings illustrated in the
correspondence map.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Scope and Delimitation of the Study
The data used were on the six provinces of CAR including Baguio City
during calendar years 2000-2006. The data were taken from the National Statistics
Coordination Board.
Significance testing is not supported in the analysis, so model comparison
and selection of a best fit model were performed. The reason that Correspondence
Analysis is an exploratory, not a confirmatory technique. Visualization of
agreement or association of the provinces and calendar years on the number of
births were included.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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REVIEW OF RELATED LITERATURE
Correspondence Analysis
Correspondence Analysis has been proven to be one of the successful
techniques for graphical analysis of contingency data. It is considered to be a
popular technique especially in France, United Kingdom and in the united States
of America. Its growing popularity among statistical practitioners demonstrates
the importance of applying correspondence analysis as a research tool.
Correspondence analysis has become a popular method in the social and
environmental sciences. The Analysis incorporates steps in translating a table to a
graphical display. First, it transforms the rows of the table into profiles, which is
the rows divided by their row totals. Second, weights are assigned to the row
profiles proportional to the marginal row totals of the contingency tables. Third, a
standardization of the profiles elements is performed by dividing them by values
proportional to the square root of the marginal column totals of the contingency
totals. The third step implies a special distance function between the profiles,
called the chi-squared distance. Finally, a weighted principal component analysis
is performed on the row profiles, identifying the plane, which best fits the row
profiles by minimizing the weighted the sum of squared (chi-squared) distances
from the points to the plane. Then the profile points are projected unto this plane
and their relative positions are interpreted. An identical and completely symmetric
analysis can be performed on the column profiles. The two analysis are equivalent
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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and their solutions are based on the singular value decomposition of the same
matrix (Greenacre, 1984).
Micheloud (1997) analyzed a table which reflected 169,836 people aged
15 or more, living in the Lausanne district of Geneva in Switzerland. Attributes
considered were maximum level of schooling attained (variable I, in rows) and
community of residence (variable J, in the column). The aim of this analysis was
to find out if there was an attraction, independence, or even repulsion between
rows and columns.
Huixin and Hao (1996) used the Correspondence Analysis in marketing
research, conducted in Zhenzou City in China. The main purpose of the project
was to estimate the market, but a new name recommended by the consulting
company for a newly developed pure water product was also tested. The tables
which were analyzed consisted of the product names marked against the product,
and names marked against the feeling of respondents.
Correspondence Analysis seeks to represent the interrelationships of row
and column variables on a two dimensional map. It can be thought of as trying to
plot a cloud of data points (the cloud having height, width and thickness) on a
single plane to give a reasonable summary of the relationships and variation
within them.
One of the study was a research of lifestyle and culture consumption in a
United Kingdom City (Featherstone et al, 1994). One aspect of the study looks at
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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the leisure activities of people living in the new inner city development. Included
in the questionnaire were the questions about the use of local facilities, from pubs
to art galleries, knowledge of and preferences in music and involvement in
political issues.
The study of Bourdieu (1979) used Correspondence Analysis to provide
detailed illustrations for his thesis which include determinant case, cultural
discrimination and choice. Choice is described as the possession of two forms of
capital, economic and cultural, with sub-groupings defined by seniority in
possession and related mode of acquisition. This technique among English and
American sociologists seems to have remained low until the publication of
Greenacre text (1984) testifying to the easier availability of appropriate computer
software (CA).This correspondence technique is versatile, it can be used with
frequency data, with percentages, and with data in the formats of ratings with
heterogeneous data sets.
The study of Neri, Solivas, and VJ.Albacea focuses on the application of
Correspondence analysis to a particular 6 x 5 contingency table. The population
of the study is the cross tabulation of graduates from the College of Arts and
Sciences, University of the Philippine Los Banos during the ten years period of
1987-1996 classified into degree program and year graduated.
This study deals with the matrices and its components as a given by the
singular value decomposition (SVD); the pre-decomposition method prior to
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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correspondence analysis and the post-decomposition method which out the row
and column coordinates.
The Cordillera Administrative Region is more heavily populated
compared to the other mountainous areas of the Philippines. In the year 2000
census, its provinces and one city had a total population of more than 356,272
while 792,922 lived in the rural areas
The distribution of the number of births naturally affects the rate of
population growth. Birth statistics were obtained from the Certificates of Live
Birth, which were transmitted by the City/Municipal Civil Registrar to the office
of the Civil Registrar General for machine processing and archiving. The total
number of Live Births reported in 2000 was 1,766,440. This was an 8.3 percent
increase in ten years. The Daily Average of Birth occurrence was 4,826. This
means an addition of three babies to the population every minute. In the country,
approximately 23 live births per 1000 population had occurred in 2000. CAR has
a similar birth rate.
Definition of Terms
Category
masses are the marginal proportions of a discrete variable. In the
terminology of correspondence analysis, the relative frequencies of the
row
totals and column totals are called the row mass and column mass, respectively.
Centroid or average profile is the weighted mean of the row and column
profiles. It is the origin of the correspondence map.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Contingency
table is a two-way table of categorical data or the row cross
tabulation of the discrete variables with marginals. The variables must be discrete
nominal, ordinal, or continuous variables segmented into ranges. The object of
the correspondence analysis is to explain the inertia (variable) in the table.
Contribution of the dimensions to point is also known as squared
correlations on quality of representation of the description of a point. These
reflect how well the principal components model is explaining any given.
Correspondence
map displays two of the dimensions which emerge from
the principal components analysis of inertia, and points are displayed in relation
to these dimensions.
Correspondence matrix P is defined as the original table X divided by the
grand total.
Eigenvalues are the characteristics roots of the principal components
solution. There is one eigenvalue for each dimension, sometimes labeled as inertia
for that dimension.
Inertia means variance in the context of correspondence analysis.
Point distance refers to the chi-square distance rather than the Euclidean between
points.
Profile
point is one of the values (categories) of one of the discrete
variables in the analysis.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Proportions if inertia accounted for by a given dimension are its
eigenvalue divided by total inertia.
Quality of a point is defined as the ratio of the squared distance from the
origin in the chosen number of dimensions, over the squared distance from the
origin the space defined by the maximum number of dimension.
Relative
inertia represents the proportion of the total inertia accounted for
by the respective point.
Row and Column profiles are the relative frequencies of the row or
column discrete variable. Profile elements are the entries in each row or column
profile.
Scores in dimensions are the scores used as coordinates for point when
plotting the correspondence map.
Singular
value is the square root of an eigenvalue.
Total
inertia is the sum of eigenvalues and the spread of points around the
centroid. Total inertia may be interpreted as the percent of inertia (variance) in the
original correspondence table explained by all computed dimensions in the
correspondence analysis. It also defined as the total Pearson chi-square for two-
way divided by the total sum.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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METHODOLOGY
Location of the Study
The study was conducted at Benguet State University including the six
Provinces of CAR and Baguio City during the calendar years 2000-2006.Figure 1
shows the location of the study namely: Abra, Apayao, Benguet, Ifugao, Kalinga,
Mt.Province and Baguio City.
.
Figure 1.Location of the Study
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Data Gathering Procedure
The data were taken from Regional Social Economic Trend 2006 0f
NSCB and Population Census 2000-2004 of NSO.
The data set which was used on this study consisted of number of births on
the six provinces of CAR and Baguio City during the calendar years 2000-2006.
The distribution on the number of births by provinces and calendar years reflect a
two-way contingency table.
Table1. Contingency table on the number of Births during the calendar years
2000-2006.
PROVINCES
CALENDAR YEARS
OF CAR
2000
2001
2002
2003
2004
2005
2006
Abra
7382
7027
7244
7214
7965
6931
7246
Apayao
2125
2001
4102
3506
2784
2529
2843
Baguio
11708 8015
7922
9334
8179
9117
9672
Benguet
16348 16250
17128
15221 19052 19245 10242
Ifugao
6625
7210
7986
10599 7508
5580
7094
Kalinga
13703 12176
12295
7485
7828
7112
6949
Mt.Province
10111 6888
6174
5899
4676
4787
5870
Source: RSET-NSCB (Regional Social Economic Trend 2006) and Population
Census-NSO (2000-2004).
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
18
Data Analysis
Correspondence analysis was used to analyze the tabulated 7x7 (7 rows by
7 columns) matrix contingency on the number of births in the six provinces of
CAR during the CY 2000-2006.Correspondence analysis finds a low-dimensional
graphical representation of the association of rows and columns of the
contingency table, where categories of rows and column from the cell frequencies
are depicted as points in a median Eucledian space. These determined so that
squared distance between certain points in the derived space bear simple
relationships to the original tabular entries.
Correspondence analysis consist of three parts; a pre-decomposition
method where the original data or contingency table is transformed by certain
conversion procedures; second, the transformed data is subjected to singular value
decomposition where a set of row or column vectors together with its associated
singular values are summarized; and third, a post decomposition method is
applied where in the row and column vectors are used to come up with the row
and column coordinates or scores.
The data were summarized, tabulated, analyzed and interpreted using
Correspondence Analysis. Computations of summary statistics were facilitated
with the use of the software STATA.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
19
INPUT
Contingency table of the number of births in the six Provinces of CAR including
Baguio City during the calendar years 2000-2006.
DATA ANALYSIS
Part I: Pre decomposition
1. Construct the correspondence matrix of the contingency table compute
the relative frequencies of each entry.
Part II: Singular Value decomposition
1. Calculate the row profiles, row masses and average row profiles.
2. Compute the column profiles, column masses and average column
profiles.
Part III: Post decomposition
1. Compute the inertia, quality and contribution of dimension to points.
2. Reduce dimensionality – look for a low dimensional space which is as
close as possible to high dimensional true space.
OUTPUT
1. Tables of numerical results – mass, inertia, quality, principal inertias, eigen
values, singular values, chi-squares, chi-square percents, and partial contribution to
inertia of row and column points.
2. Correspondence map – two - dimensional map.
INTERPRETATION
Interpret numerical results and the two-dimensional map
Figure 2. Flowchart of the mathematics of correspondence analysis
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
20
RESULTS AND DISCUSSION
This section presents the discussion, analysis and interpretation of the
findings drawn from the correspondence analysis on the number of births in the
six provinces of CAR in the calendar years 2000-2006.
Contingency Table and Correspondence Matrix
The summary on the number of births and calendar year total with
reference to Table 1 as the contingency was presented in Table 2. The results in
Table 2 indicated that the provinces of Benguet, Kalinga, Baguio and Abra have a
relatively large number of births distribution from 2000 to 2006. Among the six
provinces, Benguet ranked first in terms of population size. This province
contributed 24.4% to the 1.4 million populations in the region. Second in rank for
the largest in number of births is the province of Kalinga.
The province of Benguet which had the largest number of births has
thirteen municipalities contributing 10 % each. On the other hand, Kalinga’s large
number of births may be due to the richness of its capital, Tabuk City.
. Provinces of CAR with low number of birth population are Abra, Mt.
Province and Apayao. Therefore, the possible reasons for the low population
status maybe its land shape and land areas.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Table 2 represents the distribution of births in each province. Calendar
year 2000 had the highest number of births and generally, a download trend was
observed the succeeding years, except in 2002.
Table2. Number of Births Distribution in the Six Provinces of CAR and CY 2000-
2006.
CALENDAR YEARS
PROVINCES
2000 2001 2002 2003 2004 2005 2006 Total
OF CAR
Abra
7382 7027 7244 7214 7965 6931 7246 51009
Apayao
2125 2001 4102 3506 2784 2529 2843 19890
Baguio
11708 8015 7922 9334 8179 9117 9672 63947
Benguet
16348 16250 17128 15221 19052 19245 10242 113486
Ifugao
6625 7210 7986 10599 7508 5580 7094 52602
Kalinga
13703 12176 12295 7485 7828 7112 6949 67548
Mt.Province 10111 6888 6174 5899 4676 4787 5870 43905
Total
6800 5956 6285 5925 5799 5530 4941 41238
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Table 3 is the correspondence matrix comprising the relative frequencies.
The sum of the table entries in the correspondence matrix equaled to one. This
showed how unit of mass were distributed across the cells. The row and column
totals of the matrix of relative frequencies were the row and column mass
respectively. These showed that in the provinces of CAR, the population during
the year 2005 had Benguet with the highest relative frequency of 0.047. This is
closely followed by Kalinga with 0.018 relative frequency. On the other hand
Apayao had the lowest relative frequency of 0.00613.
A similar trend was discerned in the succeeding years, where Benguet was
consistently highest in the relative frequencies of the number of births while
Apayao was the lowest in the relative frequencies.
Table 3. Correspondence Matrix
PROVINCES
CALENDAR YEARS
OF CAR
2000 2001 2002 2003 2004 2005 2006
Abra
0.0179 0.017 0.0175 0.0175 0.019 0.017 0.0176
Apayao 5.153-03 4.852-03 9.947-03 8.502-03 6.751-03 6.132-03 6.893-3
Baguio
0.028 0.019 0.019 0.023 0.02 0.022 0.023
Benguet 0.04 0.039 0.042 0.037 0.046 0.047 0.025
Ifugao
0.016 0.018 0.019 0.026 0.018 0.014 0.017
Kalinga 0.033 0.03 0.03 0.018 0.019 0.018 0.017
Mt.Prov. 0.025 0.017 0.015 0.014 0.011 0.011 0.013
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
23
The study of Bendixen (1996) stated that examination of the row and
column profiles allows the researcher to examine the relative position of the rows
and columns to each other and thus establish distinguishing characteristics. The
row and column profiles of the contingency table are presented in Tables 4 and 5.
The last row of the row profiles and last column of the column profiles are labeled
average.
These are the proportions of the number of births in the row and column.
These values are used as averages and weights (masses) in the calculations of the
weighted distances.
As reflected in Table 4, year 2000 had the highest number of births with
1.1377, followed by year 2002 with an average of 1.1014, then year 2003 with an
average of 1.0445 number of births, year 2001 with the average of 0.9927 number
of births, followed by the year 2004 with 0.9511 number of births average, year
2005 with 0.8956 average and finally year 2006 with the least average of 0.8865.
The higher the average relative to others, the higher number of births for that
particular year.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Table 4.Row profiles
PROVINCES CALENDAR YEARS
MARGINAL
OF CAR
2000
2001
2002
2003
2004
2005
2006 TOTAL
Abra 0.145
0.1378
0.142 0.1414
0.1561 0.1359
0.142 1
Apayao 0.107
0.1006
0.206 0.1763
0.134 0.1271
0.0143
1
Baguio
0.183 0.1253 0.124
0.146
0.128 0.1426 0.1513
1
Benguet 0.144
0.1432
0.151 0.1341
0.1679 0.1696 0.0902
1
Ifugao 0.126
0.126
0.152 0.2015
0.1427 0.1061
0.1349 1
Kalinga 0.203
0.2029
0.186 0.1108
0.1159 0.1053
0.1029
1
Mt.Province 0.23 0.1569 0.141 0.1344 0.1065
0.109 0.1223
1
Average
1.1377 0.9927 1.1014 1.0445 0.9511 0.8956 0.8865
In Table 5, the province with the highest average is Benguet with 1.93.
However, the province with lowest column average is Apayao ranging with 0.34,
as compared to Kalinga with a slight average of 1.132, Baguio City follows
1.0918, then with Ifugao with 0.8984, Abra with 0.8728 and Mt.Province with
0.7378. As with row profiles, the higher the average relative to others, the higher
the number of births in the particular province.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Table 5.Column Profiles
PROVINCES
CALENDAR YEARS
AVE
OF CAR
2000 2001 2002 2003 2004 2005 2006
RAGE
Abra
0.107 0.118 0.115 0.122 0.137 0.125 0.147
0.873
Apayao
0.031 0.034 0.065 0.059 0.049 0.045 0.058 0.34
Baguio
0.172 0.135 0.126 0.158 0.14 0.165 0.196 1.092
Benguet
0.24 0.273 0.273 0.257 0.329 0.348 0.208 1.93
Ifugao
0.096 0.121 0.127 0.179 0.13 0.101 0.144 0.899
Kalinga
0.202 0.204 0.196 0.126 0.135 0.129 0.141 1.132
Mt.Province 0.149 0.116 0.098 0.099 0.081 0.087 0.109 0.74
Marginal
Total
1
1
1
1
1
1
1
Table 6 shows the decomposed chi-square total inertia which is
0.0311165. It was derived by dividing the chi-square 12,832.07, by the number of
births grand total of 412,387. In decomposing the chi-square, the extracted
dimensions of the data set with a maximum value equal to the product of the
number of rows (row-1), the number of columns (column-1) that is (7rows) x (7
columns 1) equals to 36. Correspondence Analysis allows the optimal
representation of a contingency table in two dimensional space. In table 6, the
result of the reduction of dimensions yielded six dimensions. The greatest inertia
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
26
is attributed to the first dimension with a principal inertia of 0.0146382, followed
by the second dimension with a principal dimension of 0.0094567, and decreasing
sequentially in the succeeding dimensions. This shows that the first dimension of
the principal inertia is greater than the second dimension.
Table 6. Inertia and Chi-square Decomposition of the Data Set
NUMBER
PERCENT
OF
SINGULAR PRINCIPAL CHI-
OF
CUMULATIVE
DIMENSION VALUE
INERTIA
SQUARE
INERTIA
PERCENT
1 0.12099
0.014638
6036.75
47.05
47.04
2 0.09725
0.094567
3899.91
30.39
77.44
3 0.06993
0.00489
2016.64
15.72
93.15
4 0.37723
0.001423
586.85
4.57
97.73
5 0.02595
0.000673
277.64
2.16
99.89
6 0.00589
0.0000346
14.28
0.11
100
0.0311165 12832.07 100
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
27
A singular value is interpreted as the maximum canonical correlation
between the categories of the variables for any given dimensions. The first
dimension reflects a singular value equivalent of 0.1209886 while the
corresponding value for the second dimension is 0.0972457. This implies that the
provinces of CAR and calendar years are strongly associated in the second
dimension but weakly correlated in the first axis. Principal inertia reflects the
relative importance of the dimension. Each principal inertia is the amount of
variance that a given and dimension explains the contingency table. The total
inertia which is 0.0311159 was explained lately and 30.39 percent of inertia in the
second dimension.
Garson (2005) mentioned two criteria on how to stop interrupting
dimensions. The first is the Kaiser criterion, which indicated that the rate of the
total values of the principal inertia or eigenvalues must be less than 1. The second
criterion is that variance explained should only have cumulative percent between
80 to 90 percent.
In relation to the research study of Neri et al (1998) on the application of
correspondence analysis to a particular 7x7 contingency table of the number of
births in the six provinces of CAR and calendar year 2000-2006, 88 percent of the
total inertia was explained by the first and second dimensions.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
28
Ocden (2006) also used two dimensions with .1853 as the eigenvalue and
84.53 cumulative percent, in representing the degree programs and school year
profiles.
Quality, Mass and Inertia of CAR Province
Correspondence Analysis has been successful in representing the
contingency table in tow dimensional space. The overall retention of 77.44
percent was done in the two dimensions. However, not all of the provinces of
CAR and CY 2000-2006 were equally represented. Bendixen (1996) in his study
mentioned that the quality of representation of a particular row or column
provides additional richness to the interpretation of the relationships in the
contingency table. The quality of representation of the description of a point
reflects how well the principal components model is explaining the point.
Table 7 presents that the provinces of Benguet, Mt. Province, Kalinga, and
Ifugao had a quality of 98.8 %, 91.4 %, 83.8 % and 77.1 % respectively, and were
well represented by the two dimensions. On the other hand, provinces of Apayao,
Abra, and Baguio with a quality of 54.7%, 49.2% and 28.6% respectively were
poorly represented in the two dimensions. This implies that these three provinces
were not yet heavily populated or that they have a low number of births.
The contributions for the mass, the provinces of Benguet, Baguio and
Kalinga, with respective masses of 0.275, 0.164 and 0.155, have the highest
values for masses. This can be interpreted that the Benguet and Kalinga province
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
29
have a large frequency on the number of births. However, Baguio has high
contribution in its mass, but its quality of 28.6% shows poor representation. Large
mass of a row point means relatively high frequency for that province whereas the
relatively small mass implies low frequency for the other provinces. The sequence
consisted of Mt. Province with 0.106, Abra 0.124 and Apayao 0.048
Over the years 2000-2006, Apayao province remains to have low
population in terms of number of births because of its small land area.
The contribution of points to dimensions as reflected by the column inertia in
Table 7 is used to intuit the meaning of correspondence dimensions.
It was observed that the six provinces have contributed small variance since less
than 0.1 of inertia (variance) accounted for each point.
Table 7.Summary figures of CAR Provinces and Calendar years profiles
CAR PROVINCES
QUALITY
MASS
INERTIA
Abra
0.492
0.124
0.001
Apayao
0.547
0.048
0.003
Baguio City
0.286
0.155
0.003
Benguet
0.988
0.275
0.007
Ifugao
0.771
0.128
0.005
Kalinga
0.838
0.164
0.007
Mt.Province
0.914
0.106
0.004
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
30
In Table 8, the contribution of dimension to the six provinces of CAR is
presented. The value obtained in each cell is the percent of variance in provinces
profiles explained by the given dimensions, the province of Mt. Province, Kalinga
and Benguet defined the first dimension for having high contribution of
dimension 1 to points. The provinces of CAR which are important in the second
dimension are those which got a high relative value on the contribution to the
dimensions.
Table 8.Contribution of Dimensions to the six Provinces of CAR
Provinces of CAR
DIM 1
DIM 2
Abra 0.032
0.011
Apayao 0.080 0.057
Baguio City
0.001
0.092
Benguet 0.137 0.516
Ifugao 0.099 0.270
Kalinga 0.393 0.029
Mt.Province 0.259
0.026
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
31
In dimension 2, it was indicated that the provinces of Ifugao and Benguet
had the largest contribution. Because of some expectation that if the point of one
province are higher, we do believe that from any contribution, it will always be
the largest in contributing to dimensions implying a high squared correlation.
However, the reverse is not true. That is, if a point explains a lot variance in a
dimension, usually that dimension will describe the point very well (high squared
correlation).
Row Coordinates
Table 9 presents the row coordinates, which determines the position of
points when plotted in the two dimensional space. The positive and negative
coordinates in dimension 1 of the Province of CAR are to found at the right
branch and left branch, respectively, of the horizontal axis. In like manner,
positive and negative coordinates in dimension 2 are located upward and
downward, respectively, of the vertical axis.
The first dimension group was composed of Baguio, Kalinga and
Mt.Province as one while Abra, Apayao, Benguet and Ifugao were dimensions 2
have Benguet and Kalinga separated from Abra, Apayao, Baguio, Ifugao and
Mt.Province.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
32
Table 9.Two dimensional coordinates of the Provinces of CAR
PROVINCES
DIM 1
DIM2
OF CAR
Abra -0.177
0.091
Apayao -0.448 0.34
Baguio City
0.026
0.24
Benguet -0.245
-0.427
Ifugao -0.306
0.453
Kalinga 0.538
-0.132
Mt.Province 0.543
0.154
Quality, Mass and Inertia of the Calendar Year Points
With reference to Table 10, Calendar Years 2000, 2003, 2004, 2005 and
2006 were well represented by the two-dimensional map as shown by the high
quality of 91.1%, 73.6%, and 85.8%, 95.8%, 775% and 80.1% respectively.
The calendar year 2002 has the lowest quality of 4.2%. The computed mass of CY
2000, 2002, 2003, 2001, 2004 and 2005 are almost the same in their points, the
distances between those years are not far from each calendar years, so CY 2006
with 0.120 is near to the point of said other calendar years.
For the mass values, the highest contribution of 0.165 was from year 2000,
though mass areas quite close to the other mass values. The inertia values were
also similar, still with year 2000 as having the highest value of 0.008.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
33
Table 10.Summary figures of the Calendar Year points
CALENDAR
QUALITY MASS INERTIA
YEARS
2000 0.911 0.165 0.008
2001 0.736 0.144 0.003
2002 0.042 0.152 0.003
2003 0.858 0.144 0.005
2004 0.958 0.141 0.003
2005 0.775 0.134 0.005
2006 0.801 0.120 0.005
The contributions of the Calendar Years 2000-2006 in the dimensions of
this study are presented in Table 11. The values of the calendar years are
significant in dimension 1 and dimension 2 based on the points of the dimension.
Calendar Year 2000 in dimension 1 and 2004 in dimension 2 had the highest
relative values. The second dimension was defined by the Calendar Year 2003,
2005 and 2006 with comparatively high values. This meant that 2000 and 2004
were the important points to dimension 1 whereas 2004 was important to
dimension 2.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
34
Table 11.Contribution of Dimension to the Calendar Year Points
CALENDAR
DIM 1
DIM 2
YEARS
2000 0.479 0.000
2001 0.108 0.042
2002 0.004 0.007
2003 0.127 0.239
2004 0.167 0.90
2005 0.112 0.233
2006 0.003 0.389
The two dimensional coordinates of the Calendar Year points in Table 12,
showed that the three calendar years 2000, 2001 and 2002 were grouped as one
and the last four calendar years 2003, 2004, 2005 and 2006 belonged to another
group in dimension 1. In dimension 1 calendar year with positive values was
located at the right side of the vertical axis and calendar years with negative
values were located at the branch of the vertical axis. In the second dimension,
calendar years 2003 had the only positive value and the rest dimension points
were negative. Calendar years in dimension 2 with positive value were found
above the horizontal axis and calendar years with negative value are found below
the horizontal axis.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
35
Calendar years which are located closer to each other have similar
contributions on the number of births in the Region.
Table 12.Two Coordinates of the Calendar Years
CALENDAR
DIM 1
DIM 2
YEARS
2000 0.593 -0.003
2001 0.304 -0.167
2002 0.55 -0.066
2003 -0.327 0.402
2004 -0.379 -0.250
2005 -0.317 -0.411
2006 -0.056 -0.562
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
36
The plot on the number of births points and calendar year points illustrated
the overall view of both variables on the plot.
The two dimensional map consisted of the horizontal axis with dimension
1 and the vertical axis with dimension 2. The labels for number of births profiles
in the correspondence map were Abra, Apayao, Baguio, Benguet, Ifugao, Kalinga
and Mt. Province. The labels of the calendar year profiles were 2000, 2001, 2002,
2003, 2004, 2005 and 2006
Two dimensional plots representing row or column profiles may be
examined to identify whether any row or column categories have similar profiles.
Row or column categories that have similar profiles appeared in close proximity
on the plot. This could be useful to determine whether any row or column
categories could be continued in subsequent analysis. Another area of interest is
how row and column categories interact with one another in contributing to the
overall association. It also showed how the row and column contribute to the
overall size of the residual.
FIGURE 3 showed that the horizontal axis separating high frequency
provinces from low frequency. The other axis separated negative coordinates
from positive coordinates. A row and column points close together implied a high
frequency in that cell. Ifugao was closer to 2003, Benguet with 2005, Mt.
Province and Kalinga close to 2000, the implication is that a higher number of
births in Ifugao occurred in 2003, a higher number of births in Benguet occurred
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
37
in 2005; in Mt. Province and Kalinga a higher number of births occurred in 2000.
A point could make high contribution to the inertia (variance) of a principal axis
in two ways. When it had a large distance from the centroid, even if it has a small
mass, or when it has a large mass, but small distance from the average profile.
The province of Apayao made a high contribution to the inertia (variance) in
terms of number of births, since it has large distance from the average mean
(centroid) and had a small mass.
In addition, Baguio and Abra contributed a high inertia (variance), since it
had a large mass but large distance. Dimension 1 separated the two calendar years
from the three calendar years of the period and the year 2000 on the horizontal
axis. Benguet had a high frequency but contributed low variance situated at the
negative pole while Kalinga which contributed large variance and high frequency
is located at the positive pole. Benguet and Ifugao which were far from the
horizontal axis contributed largely to the inertia of Dimension 2.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
38
0.8
0.6
2006
Ifugao
0.4
2003
Apayao
baguio
0.2
Mt. province
Abra
0
2000
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
2002
Dimension 2
kalinga
-0.2
2001
2004
-0.4
2005
Benguet
-0.6
Dimension 1
Figure.3 Correspondence analysis biplot on the number of births and the calendar
years
2000-2006
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
39
SUMMARY, CONCLUSION AND RECOMMENDATIONS
Summary
Correspondence Analysis as a relatively new technique in exploratory
analysis was used on the number of births in the six provinces of CAR during the
calendar years 2000-2006. The technique was used for measuring the association
of number of births among provinces and calendar years, at the same time,
showing the location of this association. The correspondence solution
decomposed the chi-square of the data set that resulted to the extraction of
dimensions. Researchers found that the first two dimensions associated to the
principal inertia’s with 77.44 cumulative percent of inertia explained or
represented well the number of births and calendar years points in a two
dimensional space. The total inertia in the six dimension explained 3.11 percent of
the variance in the original correspondence table. This means that 77.44 percent
of the total inertia (variance) which is 3.11 percent in the original correspondence
table was explained in the first and second dimensions.
The computed singular value in the first dimension is 0.120989 indicating
weak relationship of the number of births and calendar year variables in
Dimension 1.The second Dimension reflected strong relationship of the number
of births and calendar year points as an interpretation for 0.097246 singular
values.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
40
Findings of the study are as follows:
1. Among the provinces of CAR, Baguio, Benguet, Kalinga, Ifugao and
Mt. Provinces contributed greatly to the distribution on the number of births as
reflected by the large masses of each. On the other hand, Apayao had the least
contribution. The calendar years showed contributions to the number of births.
The mass of each year had the same unit of mass and their distances from the cells
were almost equal.
2. In the population data set on the number of births in the six provinces of
CAR during the calendar years 2000-2006, 77.44% of the variance was explained
by the Dimension 1 and Dimension 2. In the two dimensional space, the highly
represented provinces were Benguet, Ifugao, Kalinga and Mt. Province. On the
other hand Apayao was the only province of CAR which was well represented by
the two dimensions in the Correspondence map. Moreover, the provinces of CAR
which were poorly represented by the dimension in the Correspondence map were
Abra and Baguio. As to year quality, calendar years 2000, 2001, 2003, 2004, 2005
and 2006 were well presented by the dimension in the two dimension map.
Calendar year 2002 was poorly represented by the dimensional map.
3. The cumulative inertia 77.44% of variance was explained by Dimension
1 and Dimension 2. Among the six provinces of CAR, Benguet, Kalinga and
Mountain Province contributed largely to the total inertia of the rest of the
provinces had low contributions.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
41
Conclusion
Based on the findings, the researcher arrived at the following conclusions:
1.Benguet, Kalinga and Mountain Province were the leading provinces as
to number of births Furthermore, Apayao and Abra had the lowest number of
births. On the other hand, the calendar years 2000, 2003, 2004 and 2006 recorded
the highest number of births. Since Benguet, Kalinga and Mountain. Province
obtained the largest masses; these provinces had a high birth growth. Likewise,
calendar year 2000, 2003, 2004 and 2006 had the large masses.
2. The provinces of CAR which were highly explained by the dimensions
were Benguet, Kalinga, and Mountain Province. The calendar year profiles, 2000,
2003, 2004, 2005, and 2006 were highly represented by the Dimension 1 and 2.
3. Using the correspondence map, Benguet was known for its large mass
contribution.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
42
Recommendations
The following recommendations are suggested in relation to the growing
number of births in the six provinces of CAR and the use of the Correspondence
Analysis method.
1. The government should be able to address the problem of high number
of births, especially to province which were seen as consistently growing in
population.
2. Correspondence Analysis may be used for researches on frequency data
with multiple categories and with wider scope of geographical area.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
43
LITERATURE CITED
BENZECRI, Correspondence Analysis Handbook, vol.125 of statistics;
Textbooks and Monographs, Marcel Dekker, New York, NY, USA, 1992.
E.J,BEH “Biometrical Journal, vol.4 Michael Greenacres, 2005” 883,
Department of Economics and Business, Universidad Poppeu Fabra,
revised” no.4, pp.413-429, 1998.
GREENACRE, MICHAEL J. (1984) Theory and Applications of Correspondence
Analysis. London: academic press.
GROENEN, P.J.F. and VAN DER HEIDEN, and P.G.M.1980. Analyzing
asymmetry two wave two-variable panel data with generalized
correspondence and log linear models. In E.Diday(ED), Data analysis,
learning symbolic and numeric knowledge. Pp 31-38.
JAMBU, MICHAEL. (1991).Exploratory and multivariate Data Analysis, Boston
Academic
Press.
LUDWIG, J AND J REYNOLDS.1998.Statistical Ecology: A primer on Methods
and Computing. Wiley, New York. Easy to follow outline procedures
involved in PCA and CA; working through the chapter on PCA helps to
understand
CA.
NEI, L.F. et al. 1998.Correspondence Analysis as Applied to 6x5 Contingency
Data. The Philippine Statistician.vol.21, Nos.4.Pp.67-75.
PIELOU, E.C.1984.Interpretation of ecological Data: A Primer on Classification
and Ordination. Wiley New York.
SEARLE, S.1982.Matri Algebra Useful for Statistics. Wiley, New York. If you
have time, the best, most accessible introduction to matrix algebra for
these
purposes.
VON POPPEL, F.POST.W.and GROENEN, P.J.F.1997.Age preferences of
Spouses, the Netherlands 1850-1993.An application of correspondence
analysis in population and family in the low countries.Pp 191-218.
GREENACRE, M 1984.Ratio Maps and Correspondence Analysis
http://www.Econ.upof.es/deehome/whatr/wpapers/pests cripts/598.pdf
http://search.yahoo.com/search;
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
44
APPENDIX A. Letter of Request
Benguet State University
College of Arts and Sciences
MATH-PHYSICS-STATISTICS DEPARTMENT
La Trinidad, Benguet
February
6,
2008
BENJAMIN Y. NAVARRO
Head, NSCB- CAR
2/F JA Apartment, # 39
Upper Engineers Hill, 2600 Baguio City
Sir:
Greetings!
We are undergraduate students of Benguet State University taking Bachelor of
Science in Applied Statistics. We are in the process of conducting our thesis
entitled “Correspondence Analysis on the number of births in the six provinces of
Cordillera Administrative Region during the years 2000-2006”.
In this connection may we be permitted to get the necessary data for our
study from good office. Rest assured that all data gathered will be held
confidential and it shall be used only to serve the purposes of our study.
Your favorable response on this request will be highly appreciated.
Respectfully yours,
(Sgd) Crisanta P. Apit
(Sgd)
Marifee
K.
Logro
(Sgd) Noemi S. Palubos
Noted:
DR. MARIA AZUCENA B. LUBRICA
Thesis Adviser
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
45
Benguet State University
College
of
Arts
and
Sciences
MATH-PHYSICS-STATISTICS
DEPATRMENT
La
Trinidad,
Benguet
February
6,
2008
Engr.OLIVIA GULLA
Head, NSO - Regional
Junifer Bldg. Bonifacio Street
2600 Baguio City
Madam:
Greetings!
We are undergraduate students of Benguet State University taking Bachelor of
Science in Applied Statistics. We are in the process of conducting our thesis
entitled “Correspondence Analysis on the number of births in the six provinces of
Cordillera Administrative Region during the years 2000-2006”.
In this connection may we be permitted to get the necessary data for our
study from good office. Rest assured that all data gathered will be held
confidential and it shall be used only to serve the purposes of our study.
Your favorable response on this request will be highly appreciated.
Respectfully yours,
(Sgd) Crisanta P. Apit
(Sgd) Marifee K. Logro
(Sgd)
Noemi
S.
Palubos
Noted:
DR.MARIA AZUCENA B. LUBRICA
Thesis Adviser
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
46
Appendix B. Number of Births Registered by Month and Provinces (2000-2006)
CY
2000
CAR
ABRA
CITY
NCE
APAYAO
BAGUIO
BENGUET
IFUGAO
KALINGA
MT.PROVI
TOTAL
54169 7382
2125 11708
16348
6625 13703
10111
JANUARY 6380
448
210
988
1592
584
1109
2647
FEBRAURY 4676 818
331
946
865
730 1361 902
MARCH 4784
756
227
822
1250
482
1361
935
APRIL 5088
376
180
879
1317
587
2075
733
MAY 3930
611
160
778
1347
511
748
713
JUNE 4972
725
115
922
1375
782
1319
771
JULY 4586
823
143
888
1423
569
1106
665
AUGUST 3946
549
141
854
1281
522
1070
524
SEPTEMBER
4323 618
210
945
1497
514 1088 606
OCTOBER 3744
516
178
980
1434
426 762
606
DECEMBER 3806 552
120
1146
1490
477 852 435
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
47
CE
AO
IO
O
GA
CAR
ABRA
MT.
CY 2001
APAY
BAGU
IFUGA
BENGUET
KALIN
PROVIN
TOTAL
49551 7027
2001
8015
7210 12176
6888 16250
JANUARY
3547 510
152
610
463
750
409 1415
FEBRAURY 3589 763
204
580
562
786
472 1006
MARCH
3946 424
115
637
504
1184
576 1258
APRIL
4146 461
117
650
695
1052
669 1269
MAY
3999 596
139
683
529
1008
493 1373
JUNE
4836 796
152
690
517
1419
615 1489
JULY
4423 762
175
540
645
1114
617 1285
AUGUST
4409 613
181
684
513
1241
715 1327
SEPTEMBER
4272 626
193
710
709
901
515 1461
OCTOBER
3876 621
194
674
755
787
353 1360
NOVEMBER 4652 603
178
715
774
1024
697 1554
DECEMBER 3856 252
201
850
544
910
697 1453
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
48
CE
AO
IO
O
GA
CAR
MT.
CY 2002
ABRA
APAY
BAGU
BENGUET
IFUGA
KALIN
PROVIN
TOTAL
50827 7244
4102
7922
7986 12295
6174
17128
JANUARY 3117
426
307
450
367
992
465 867
FEBRAURY 4676
830
319
582
529
1143
368
1894
MARCH 4043
582
486
650
614
1053
481
1313
APRIL 3855
437
696
669
508
1374
323
1213
MAY 4729
680
455
730
705
1360
323
1661
JUNE 4581
790
287
790
790
1119
413
1469
JULY 4421
643
292
835
750
1087
473
1468
AUGUST 4375
613
268
816
599
801
1088 1274
SEPTEMBER
4361 603
276
830
707
807
883
1361
OCTOBER 4375
665
244
590
655
963
435 1657
NOVEMBER 4302 393
267
420
1047
859
461
1542
DECEMBER 3904
582
205
530
715
737
461
1409
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
49
CE
AO
IO
O
GA
CAR
ABRA
MT,
CY 2003
APAY
BAGU
BENGUET
IFUGA
KALIN
PROVIN
TOTAL
59258 7214
3506
9334
10559
7485
5899
15221
JANUARY
5043
738
241
777
757
720
464
1346
FEBRUARY 4729 561
352
904
897
732
416
867
MARCH 5506
568
312
616
1308
747
466 1489
APRIL 4194
536
239
679
506
562
466
1206
MAY 4652
699
256
677
526
798
460
1236
JUNE 5221
666
320
922
721
702
573
1317
JULY 5351
539
311
778
941
670
630
1482
AUGUST 4568
501
283
654
679
510
530 1411
SEPTEMBER
4889 676
361
845
769
501
500
1237
OCTOBER 5289
639
257
910
1763
545
518
657
NOVEMBER 5130 585
330
825
843
553
438
1556
DECEMBER 4686 506
244
747
889
445
438
1417
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
50
CE
AO
IO
O
GA
CAR
ABRA
MT.
CY 2004
APAY
BAGU
BENGUET
IFUGA
KALIN
PROVIN
TOTAL
49813 7965
2784
8179
7508
7828 4676
8179
JANUARY
4686
778
247
758
839
524
445
758
FEBRUARY 4434
657
331
865
784
666 470
865
MARCH 5062
694
250
635
1138
793
451
635
APRIL 4152
683
192
542
717
646
366
542
MAY 4237
784
262
641
549
731
392
641
JUNE 4787
846
264
543
710
972
407
543
JULY 3553
595
203
520
516
373
363
520
AUGUST 3879
682
236
652
465
579
265
652
SEPTEMBER 3997 700
161
630
483
676 361
630
OCTOBER 4275
667
215
854
475
777
426
854
NOVEMBER 3432 549
202
753
434
619 385
753
DECEMBER 3319 330
221
786
398
472 345
786
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
51
CE
AO
IO
O
GA
CAR
ABRA
MT.
CY 2005
APAY
BAGU
BENGUET
IFUGA
KALIN
PROVIN
TOTAL
46013 6931
2529
9117
5580
7112
4787
19254
JANUARY 3574
575
221
789
430
472
457 1559
FEBRUARY 4348
670
221
720
459
725
436 1837
MARCH 4013
681
204
680
502
693
418
1515
APRIL 3715
350
195
630
486
675
364
1645
MAY 3863
594
269
759
396
492
415
1697
JUNE 3889
714
163
856
238
766
430
1578
JULY 4134
630
204
588
478
785
381
1656
AUGUST 3972
546
209
723
734
645
405 1433
SEPTEMBER
3681 535
225
840
489
490
343
1599
OCTOBER 3700
667
215
759
475
483
361 1539
NOVEMBER 3519
529
199
820
412
451
326
1602
DECEMBER 3605
440
204
953
481
435
451 1594
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
52
CAR
ABRA
MT.
CY 2006
APAYAO
BAGUIO
BENGUET
IFUGAO
KALINGA
PROVINCE
TOTAL
44343 7246
2843
9672
7094
6949
5370 10242
JANUARY 4335
885
219
885
494
603
385 864
FEBRUARY 3720
740
279
680
379
483
407 752
MARCH 4353
980
344
758
507
497
382
885
APRIL 3344
577
194
610
402
459
323
779
MAY 4456
809
271
769
587
588
450
982
JUNE 4680
809
272
985
514
668
479
953
JULY 3763
466
199
669
756
554
412
707
AUGUST 4005
521
180
820
746
454
491
793
SEPTEMBER
4151 542
193
850
689
459
614 804
OCTOBER 4615
542
255
835
943
729
515 871
NOVEMBER 2921 467
230
954
596
680
495 876
DECEMBER 3621 450
207
857
481
775
417 976
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
53
Appendix C. Inertia and Chi-square Decomposition
Singular
Principal
chi-square
Percent of
Value Inertia
Inertia
0.120989 0.014638 6036.75 47.04
0.097246 0.094567 3899.91 30.39
0.069929 0.00489 2016.64 15.72
0.377229 0.001423 586.85 4.57
0.025947 0.000673 277.64 2.16
0.005885 3.46E-05 14.28
0.11
12832.07 100
Row Coordinates
CAR Provinces Dim 1 Dim2
Abra -0.177 0.091
Apayao -0.448 0.340
Baguio 0.026 0.240
Benguet -0.245 -0.427
Ifugao -0.306 0.453
Kalinga 0.538 - 0.132
Mt.Province 0.543 0.154
Column
Coordinates
Calendar Years Dim 1 Dim 2
2000 0.593 -0.003
2001 0.304 -0.167
2002 0.55 -0.066
2003 -0.327 0.402
2004 -0.379 -0.250
2005 -0.317 -0.411
2006 -0.056 -0.562
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
54
Appendix D. STATA OUTPUT
CA PROVINCE YEAR [fweight = FREQUENCY]
Correspondence analysis Number of obs= 412387
Pearson chi2 (36) = 12827.59 Number of dim. = 2
Expl. Inertia (%)=77.43
Prob > chi2 = 0.0000
Total inertia = 0.0311
7 active rows
7 active columns
Singular principal cumul
Dimensions values inertia chi2 percent percent
Dim 1 .1209764 .0146353 6035.40 47.05 47.05
Dim 2 .0972101 .0094498 3896.98 30.38 77.43
Dim 3 . 0699272 .0048898 2016.49 15.72 93.15
Dim 4 .0377264 .0014233 586.94 4.58 97.73
Dim 5 .0259401 .0006729 277.49 2.16 99.89
Dim 6 .0058858 .0000346 14.29 0.11 100.00
Total .0311057 12827.59 100
Statistics for row and column categories in symmetric normalization.
Overall dimension_1
Categories mass quality inertia coord sqcorr contrib.
PROVINCE
1 0.124 0.492 0.001 -0.178 0.407 0.032
2 0.048 0.546 0.003 -0.448 0.374 0.080
3 0.155 0.286 0.003 0.026 0.004 0.001
4 0.275 0.988 0.007 -0.245 0.286 0.136
5 0.128 0.771 0.005 -0.306 0.280 0.099
6 0.164 0.838 0.007 0.538 0.800 0.393
7 0.106 0.914 0.004 0.543 0.858 0.259
YEAR
1 0.165 0.911 0.008 0.593 0.911 0.479
2 0.144 0.736 0.003 0.302 0.590 0.109
3 0.152 0.042 0.003 0.054 0.019 0.004
4 0.144 0.858 0.005 -0.328 0.389 0.128
5 0.141 0.958 0.003 -0.379 0.710 0.167
6 0.134 0.774 0.005 -0.317 0.329 0.111
7 0.120 0.801 0.005 -0.056 0.010 0.003
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
55
dimension_2
Categories coord sqcorr contrib.
PROVINCE
1 0.091 0.085 0.010
2 0.339 0.172 0.057
3 0.240 0.282 0.092
4 -0.427 0.701 0.516
5 0.453 0.491 0.269
6 -0.131 0.038 0.029
7 0.154 0.056 0.026
YEAR
1 -0.003 0.000 0.000
2 -0.167 0.146 0.042
3 -0.067 0.023 0.007
4 0.402 0.469 0.238
5 -0.250 0.248 0.091
6 -0.411 0.445 0.233
7 0.562 0.791 0.389
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
56
Appendix E. Plot of Correspondence Solution
.6
7
5
.4
4
2
3
.2
PROVINCE
7
1
0
1
3
6
2
-.2
5
-.4
6 4
-.6
-.6
-.4
-.2
0
.2
.4
.6
YEAR
o PROVINCE
YEAR
coordinates in symmetric normalization
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
57
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
CRISANTA P. APIT, MARIFEE K.LOGRO, NOEMI S. PALUBOS. April 2008.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006.Benguet State University, La Trinidad
Benguet.
Adviser: Maria Azucena B. Lubrica, Ph.D
ABSTRACT
Correspondence Analysis is a multivariate method for exploring cross-tabular
data by converting such tables into graphical displays, called maps,” and related
numerical statistics. It is a tool commonly used in many disciplines to identify and
visualize the association between two categorical variables.
The technique was applied to the contingency table on the number of births in the
six provinces of the Cordillera Administrative Region during the Calendar years 2000-
2006. The row variable consists of the six provinces of Cordillera Administrative Region
namely: Abra, Apayao, Benguet, Kalinga, Mt. Province, Ifugao and in the City of
Baguio. The column variable consists of the calendar year categories, namely: 2000,
2001, 2002, 2003, 2004, 2005 and 2006.
Correspondence Analysis was used to analyze the 7x7 ( 7 rows by 7 columns)
contingency table on the number of births in the six provinces of CAR during the years
2000-2006. It also intended to determine the weights (masses), quality and variance
(inertia) of the six provinces and Baguio City, and calendar year points.
Results of inertia and chi-square decomposition explained 77.44 cumulative
percent of variance in the first two dimensions. The root of the total inertia 0.0311154
equals 0.1764 as the eigen value. This suggested that the first two dimensions appear to
be satisfactory in representing the CAR provinces and calendar year profiles.
The Cordillera Administrative Region which was highly explained in the graph
were Benguet and Mt. Province. The rest of the provinces were quite well represented by
the dimensions, except Baguio which was poorly explained. The calendar year profile
points were well represented, except the calendar year 2002 in the two-dimensional map.
However, only the CY 2000 and 2004 were highly explained.
In the two-dimensional map, dimension 1 was defined by three provinces of CAR,
namely: Benguet, Kalinga, and Mt. Province and the CY 2003, 2005 and 2006 defined
the second dimension.
The categories with large mass meant high frequency and low mass implied low
frequency with respect to the entire data set. A dimension with high contribution to point
indicates that the dimension represents well the point in the dimensional map while the
low contribution of a dimension to point shows that the dimension explains poorly the
point in the map.
ii
TABLE OF CONTENTS
Page
Bibliography…………………………………………………………………….....i
Abstract……………………………………………………………………………i
Table of Contents………………………………………….……………………..iii
INTRODUCTION
Background of the Study………………………………………………….1
Objective of the Study…………………………………………………….3
Importance of the Study…………………………………………………...3
Scope and Delimitation……………………………………………............4
REVIEW OF RELATED LITERATURE
Correspondence
Analysis………………………………………………….5
Definition of Terms………………………………………………………..8
THEORETICAL FRAMEWORK……………………………..………………...11
METHODOLOGY
Location of the Study…………………………………………………….16
Data Gathering Procedure………………………………………………..17
Data Analysis…………………………………………………………………….18
RESULTS AND DISCUSSION
Contingency Table and Correspondence Matrix………………………………...19
Quality, Mass and Inertia of CAR Provinces……………………………………27
Row Coordinates.................…………………………….….……………………29
Quality, Mass and Inertia of the Calendar Year Points….………………………30
iii
Correspondence Map …………………………....................................................37
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
Summary…………………………………………………………………38
Conclusions………………………………………………………………39
Recommendations…………………………………………………..........41
LITERATURE CITED…………………………………...…………………..….43
APPENDICES
A. Letter of request to the National Statistics Office……………………44
Letter of request to the National Statistics Coordination Board ….... .45
B. Number of Registered births by month and Provinces……………….46
C. Inertia and Chi-square Output………………………………...………52
D.
STATA
Output…………………………………………………….….54
E. Plot of Correspondence Solution………………………………..….…56
iv
1
INTRODUCTION
Background of the Study
Cordillera Administrative Region (CAR) is at the central part of northern
Luzon. This Region is a land-locked region, consisting of six provinces: Abra,
Apayao, Benguet, Ifugao, Kalinga, Mountain Province, and Baguio City, a first
class, highly urbanized city, which is the regional center. Cordillera encompasses
most of the areas within the Cordillera Central mountain ranges of Luzon, the
largest ranges in the country. This Region is home to numerous indigenous tribes
collectively called Igorots.
CAR is more heavily populated compared to other mountainous areas of
the Philippines. Based on the 2000 census, its six provinces and one city have a
total population of 1,365,220 people. With a land area of 18,294 square
kilometers, the population density is 75 per square kilometer.
Among the six provinces of CAR, Benguet ranked first in terms of
population size with 1,365,220 people in the 2000 census, its population density is
275 people per square kilometer. This province contributed 24.2% of the
population in the region, and 0.43% to the Philippine population of 76.5 million.
From 1995 to 2000, its annual growth rate is 1.0990, which is much lower than
the national average of 2.43%. The average household is 5.2 persons, a little
higher than the national average of 4.99. Benguet, with La Trinidad as its capital,
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
2
it is often called the Salad Bowl of the Philippines, It has agriculture, mining and
tourism as major industries..
Abra has a rugged terrain, with mountains and hills rising along its
perimeter and interior. This basin-like province is drained by the Abra River. Its
population of 20,491 is the 12th smallest in the country with a density of 53 people
per square kilometer. Abra’s economy is agriculture. With its capital in Bangued.
Ifugao with Lagawe as its capital is also a landlocked mountainous region
characterized by rugged terrain, river valleys, and massive forests. Its population
of 161,623 is the 9th smallest in the country, with a density of 64 people per
square kilometer. The 2000 year old Banaue Rice Terraces is the main tourist
attraction of the province.
Kalinga is rugged and sloping with mountain peaks. Its population of
174,023 is the 11th smallest and its density of 56 people per square kilometer is
the 6th lowest. The people of Kalinga are the most extensive rice farmers among
the Cordillerans. Founded in 1995, its capital is Tabuk City.
Apayao become a province when it was separated from Kalinga in 1995.
Kabugao became its capital. Its population is 97,129, which is the 4th smallest
and it has the lowest density of 25 people per square kilometer.
Mountain Province was named as such because it is found in the
Cordillera mountain range. Prior to 1966, Mountain Province included Benguet,
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
3
Kalinga-Apayao and Ifugao. Its population of 140,349 is the 6th smallest and its
density of 67 people per square kilometer is the 10th lowest.
Objectives of the Study
The general objective of the study is to apply correspondence analysis to
the number of births in the six provinces of CAR, including Baguio City, during
the calendar years 2000-2006.Specifically, the study aimed to determine the
association of the six provinces and calendar years on the number of births in the
correspondence map.
Importance of the Study
The findings of the study would provide a comprehensive understanding on the
distribution of the number of births when taking into consideration the six
provinces of CAR including Baguio City and the seven calendar year period.
This study would also be a way of presenting graphically these CAR
provinces in relation to the distribution on the number of births. Such information
would be useful in the fiscal management of the Region since appropriate
budgetary allocation could be given based on the groupings illustrated in the
correspondence map.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
4
Scope and Delimitation of the Study
The data used were on the six provinces of CAR including Baguio City
during calendar years 2000-2006. The data were taken from the National Statistics
Coordination Board.
Significance testing is not supported in the analysis, so model comparison
and selection of a best fit model were performed. The reason that Correspondence
Analysis is an exploratory, not a confirmatory technique. Visualization of
agreement or association of the provinces and calendar years on the number of
births were included.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
5
REVIEW OF RELATED LITERATURE
Correspondence Analysis
Correspondence Analysis has been proven to be one of the successful
techniques for graphical analysis of contingency data. It is considered to be a
popular technique especially in France, United Kingdom and in the united States
of America. Its growing popularity among statistical practitioners demonstrates
the importance of applying correspondence analysis as a research tool.
Correspondence analysis has become a popular method in the social and
environmental sciences. The Analysis incorporates steps in translating a table to a
graphical display. First, it transforms the rows of the table into profiles, which is
the rows divided by their row totals. Second, weights are assigned to the row
profiles proportional to the marginal row totals of the contingency tables. Third, a
standardization of the profiles elements is performed by dividing them by values
proportional to the square root of the marginal column totals of the contingency
totals. The third step implies a special distance function between the profiles,
called the chi-squared distance. Finally, a weighted principal component analysis
is performed on the row profiles, identifying the plane, which best fits the row
profiles by minimizing the weighted the sum of squared (chi-squared) distances
from the points to the plane. Then the profile points are projected unto this plane
and their relative positions are interpreted. An identical and completely symmetric
analysis can be performed on the column profiles. The two analysis are equivalent
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
6
and their solutions are based on the singular value decomposition of the same
matrix (Greenacre, 1984).
Micheloud (1997) analyzed a table which reflected 169,836 people aged
15 or more, living in the Lausanne district of Geneva in Switzerland. Attributes
considered were maximum level of schooling attained (variable I, in rows) and
community of residence (variable J, in the column). The aim of this analysis was
to find out if there was an attraction, independence, or even repulsion between
rows and columns.
Huixin and Hao (1996) used the Correspondence Analysis in marketing
research, conducted in Zhenzou City in China. The main purpose of the project
was to estimate the market, but a new name recommended by the consulting
company for a newly developed pure water product was also tested. The tables
which were analyzed consisted of the product names marked against the product,
and names marked against the feeling of respondents.
Correspondence Analysis seeks to represent the interrelationships of row
and column variables on a two dimensional map. It can be thought of as trying to
plot a cloud of data points (the cloud having height, width and thickness) on a
single plane to give a reasonable summary of the relationships and variation
within them.
One of the study was a research of lifestyle and culture consumption in a
United Kingdom City (Featherstone et al, 1994). One aspect of the study looks at
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
7
the leisure activities of people living in the new inner city development. Included
in the questionnaire were the questions about the use of local facilities, from pubs
to art galleries, knowledge of and preferences in music and involvement in
political issues.
The study of Bourdieu (1979) used Correspondence Analysis to provide
detailed illustrations for his thesis which include determinant case, cultural
discrimination and choice. Choice is described as the possession of two forms of
capital, economic and cultural, with sub-groupings defined by seniority in
possession and related mode of acquisition. This technique among English and
American sociologists seems to have remained low until the publication of
Greenacre text (1984) testifying to the easier availability of appropriate computer
software (CA).This correspondence technique is versatile, it can be used with
frequency data, with percentages, and with data in the formats of ratings with
heterogeneous data sets.
The study of Neri, Solivas, and VJ.Albacea focuses on the application of
Correspondence analysis to a particular 6 x 5 contingency table. The population
of the study is the cross tabulation of graduates from the College of Arts and
Sciences, University of the Philippine Los Banos during the ten years period of
1987-1996 classified into degree program and year graduated.
This study deals with the matrices and its components as a given by the
singular value decomposition (SVD); the pre-decomposition method prior to
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
8
correspondence analysis and the post-decomposition method which out the row
and column coordinates.
The Cordillera Administrative Region is more heavily populated
compared to the other mountainous areas of the Philippines. In the year 2000
census, its provinces and one city had a total population of more than 356,272
while 792,922 lived in the rural areas
The distribution of the number of births naturally affects the rate of
population growth. Birth statistics were obtained from the Certificates of Live
Birth, which were transmitted by the City/Municipal Civil Registrar to the office
of the Civil Registrar General for machine processing and archiving. The total
number of Live Births reported in 2000 was 1,766,440. This was an 8.3 percent
increase in ten years. The Daily Average of Birth occurrence was 4,826. This
means an addition of three babies to the population every minute. In the country,
approximately 23 live births per 1000 population had occurred in 2000. CAR has
a similar birth rate.
Definition of Terms
Category
masses are the marginal proportions of a discrete variable. In the
terminology of correspondence analysis, the relative frequencies of the
row
totals and column totals are called the row mass and column mass, respectively.
Centroid or average profile is the weighted mean of the row and column
profiles. It is the origin of the correspondence map.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
9
Contingency
table is a two-way table of categorical data or the row cross
tabulation of the discrete variables with marginals. The variables must be discrete
nominal, ordinal, or continuous variables segmented into ranges. The object of
the correspondence analysis is to explain the inertia (variable) in the table.
Contribution of the dimensions to point is also known as squared
correlations on quality of representation of the description of a point. These
reflect how well the principal components model is explaining any given.
Correspondence
map displays two of the dimensions which emerge from
the principal components analysis of inertia, and points are displayed in relation
to these dimensions.
Correspondence matrix P is defined as the original table X divided by the
grand total.
Eigenvalues are the characteristics roots of the principal components
solution. There is one eigenvalue for each dimension, sometimes labeled as inertia
for that dimension.
Inertia means variance in the context of correspondence analysis.
Point distance refers to the chi-square distance rather than the Euclidean between
points.
Profile
point is one of the values (categories) of one of the discrete
variables in the analysis.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
10
Proportions if inertia accounted for by a given dimension are its
eigenvalue divided by total inertia.
Quality of a point is defined as the ratio of the squared distance from the
origin in the chosen number of dimensions, over the squared distance from the
origin the space defined by the maximum number of dimension.
Relative
inertia represents the proportion of the total inertia accounted for
by the respective point.
Row and Column profiles are the relative frequencies of the row or
column discrete variable. Profile elements are the entries in each row or column
profile.
Scores in dimensions are the scores used as coordinates for point when
plotting the correspondence map.
Singular
value is the square root of an eigenvalue.
Total
inertia is the sum of eigenvalues and the spread of points around the
centroid. Total inertia may be interpreted as the percent of inertia (variance) in the
original correspondence table explained by all computed dimensions in the
correspondence analysis. It also defined as the total Pearson chi-square for two-
way divided by the total sum.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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METHODOLOGY
Location of the Study
The study was conducted at Benguet State University including the six
Provinces of CAR and Baguio City during the calendar years 2000-2006.Figure 1
shows the location of the study namely: Abra, Apayao, Benguet, Ifugao, Kalinga,
Mt.Province and Baguio City.
.
Figure 1.Location of the Study
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Data Gathering Procedure
The data were taken from Regional Social Economic Trend 2006 0f
NSCB and Population Census 2000-2004 of NSO.
The data set which was used on this study consisted of number of births on
the six provinces of CAR and Baguio City during the calendar years 2000-2006.
The distribution on the number of births by provinces and calendar years reflect a
two-way contingency table.
Table1. Contingency table on the number of Births during the calendar years
2000-2006.
PROVINCES
CALENDAR YEARS
OF CAR
2000
2001
2002
2003
2004
2005
2006
Abra
7382
7027
7244
7214
7965
6931
7246
Apayao
2125
2001
4102
3506
2784
2529
2843
Baguio
11708 8015
7922
9334
8179
9117
9672
Benguet
16348 16250
17128
15221 19052 19245 10242
Ifugao
6625
7210
7986
10599 7508
5580
7094
Kalinga
13703 12176
12295
7485
7828
7112
6949
Mt.Province
10111 6888
6174
5899
4676
4787
5870
Source: RSET-NSCB (Regional Social Economic Trend 2006) and Population
Census-NSO (2000-2004).
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Data Analysis
Correspondence analysis was used to analyze the tabulated 7x7 (7 rows by
7 columns) matrix contingency on the number of births in the six provinces of
CAR during the CY 2000-2006.Correspondence analysis finds a low-dimensional
graphical representation of the association of rows and columns of the
contingency table, where categories of rows and column from the cell frequencies
are depicted as points in a median Eucledian space. These determined so that
squared distance between certain points in the derived space bear simple
relationships to the original tabular entries.
Correspondence analysis consist of three parts; a pre-decomposition
method where the original data or contingency table is transformed by certain
conversion procedures; second, the transformed data is subjected to singular value
decomposition where a set of row or column vectors together with its associated
singular values are summarized; and third, a post decomposition method is
applied where in the row and column vectors are used to come up with the row
and column coordinates or scores.
The data were summarized, tabulated, analyzed and interpreted using
Correspondence Analysis. Computations of summary statistics were facilitated
with the use of the software STATA.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
19
INPUT
Contingency table of the number of births in the six Provinces of CAR including
Baguio City during the calendar years 2000-2006.
DATA ANALYSIS
Part I: Pre decomposition
1. Construct the correspondence matrix of the contingency table compute
the relative frequencies of each entry.
Part II: Singular Value decomposition
1. Calculate the row profiles, row masses and average row profiles.
2. Compute the column profiles, column masses and average column
profiles.
Part III: Post decomposition
1. Compute the inertia, quality and contribution of dimension to points.
2. Reduce dimensionality – look for a low dimensional space which is as
close as possible to high dimensional true space.
OUTPUT
1. Tables of numerical results – mass, inertia, quality, principal inertias, eigen
values, singular values, chi-squares, chi-square percents, and partial contribution to
inertia of row and column points.
2. Correspondence map – two - dimensional map.
INTERPRETATION
Interpret numerical results and the two-dimensional map
Figure 2. Flowchart of the mathematics of correspondence analysis
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
20
RESULTS AND DISCUSSION
This section presents the discussion, analysis and interpretation of the
findings drawn from the correspondence analysis on the number of births in the
six provinces of CAR in the calendar years 2000-2006.
Contingency Table and Correspondence Matrix
The summary on the number of births and calendar year total with
reference to Table 1 as the contingency was presented in Table 2. The results in
Table 2 indicated that the provinces of Benguet, Kalinga, Baguio and Abra have a
relatively large number of births distribution from 2000 to 2006. Among the six
provinces, Benguet ranked first in terms of population size. This province
contributed 24.4% to the 1.4 million populations in the region. Second in rank for
the largest in number of births is the province of Kalinga.
The province of Benguet which had the largest number of births has
thirteen municipalities contributing 10 % each. On the other hand, Kalinga’s large
number of births may be due to the richness of its capital, Tabuk City.
. Provinces of CAR with low number of birth population are Abra, Mt.
Province and Apayao. Therefore, the possible reasons for the low population
status maybe its land shape and land areas.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
21
Table 2 represents the distribution of births in each province. Calendar
year 2000 had the highest number of births and generally, a download trend was
observed the succeeding years, except in 2002.
Table2. Number of Births Distribution in the Six Provinces of CAR and CY 2000-
2006.
CALENDAR YEARS
PROVINCES
2000 2001 2002 2003 2004 2005 2006 Total
OF CAR
Abra
7382 7027 7244 7214 7965 6931 7246 51009
Apayao
2125 2001 4102 3506 2784 2529 2843 19890
Baguio
11708 8015 7922 9334 8179 9117 9672 63947
Benguet
16348 16250 17128 15221 19052 19245 10242 113486
Ifugao
6625 7210 7986 10599 7508 5580 7094 52602
Kalinga
13703 12176 12295 7485 7828 7112 6949 67548
Mt.Province 10111 6888 6174 5899 4676 4787 5870 43905
Total
6800 5956 6285 5925 5799 5530 4941 41238
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
22
Table 3 is the correspondence matrix comprising the relative frequencies.
The sum of the table entries in the correspondence matrix equaled to one. This
showed how unit of mass were distributed across the cells. The row and column
totals of the matrix of relative frequencies were the row and column mass
respectively. These showed that in the provinces of CAR, the population during
the year 2005 had Benguet with the highest relative frequency of 0.047. This is
closely followed by Kalinga with 0.018 relative frequency. On the other hand
Apayao had the lowest relative frequency of 0.00613.
A similar trend was discerned in the succeeding years, where Benguet was
consistently highest in the relative frequencies of the number of births while
Apayao was the lowest in the relative frequencies.
Table 3. Correspondence Matrix
PROVINCES
CALENDAR YEARS
OF CAR
2000 2001 2002 2003 2004 2005 2006
Abra
0.0179 0.017 0.0175 0.0175 0.019 0.017 0.0176
Apayao 5.153-03 4.852-03 9.947-03 8.502-03 6.751-03 6.132-03 6.893-3
Baguio
0.028 0.019 0.019 0.023 0.02 0.022 0.023
Benguet 0.04 0.039 0.042 0.037 0.046 0.047 0.025
Ifugao
0.016 0.018 0.019 0.026 0.018 0.014 0.017
Kalinga 0.033 0.03 0.03 0.018 0.019 0.018 0.017
Mt.Prov. 0.025 0.017 0.015 0.014 0.011 0.011 0.013
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
23
The study of Bendixen (1996) stated that examination of the row and
column profiles allows the researcher to examine the relative position of the rows
and columns to each other and thus establish distinguishing characteristics. The
row and column profiles of the contingency table are presented in Tables 4 and 5.
The last row of the row profiles and last column of the column profiles are labeled
average.
These are the proportions of the number of births in the row and column.
These values are used as averages and weights (masses) in the calculations of the
weighted distances.
As reflected in Table 4, year 2000 had the highest number of births with
1.1377, followed by year 2002 with an average of 1.1014, then year 2003 with an
average of 1.0445 number of births, year 2001 with the average of 0.9927 number
of births, followed by the year 2004 with 0.9511 number of births average, year
2005 with 0.8956 average and finally year 2006 with the least average of 0.8865.
The higher the average relative to others, the higher number of births for that
particular year.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Table 4.Row profiles
PROVINCES CALENDAR YEARS
MARGINAL
OF CAR
2000
2001
2002
2003
2004
2005
2006 TOTAL
Abra 0.145
0.1378
0.142 0.1414
0.1561 0.1359
0.142 1
Apayao 0.107
0.1006
0.206 0.1763
0.134 0.1271
0.0143
1
Baguio
0.183 0.1253 0.124
0.146
0.128 0.1426 0.1513
1
Benguet 0.144
0.1432
0.151 0.1341
0.1679 0.1696 0.0902
1
Ifugao 0.126
0.126
0.152 0.2015
0.1427 0.1061
0.1349 1
Kalinga 0.203
0.2029
0.186 0.1108
0.1159 0.1053
0.1029
1
Mt.Province 0.23 0.1569 0.141 0.1344 0.1065
0.109 0.1223
1
Average
1.1377 0.9927 1.1014 1.0445 0.9511 0.8956 0.8865
In Table 5, the province with the highest average is Benguet with 1.93.
However, the province with lowest column average is Apayao ranging with 0.34,
as compared to Kalinga with a slight average of 1.132, Baguio City follows
1.0918, then with Ifugao with 0.8984, Abra with 0.8728 and Mt.Province with
0.7378. As with row profiles, the higher the average relative to others, the higher
the number of births in the particular province.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
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Table 5.Column Profiles
PROVINCES
CALENDAR YEARS
AVE
OF CAR
2000 2001 2002 2003 2004 2005 2006
RAGE
Abra
0.107 0.118 0.115 0.122 0.137 0.125 0.147
0.873
Apayao
0.031 0.034 0.065 0.059 0.049 0.045 0.058 0.34
Baguio
0.172 0.135 0.126 0.158 0.14 0.165 0.196 1.092
Benguet
0.24 0.273 0.273 0.257 0.329 0.348 0.208 1.93
Ifugao
0.096 0.121 0.127 0.179 0.13 0.101 0.144 0.899
Kalinga
0.202 0.204 0.196 0.126 0.135 0.129 0.141 1.132
Mt.Province 0.149 0.116 0.098 0.099 0.081 0.087 0.109 0.74
Marginal
Total
1
1
1
1
1
1
1
Table 6 shows the decomposed chi-square total inertia which is
0.0311165. It was derived by dividing the chi-square 12,832.07, by the number of
births grand total of 412,387. In decomposing the chi-square, the extracted
dimensions of the data set with a maximum value equal to the product of the
number of rows (row-1), the number of columns (column-1) that is (7rows) x (7
columns 1) equals to 36. Correspondence Analysis allows the optimal
representation of a contingency table in two dimensional space. In table 6, the
result of the reduction of dimensions yielded six dimensions. The greatest inertia
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
26
is attributed to the first dimension with a principal inertia of 0.0146382, followed
by the second dimension with a principal dimension of 0.0094567, and decreasing
sequentially in the succeeding dimensions. This shows that the first dimension of
the principal inertia is greater than the second dimension.
Table 6. Inertia and Chi-square Decomposition of the Data Set
NUMBER
PERCENT
OF
SINGULAR PRINCIPAL CHI-
OF
CUMULATIVE
DIMENSION VALUE
INERTIA
SQUARE
INERTIA
PERCENT
1 0.12099
0.014638
6036.75
47.05
47.04
2 0.09725
0.094567
3899.91
30.39
77.44
3 0.06993
0.00489
2016.64
15.72
93.15
4 0.37723
0.001423
586.85
4.57
97.73
5 0.02595
0.000673
277.64
2.16
99.89
6 0.00589
0.0000346
14.28
0.11
100
0.0311165 12832.07 100
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
27
A singular value is interpreted as the maximum canonical correlation
between the categories of the variables for any given dimensions. The first
dimension reflects a singular value equivalent of 0.1209886 while the
corresponding value for the second dimension is 0.0972457. This implies that the
provinces of CAR and calendar years are strongly associated in the second
dimension but weakly correlated in the first axis. Principal inertia reflects the
relative importance of the dimension. Each principal inertia is the amount of
variance that a given and dimension explains the contingency table. The total
inertia which is 0.0311159 was explained lately and 30.39 percent of inertia in the
second dimension.
Garson (2005) mentioned two criteria on how to stop interrupting
dimensions. The first is the Kaiser criterion, which indicated that the rate of the
total values of the principal inertia or eigenvalues must be less than 1. The second
criterion is that variance explained should only have cumulative percent between
80 to 90 percent.
In relation to the research study of Neri et al (1998) on the application of
correspondence analysis to a particular 7x7 contingency table of the number of
births in the six provinces of CAR and calendar year 2000-2006, 88 percent of the
total inertia was explained by the first and second dimensions.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
28
Ocden (2006) also used two dimensions with .1853 as the eigenvalue and
84.53 cumulative percent, in representing the degree programs and school year
profiles.
Quality, Mass and Inertia of CAR Province
Correspondence Analysis has been successful in representing the
contingency table in tow dimensional space. The overall retention of 77.44
percent was done in the two dimensions. However, not all of the provinces of
CAR and CY 2000-2006 were equally represented. Bendixen (1996) in his study
mentioned that the quality of representation of a particular row or column
provides additional richness to the interpretation of the relationships in the
contingency table. The quality of representation of the description of a point
reflects how well the principal components model is explaining the point.
Table 7 presents that the provinces of Benguet, Mt. Province, Kalinga, and
Ifugao had a quality of 98.8 %, 91.4 %, 83.8 % and 77.1 % respectively, and were
well represented by the two dimensions. On the other hand, provinces of Apayao,
Abra, and Baguio with a quality of 54.7%, 49.2% and 28.6% respectively were
poorly represented in the two dimensions. This implies that these three provinces
were not yet heavily populated or that they have a low number of births.
The contributions for the mass, the provinces of Benguet, Baguio and
Kalinga, with respective masses of 0.275, 0.164 and 0.155, have the highest
values for masses. This can be interpreted that the Benguet and Kalinga province
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
29
have a large frequency on the number of births. However, Baguio has high
contribution in its mass, but its quality of 28.6% shows poor representation. Large
mass of a row point means relatively high frequency for that province whereas the
relatively small mass implies low frequency for the other provinces. The sequence
consisted of Mt. Province with 0.106, Abra 0.124 and Apayao 0.048
Over the years 2000-2006, Apayao province remains to have low
population in terms of number of births because of its small land area.
The contribution of points to dimensions as reflected by the column inertia in
Table 7 is used to intuit the meaning of correspondence dimensions.
It was observed that the six provinces have contributed small variance since less
than 0.1 of inertia (variance) accounted for each point.
Table 7.Summary figures of CAR Provinces and Calendar years profiles
CAR PROVINCES
QUALITY
MASS
INERTIA
Abra
0.492
0.124
0.001
Apayao
0.547
0.048
0.003
Baguio City
0.286
0.155
0.003
Benguet
0.988
0.275
0.007
Ifugao
0.771
0.128
0.005
Kalinga
0.838
0.164
0.007
Mt.Province
0.914
0.106
0.004
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
30
In Table 8, the contribution of dimension to the six provinces of CAR is
presented. The value obtained in each cell is the percent of variance in provinces
profiles explained by the given dimensions, the province of Mt. Province, Kalinga
and Benguet defined the first dimension for having high contribution of
dimension 1 to points. The provinces of CAR which are important in the second
dimension are those which got a high relative value on the contribution to the
dimensions.
Table 8.Contribution of Dimensions to the six Provinces of CAR
Provinces of CAR
DIM 1
DIM 2
Abra 0.032
0.011
Apayao 0.080 0.057
Baguio City
0.001
0.092
Benguet 0.137 0.516
Ifugao 0.099 0.270
Kalinga 0.393 0.029
Mt.Province 0.259
0.026
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
31
In dimension 2, it was indicated that the provinces of Ifugao and Benguet
had the largest contribution. Because of some expectation that if the point of one
province are higher, we do believe that from any contribution, it will always be
the largest in contributing to dimensions implying a high squared correlation.
However, the reverse is not true. That is, if a point explains a lot variance in a
dimension, usually that dimension will describe the point very well (high squared
correlation).
Row Coordinates
Table 9 presents the row coordinates, which determines the position of
points when plotted in the two dimensional space. The positive and negative
coordinates in dimension 1 of the Province of CAR are to found at the right
branch and left branch, respectively, of the horizontal axis. In like manner,
positive and negative coordinates in dimension 2 are located upward and
downward, respectively, of the vertical axis.
The first dimension group was composed of Baguio, Kalinga and
Mt.Province as one while Abra, Apayao, Benguet and Ifugao were dimensions 2
have Benguet and Kalinga separated from Abra, Apayao, Baguio, Ifugao and
Mt.Province.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
32
Table 9.Two dimensional coordinates of the Provinces of CAR
PROVINCES
DIM 1
DIM2
OF CAR
Abra -0.177
0.091
Apayao -0.448 0.34
Baguio City
0.026
0.24
Benguet -0.245
-0.427
Ifugao -0.306
0.453
Kalinga 0.538
-0.132
Mt.Province 0.543
0.154
Quality, Mass and Inertia of the Calendar Year Points
With reference to Table 10, Calendar Years 2000, 2003, 2004, 2005 and
2006 were well represented by the two-dimensional map as shown by the high
quality of 91.1%, 73.6%, and 85.8%, 95.8%, 775% and 80.1% respectively.
The calendar year 2002 has the lowest quality of 4.2%. The computed mass of CY
2000, 2002, 2003, 2001, 2004 and 2005 are almost the same in their points, the
distances between those years are not far from each calendar years, so CY 2006
with 0.120 is near to the point of said other calendar years.
For the mass values, the highest contribution of 0.165 was from year 2000,
though mass areas quite close to the other mass values. The inertia values were
also similar, still with year 2000 as having the highest value of 0.008.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
33
Table 10.Summary figures of the Calendar Year points
CALENDAR
QUALITY MASS INERTIA
YEARS
2000 0.911 0.165 0.008
2001 0.736 0.144 0.003
2002 0.042 0.152 0.003
2003 0.858 0.144 0.005
2004 0.958 0.141 0.003
2005 0.775 0.134 0.005
2006 0.801 0.120 0.005
The contributions of the Calendar Years 2000-2006 in the dimensions of
this study are presented in Table 11. The values of the calendar years are
significant in dimension 1 and dimension 2 based on the points of the dimension.
Calendar Year 2000 in dimension 1 and 2004 in dimension 2 had the highest
relative values. The second dimension was defined by the Calendar Year 2003,
2005 and 2006 with comparatively high values. This meant that 2000 and 2004
were the important points to dimension 1 whereas 2004 was important to
dimension 2.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
34
Table 11.Contribution of Dimension to the Calendar Year Points
CALENDAR
DIM 1
DIM 2
YEARS
2000 0.479 0.000
2001 0.108 0.042
2002 0.004 0.007
2003 0.127 0.239
2004 0.167 0.90
2005 0.112 0.233
2006 0.003 0.389
The two dimensional coordinates of the Calendar Year points in Table 12,
showed that the three calendar years 2000, 2001 and 2002 were grouped as one
and the last four calendar years 2003, 2004, 2005 and 2006 belonged to another
group in dimension 1. In dimension 1 calendar year with positive values was
located at the right side of the vertical axis and calendar years with negative
values were located at the branch of the vertical axis. In the second dimension,
calendar years 2003 had the only positive value and the rest dimension points
were negative. Calendar years in dimension 2 with positive value were found
above the horizontal axis and calendar years with negative value are found below
the horizontal axis.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
35
Calendar years which are located closer to each other have similar
contributions on the number of births in the Region.
Table 12.Two Coordinates of the Calendar Years
CALENDAR
DIM 1
DIM 2
YEARS
2000 0.593 -0.003
2001 0.304 -0.167
2002 0.55 -0.066
2003 -0.327 0.402
2004 -0.379 -0.250
2005 -0.317 -0.411
2006 -0.056 -0.562
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
36
The plot on the number of births points and calendar year points illustrated
the overall view of both variables on the plot.
The two dimensional map consisted of the horizontal axis with dimension
1 and the vertical axis with dimension 2. The labels for number of births profiles
in the correspondence map were Abra, Apayao, Baguio, Benguet, Ifugao, Kalinga
and Mt. Province. The labels of the calendar year profiles were 2000, 2001, 2002,
2003, 2004, 2005 and 2006
Two dimensional plots representing row or column profiles may be
examined to identify whether any row or column categories have similar profiles.
Row or column categories that have similar profiles appeared in close proximity
on the plot. This could be useful to determine whether any row or column
categories could be continued in subsequent analysis. Another area of interest is
how row and column categories interact with one another in contributing to the
overall association. It also showed how the row and column contribute to the
overall size of the residual.
FIGURE 3 showed that the horizontal axis separating high frequency
provinces from low frequency. The other axis separated negative coordinates
from positive coordinates. A row and column points close together implied a high
frequency in that cell. Ifugao was closer to 2003, Benguet with 2005, Mt.
Province and Kalinga close to 2000, the implication is that a higher number of
births in Ifugao occurred in 2003, a higher number of births in Benguet occurred
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
37
in 2005; in Mt. Province and Kalinga a higher number of births occurred in 2000.
A point could make high contribution to the inertia (variance) of a principal axis
in two ways. When it had a large distance from the centroid, even if it has a small
mass, or when it has a large mass, but small distance from the average profile.
The province of Apayao made a high contribution to the inertia (variance) in
terms of number of births, since it has large distance from the average mean
(centroid) and had a small mass.
In addition, Baguio and Abra contributed a high inertia (variance), since it
had a large mass but large distance. Dimension 1 separated the two calendar years
from the three calendar years of the period and the year 2000 on the horizontal
axis. Benguet had a high frequency but contributed low variance situated at the
negative pole while Kalinga which contributed large variance and high frequency
is located at the positive pole. Benguet and Ifugao which were far from the
horizontal axis contributed largely to the inertia of Dimension 2.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
38
0.8
0.6
2006
Ifugao
0.4
2003
Apayao
baguio
0.2
Mt. province
Abra
0
2000
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
2002
Dimension 2
kalinga
-0.2
2001
2004
-0.4
2005
Benguet
-0.6
Dimension 1
Figure.3 Correspondence analysis biplot on the number of births and the calendar
years
2000-2006
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
39
SUMMARY, CONCLUSION AND RECOMMENDATIONS
Summary
Correspondence Analysis as a relatively new technique in exploratory
analysis was used on the number of births in the six provinces of CAR during the
calendar years 2000-2006. The technique was used for measuring the association
of number of births among provinces and calendar years, at the same time,
showing the location of this association. The correspondence solution
decomposed the chi-square of the data set that resulted to the extraction of
dimensions. Researchers found that the first two dimensions associated to the
principal inertia’s with 77.44 cumulative percent of inertia explained or
represented well the number of births and calendar years points in a two
dimensional space. The total inertia in the six dimension explained 3.11 percent of
the variance in the original correspondence table. This means that 77.44 percent
of the total inertia (variance) which is 3.11 percent in the original correspondence
table was explained in the first and second dimensions.
The computed singular value in the first dimension is 0.120989 indicating
weak relationship of the number of births and calendar year variables in
Dimension 1.The second Dimension reflected strong relationship of the number
of births and calendar year points as an interpretation for 0.097246 singular
values.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
40
Findings of the study are as follows:
1. Among the provinces of CAR, Baguio, Benguet, Kalinga, Ifugao and
Mt. Provinces contributed greatly to the distribution on the number of births as
reflected by the large masses of each. On the other hand, Apayao had the least
contribution. The calendar years showed contributions to the number of births.
The mass of each year had the same unit of mass and their distances from the cells
were almost equal.
2. In the population data set on the number of births in the six provinces of
CAR during the calendar years 2000-2006, 77.44% of the variance was explained
by the Dimension 1 and Dimension 2. In the two dimensional space, the highly
represented provinces were Benguet, Ifugao, Kalinga and Mt. Province. On the
other hand Apayao was the only province of CAR which was well represented by
the two dimensions in the Correspondence map. Moreover, the provinces of CAR
which were poorly represented by the dimension in the Correspondence map were
Abra and Baguio. As to year quality, calendar years 2000, 2001, 2003, 2004, 2005
and 2006 were well presented by the dimension in the two dimension map.
Calendar year 2002 was poorly represented by the dimensional map.
3. The cumulative inertia 77.44% of variance was explained by Dimension
1 and Dimension 2. Among the six provinces of CAR, Benguet, Kalinga and
Mountain Province contributed largely to the total inertia of the rest of the
provinces had low contributions.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
41
Conclusion
Based on the findings, the researcher arrived at the following conclusions:
1.Benguet, Kalinga and Mountain Province were the leading provinces as
to number of births Furthermore, Apayao and Abra had the lowest number of
births. On the other hand, the calendar years 2000, 2003, 2004 and 2006 recorded
the highest number of births. Since Benguet, Kalinga and Mountain. Province
obtained the largest masses; these provinces had a high birth growth. Likewise,
calendar year 2000, 2003, 2004 and 2006 had the large masses.
2. The provinces of CAR which were highly explained by the dimensions
were Benguet, Kalinga, and Mountain Province. The calendar year profiles, 2000,
2003, 2004, 2005, and 2006 were highly represented by the Dimension 1 and 2.
3. Using the correspondence map, Benguet was known for its large mass
contribution.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
42
Recommendations
The following recommendations are suggested in relation to the growing
number of births in the six provinces of CAR and the use of the Correspondence
Analysis method.
1. The government should be able to address the problem of high number
of births, especially to province which were seen as consistently growing in
population.
2. Correspondence Analysis may be used for researches on frequency data
with multiple categories and with wider scope of geographical area.
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
43
LITERATURE CITED
BENZECRI, Correspondence Analysis Handbook, vol.125 of statistics;
Textbooks and Monographs, Marcel Dekker, New York, NY, USA, 1992.
E.J,BEH “Biometrical Journal, vol.4 Michael Greenacres, 2005” 883,
Department of Economics and Business, Universidad Poppeu Fabra,
revised” no.4, pp.413-429, 1998.
GREENACRE, MICHAEL J. (1984) Theory and Applications of Correspondence
Analysis. London: academic press.
GROENEN, P.J.F. and VAN DER HEIDEN, and P.G.M.1980. Analyzing
asymmetry two wave two-variable panel data with generalized
correspondence and log linear models. In E.Diday(ED), Data analysis,
learning symbolic and numeric knowledge. Pp 31-38.
JAMBU, MICHAEL. (1991).Exploratory and multivariate Data Analysis, Boston
Academic
Press.
LUDWIG, J AND J REYNOLDS.1998.Statistical Ecology: A primer on Methods
and Computing. Wiley, New York. Easy to follow outline procedures
involved in PCA and CA; working through the chapter on PCA helps to
understand
CA.
NEI, L.F. et al. 1998.Correspondence Analysis as Applied to 6x5 Contingency
Data. The Philippine Statistician.vol.21, Nos.4.Pp.67-75.
PIELOU, E.C.1984.Interpretation of ecological Data: A Primer on Classification
and Ordination. Wiley New York.
SEARLE, S.1982.Matri Algebra Useful for Statistics. Wiley, New York. If you
have time, the best, most accessible introduction to matrix algebra for
these
purposes.
VON POPPEL, F.POST.W.and GROENEN, P.J.F.1997.Age preferences of
Spouses, the Netherlands 1850-1993.An application of correspondence
analysis in population and family in the low countries.Pp 191-218.
GREENACRE, M 1984.Ratio Maps and Correspondence Analysis
http://www.Econ.upof.es/deehome/whatr/wpapers/pests cripts/598.pdf
http://search.yahoo.com/search;
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
44
APPENDIX A. Letter of Request
Benguet State University
College of Arts and Sciences
MATH-PHYSICS-STATISTICS DEPARTMENT
La Trinidad, Benguet
February
6,
2008
BENJAMIN Y. NAVARRO
Head, NSCB- CAR
2/F JA Apartment, # 39
Upper Engineers Hill, 2600 Baguio City
Sir:
Greetings!
We are undergraduate students of Benguet State University taking Bachelor of
Science in Applied Statistics. We are in the process of conducting our thesis
entitled “Correspondence Analysis on the number of births in the six provinces of
Cordillera Administrative Region during the years 2000-2006”.
In this connection may we be permitted to get the necessary data for our
study from good office. Rest assured that all data gathered will be held
confidential and it shall be used only to serve the purposes of our study.
Your favorable response on this request will be highly appreciated.
Respectfully yours,
(Sgd) Crisanta P. Apit
(Sgd)
Marifee
K.
Logro
(Sgd) Noemi S. Palubos
Noted:
DR. MARIA AZUCENA B. LUBRICA
Thesis Adviser
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
45
Benguet State University
College
of
Arts
and
Sciences
MATH-PHYSICS-STATISTICS
DEPATRMENT
La
Trinidad,
Benguet
February
6,
2008
Engr.OLIVIA GULLA
Head, NSO - Regional
Junifer Bldg. Bonifacio Street
2600 Baguio City
Madam:
Greetings!
We are undergraduate students of Benguet State University taking Bachelor of
Science in Applied Statistics. We are in the process of conducting our thesis
entitled “Correspondence Analysis on the number of births in the six provinces of
Cordillera Administrative Region during the years 2000-2006”.
In this connection may we be permitted to get the necessary data for our
study from good office. Rest assured that all data gathered will be held
confidential and it shall be used only to serve the purposes of our study.
Your favorable response on this request will be highly appreciated.
Respectfully yours,
(Sgd) Crisanta P. Apit
(Sgd) Marifee K. Logro
(Sgd)
Noemi
S.
Palubos
Noted:
DR.MARIA AZUCENA B. LUBRICA
Thesis Adviser
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
46
Appendix B. Number of Births Registered by Month and Provinces (2000-2006)
CY
2000
CAR
ABRA
CITY
NCE
APAYAO
BAGUIO
BENGUET
IFUGAO
KALINGA
MT.PROVI
TOTAL
54169 7382
2125 11708
16348
6625 13703
10111
JANUARY 6380
448
210
988
1592
584
1109
2647
FEBRAURY 4676 818
331
946
865
730 1361 902
MARCH 4784
756
227
822
1250
482
1361
935
APRIL 5088
376
180
879
1317
587
2075
733
MAY 3930
611
160
778
1347
511
748
713
JUNE 4972
725
115
922
1375
782
1319
771
JULY 4586
823
143
888
1423
569
1106
665
AUGUST 3946
549
141
854
1281
522
1070
524
SEPTEMBER
4323 618
210
945
1497
514 1088 606
OCTOBER 3744
516
178
980
1434
426 762
606
DECEMBER 3806 552
120
1146
1490
477 852 435
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
47
CE
AO
IO
O
GA
CAR
ABRA
MT.
CY 2001
APAY
BAGU
IFUGA
BENGUET
KALIN
PROVIN
TOTAL
49551 7027
2001
8015
7210 12176
6888 16250
JANUARY
3547 510
152
610
463
750
409 1415
FEBRAURY 3589 763
204
580
562
786
472 1006
MARCH
3946 424
115
637
504
1184
576 1258
APRIL
4146 461
117
650
695
1052
669 1269
MAY
3999 596
139
683
529
1008
493 1373
JUNE
4836 796
152
690
517
1419
615 1489
JULY
4423 762
175
540
645
1114
617 1285
AUGUST
4409 613
181
684
513
1241
715 1327
SEPTEMBER
4272 626
193
710
709
901
515 1461
OCTOBER
3876 621
194
674
755
787
353 1360
NOVEMBER 4652 603
178
715
774
1024
697 1554
DECEMBER 3856 252
201
850
544
910
697 1453
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
48
CE
AO
IO
O
GA
CAR
MT.
CY 2002
ABRA
APAY
BAGU
BENGUET
IFUGA
KALIN
PROVIN
TOTAL
50827 7244
4102
7922
7986 12295
6174
17128
JANUARY 3117
426
307
450
367
992
465 867
FEBRAURY 4676
830
319
582
529
1143
368
1894
MARCH 4043
582
486
650
614
1053
481
1313
APRIL 3855
437
696
669
508
1374
323
1213
MAY 4729
680
455
730
705
1360
323
1661
JUNE 4581
790
287
790
790
1119
413
1469
JULY 4421
643
292
835
750
1087
473
1468
AUGUST 4375
613
268
816
599
801
1088 1274
SEPTEMBER
4361 603
276
830
707
807
883
1361
OCTOBER 4375
665
244
590
655
963
435 1657
NOVEMBER 4302 393
267
420
1047
859
461
1542
DECEMBER 3904
582
205
530
715
737
461
1409
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
49
CE
AO
IO
O
GA
CAR
ABRA
MT,
CY 2003
APAY
BAGU
BENGUET
IFUGA
KALIN
PROVIN
TOTAL
59258 7214
3506
9334
10559
7485
5899
15221
JANUARY
5043
738
241
777
757
720
464
1346
FEBRUARY 4729 561
352
904
897
732
416
867
MARCH 5506
568
312
616
1308
747
466 1489
APRIL 4194
536
239
679
506
562
466
1206
MAY 4652
699
256
677
526
798
460
1236
JUNE 5221
666
320
922
721
702
573
1317
JULY 5351
539
311
778
941
670
630
1482
AUGUST 4568
501
283
654
679
510
530 1411
SEPTEMBER
4889 676
361
845
769
501
500
1237
OCTOBER 5289
639
257
910
1763
545
518
657
NOVEMBER 5130 585
330
825
843
553
438
1556
DECEMBER 4686 506
244
747
889
445
438
1417
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
50
CE
AO
IO
O
GA
CAR
ABRA
MT.
CY 2004
APAY
BAGU
BENGUET
IFUGA
KALIN
PROVIN
TOTAL
49813 7965
2784
8179
7508
7828 4676
8179
JANUARY
4686
778
247
758
839
524
445
758
FEBRUARY 4434
657
331
865
784
666 470
865
MARCH 5062
694
250
635
1138
793
451
635
APRIL 4152
683
192
542
717
646
366
542
MAY 4237
784
262
641
549
731
392
641
JUNE 4787
846
264
543
710
972
407
543
JULY 3553
595
203
520
516
373
363
520
AUGUST 3879
682
236
652
465
579
265
652
SEPTEMBER 3997 700
161
630
483
676 361
630
OCTOBER 4275
667
215
854
475
777
426
854
NOVEMBER 3432 549
202
753
434
619 385
753
DECEMBER 3319 330
221
786
398
472 345
786
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
51
CE
AO
IO
O
GA
CAR
ABRA
MT.
CY 2005
APAY
BAGU
BENGUET
IFUGA
KALIN
PROVIN
TOTAL
46013 6931
2529
9117
5580
7112
4787
19254
JANUARY 3574
575
221
789
430
472
457 1559
FEBRUARY 4348
670
221
720
459
725
436 1837
MARCH 4013
681
204
680
502
693
418
1515
APRIL 3715
350
195
630
486
675
364
1645
MAY 3863
594
269
759
396
492
415
1697
JUNE 3889
714
163
856
238
766
430
1578
JULY 4134
630
204
588
478
785
381
1656
AUGUST 3972
546
209
723
734
645
405 1433
SEPTEMBER
3681 535
225
840
489
490
343
1599
OCTOBER 3700
667
215
759
475
483
361 1539
NOVEMBER 3519
529
199
820
412
451
326
1602
DECEMBER 3605
440
204
953
481
435
451 1594
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
52
CAR
ABRA
MT.
CY 2006
APAYAO
BAGUIO
BENGUET
IFUGAO
KALINGA
PROVINCE
TOTAL
44343 7246
2843
9672
7094
6949
5370 10242
JANUARY 4335
885
219
885
494
603
385 864
FEBRUARY 3720
740
279
680
379
483
407 752
MARCH 4353
980
344
758
507
497
382
885
APRIL 3344
577
194
610
402
459
323
779
MAY 4456
809
271
769
587
588
450
982
JUNE 4680
809
272
985
514
668
479
953
JULY 3763
466
199
669
756
554
412
707
AUGUST 4005
521
180
820
746
454
491
793
SEPTEMBER
4151 542
193
850
689
459
614 804
OCTOBER 4615
542
255
835
943
729
515 871
NOVEMBER 2921 467
230
954
596
680
495 876
DECEMBER 3621 450
207
857
481
775
417 976
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
53
Appendix C. Inertia and Chi-square Decomposition
Singular
Principal
chi-square
Percent of
Value Inertia
Inertia
0.120989 0.014638 6036.75 47.04
0.097246 0.094567 3899.91 30.39
0.069929 0.00489 2016.64 15.72
0.377229 0.001423 586.85 4.57
0.025947 0.000673 277.64 2.16
0.005885 3.46E-05 14.28
0.11
12832.07 100
Row Coordinates
CAR Provinces Dim 1 Dim2
Abra -0.177 0.091
Apayao -0.448 0.340
Baguio 0.026 0.240
Benguet -0.245 -0.427
Ifugao -0.306 0.453
Kalinga 0.538 - 0.132
Mt.Province 0.543 0.154
Column
Coordinates
Calendar Years Dim 1 Dim 2
2000 0.593 -0.003
2001 0.304 -0.167
2002 0.55 -0.066
2003 -0.327 0.402
2004 -0.379 -0.250
2005 -0.317 -0.411
2006 -0.056 -0.562
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
54
Appendix D. STATA OUTPUT
CA PROVINCE YEAR [fweight = FREQUENCY]
Correspondence analysis Number of obs= 412387
Pearson chi2 (36) = 12827.59 Number of dim. = 2
Expl. Inertia (%)=77.43
Prob > chi2 = 0.0000
Total inertia = 0.0311
7 active rows
7 active columns
Singular principal cumul
Dimensions values inertia chi2 percent percent
Dim 1 .1209764 .0146353 6035.40 47.05 47.05
Dim 2 .0972101 .0094498 3896.98 30.38 77.43
Dim 3 . 0699272 .0048898 2016.49 15.72 93.15
Dim 4 .0377264 .0014233 586.94 4.58 97.73
Dim 5 .0259401 .0006729 277.49 2.16 99.89
Dim 6 .0058858 .0000346 14.29 0.11 100.00
Total .0311057 12827.59 100
Statistics for row and column categories in symmetric normalization.
Overall dimension_1
Categories mass quality inertia coord sqcorr contrib.
PROVINCE
1 0.124 0.492 0.001 -0.178 0.407 0.032
2 0.048 0.546 0.003 -0.448 0.374 0.080
3 0.155 0.286 0.003 0.026 0.004 0.001
4 0.275 0.988 0.007 -0.245 0.286 0.136
5 0.128 0.771 0.005 -0.306 0.280 0.099
6 0.164 0.838 0.007 0.538 0.800 0.393
7 0.106 0.914 0.004 0.543 0.858 0.259
YEAR
1 0.165 0.911 0.008 0.593 0.911 0.479
2 0.144 0.736 0.003 0.302 0.590 0.109
3 0.152 0.042 0.003 0.054 0.019 0.004
4 0.144 0.858 0.005 -0.328 0.389 0.128
5 0.141 0.958 0.003 -0.379 0.710 0.167
6 0.134 0.774 0.005 -0.317 0.329 0.111
7 0.120 0.801 0.005 -0.056 0.010 0.003
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
55
dimension_2
Categories coord sqcorr contrib.
PROVINCE
1 0.091 0.085 0.010
2 0.339 0.172 0.057
3 0.240 0.282 0.092
4 -0.427 0.701 0.516
5 0.453 0.491 0.269
6 -0.131 0.038 0.029
7 0.154 0.056 0.026
YEAR
1 -0.003 0.000 0.000
2 -0.167 0.146 0.042
3 -0.067 0.023 0.007
4 0.402 0.469 0.238
5 -0.250 0.248 0.091
6 -0.411 0.445 0.233
7 0.562 0.791 0.389
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
56
Appendix E. Plot of Correspondence Solution
.6
7
5
.4
4
2
3
.2
PROVINCE
7
1
0
1
3
6
2
-.2
5
-.4
6 4
-.6
-.6
-.4
-.2
0
.2
.4
.6
YEAR
o PROVINCE
YEAR
coordinates in symmetric normalization
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
57
Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006/ Crisanta P. Apit; et al. 2008
Document Outline
- Correspondence Analysis on the Number of Births in the Six Provinces of Cordillera
Administrative Region during the years 2000-2006
- BIBLIOGRAPHY
- ABSTRACT
- TABLE OF CONTENTS
- INTRODUCTION
- REVIEW OF RELATED LITERATURE
- THEORITICAL FRAMEWORK
- METHODOLOGY
- RESULTS AND DISCUSSION
- SUMMARY, CONCLUSION AND RECOMMENDATIONS
- LITERATURE CITED
- APPENDIX