Table Of ContentFactor analysis applied to developed
and developing countries
•
u
Tilburg Studies on Economics
1
Edited by the
Tilburg Institute of Economics
of the Tilburg School of Economics
Members of the Board
P.A. Verheijen, Chairman
Th.C.M.J. van de Klundert
H.W.J. Bosman
Director of Research
J.J.J. Dalmulder
A study on Econometrics
Factor analysis applied
to developed and
developing countries
J.R.F. Schilderinck
Department of Econometrics,
Tilburg School of Economics
Preface by J.J.J. Dalmulder
Professor in Econometrics and
Mathematical Economics, Head of the
Department of Econometrics, Tilburg School
of Economics
1970
Rotterdam University Press
Wolters -Noordhoff Publishing, Groningen
The Netherlands
Distributors: Rotterdam University Press, P.O. Box 1474, Rotterdam, The Netherlands.
ISBN 978-90-237-2901-3 ISBN 978-94-015-7202-6 (eBook)
DOI 10.1007/978-94-015-7202-6
Copyright © 1970 by Universitaire Pers Rotterdam
No part of this work may be reproduced in any form, by print, photoprint, microfilm
or any other means, without written permission from the publisher.
Preface
The Tilburg Institute of Economics - Institute of the Economic Faculty of
the Tilburg University - proposes itself to publish results of economic research
taking part in the F acul ty .
To facilitate the choice of the potential reader, every publication will be
marked by the department, where the publication took its origin. As
Mr. Schilderinck's 'Factor Analysis' applied to developed and developing
countries, is a result of research in the Econometric Department, it is mark
ed Econometrics.
Every publication will be published under the supervision of the head of
the department. For this reason this preface is written by the head of the
Econometric Department.
Mr. Schilderinck's study forms an introduction to a larger project of
research, which proposes itself to develop methods of analysis, which try to
eliminate the difficulties of multi-collinearity and the arbitrariness of the
introduction of lags in regression analysis.
This study applies the method of factor analysis to statistical material
collected by the Institute of Development Problems of our University.
Prof. Dr. J. J. J. Dalmulder
Head of Department of Econometrics
v
Contents
PREFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. v
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .. IX
1. AIM OF FACTOR ANALYSIS . . . . . . . . . . . . . . . . . . . . .
2. THE METHOD OF FACTOR ANALYSIS. 3
2.1 Normalisation of the variables . . . 3
2.2 Correlation and variance in factor analysis . 4
2.3 The model of the factor analysis 5
2.4 Solution of the model ..... . 9
2.5 Interpretation of the final aspects . 17
3. APPLICATION OF FACTOR ANALYSIS TO DATA
FROM DEVELOPING COUNTRIES . . . . . . . . . . . . . . . . . . . .. 22
3.1 The variables . . . . . . . . . . . . . . . . . . 22
3.2 Working out the factor analysis . . . . . . . . 26
3.3 Interpretation of the results according to areas 33
3.4 Interpretation of the results according to final aspects. 43
SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51
VII
Introduction
With statistical research on a fairly large scale, one is constantly establishing
relationships between the variables under examination without being in a
position to state with certainty the difference in significance between these
relationships of the variables. This problem is not peculiar to economic
research; it is also present, for example, in sociological, psychological and
biological research. The problem is statistical; various methods have been
developed to reveal the most important of the many possible relationships
between the variables. One of these methods is factor analysis.
Factor analysis is based on the assumption that there are a number of
general causal factors which give rise to the various relationships between
the variables under examination. The number of general causal factors will
on the whole be considerably smaller than the number of relationships.
Many relationships between variables are, for the most part, due to the same
general causal factor. These general causal factors are referred to in the
literature as factors, components, conditions, or dimensions. This difference
in defmition arises in fact from the different technical ways of developing
factor analysis. The method of factor analysis can now therefore be defined
as follows.
Factor analysis is the attempt, based on statistical observations, to deter
mine the quantitative relationships between variables where the relation
ships are due to separate conditioning factors or general causal factors. By a
relationship is meant a certain pattern of motion between two or more of
the variables under examination. Such a pattern of motion is expressed in
coefficients or percentages which indicate to what extent the variances of
the variables in question are influenced by a certain general causal factor.
This factor is common to the variables which form part of a specific pattern
of motion.
IX
1. Aim of factor analysis
The aim of factor analysis is to group by means of a kind of transformation
the unarranged empirical data of the variables under examination in such a
way that:
(a) a smaller whole is obtained from the original material, whereby all the
information given is reproduced in summarised form;
(b) Factors are obtained which each produce a separate pattern of motion
between the variables;
(c) the pattern of motion can be interpreted logically.
The number of possible patterns of motion is dependent on the number of
variables involved in the examination. If there are n variables in a factor
examination, then n2 different relationships between variables (factors) are
theoretically possible, of which only n are possible at the same time. A
selection must be made from this theoretically possible number.
Factor analysis does not only perform this selection of important rela
tionships but also aims at interpreting the relationship which results from
each of the separate factors. As each choice and each interpretation is to a
greater or less extent subjective, factor analysis is open to criticism on this
point. Having obtained the results of a factor analysis, one cannot claim to
have established the only possible true relationships.
Despite this apt criticism, the method of factor analysis is an important
aid in observing the mutual relationships between the variables under exami
nation. These relationships can, furthermore, improve the establishment of a
certain theory. Conversely, a certain theory can also be tested by means of a
factor analysis. If, for example, one assumes certain relationships between
variables, one must be able to justify this assumption by means of a factor
analysis. If one determines the relationships to be observed by means of a
system of regression equations, then a factor analysis indicates how many
equations are necessary before a solution can be reached.
Factor analysis can produce other important results in comparative ana
lysis. For example, if one typifies a number of enterprises by various rele-
vant index numbers, then one can appraise the enterprises concerned by
comparing step by step the corresponding factors. Factor analysis is used
most of all in comparative analysis.
2
2. The method of factor analysis
2.1 NORMALISATION OF THE VARIABLES
In factor analysis, one tries to discover the general factors which cause the
variables in question to show a relationship between each other. This is done
by defining a number of vectors which fully describe the variables. Each
vector represents another general causal factor, condition, aspect or which
ever other name it is given. This kind of a factor can be regarded as a
theoretical or hypothetical variable.
In general, factor analysis does not begin with the original observations of
the variables. It sets about normalising them in a certain way in order to
make a mutual comparison possible. Normalisation is done by expressing
the deviations from the original observations with regard to their arithme
tical mean in their standard deviations. If the number of observations ranges
from 1 to N and the number of variables from 1 to n, ani Xi represents a
variable for which the observations have been normalised, then the follow
ing formula is obtained:
Xig
z. =- (1)
19 UXj
where
Xig = Xig - Xi (i = 1, 2, ... n; g = 1, 2, ... N)
:EX.
- g 19
X=-- (2)
1 N
Fa! - 2 2
~(X.-X.) :Ex .
U = a = y. /' g 19 I =y. ./ g 19 (3)
Xi Xi N N
The expected value (Le. the mean) of a normalised variable like this equals 0
and its variance equals 1.
3
