# AN OVERVIEW OF MULTIVARIATE DATA ANALYSIS by guf14004

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AN OVERVIEW OF MULTIVARIATE DATA ANALYSIS
AND ITS APPLICATION
Steph Subanidja*

A first literature of multivariate   object under investigation. Moreover,
data analysis was published almost 20         any simultaneous analysis of more than
years ago. Recently, it has been              two variables can be loosely considered
becoming a comprehensive method to            multivariate analysis. What kinds of data
analyze complex data and multiple             should be analyzed by using multivariate
correlations among variables. As an           analysis?
improvement of some software packages                 There are two basic kinds of
in a computer program, researchers and        data: non-metric for qualitative data and
decision makers, become easier to             metric for quantitative data. Non-metric
analyze the complex data and                  data are attributes, characteristics or
phenomena accurately.                         categorical       data.       Non-metric
The computer technology has          measurements can be made with either a
the     analysis     of,    for  example,     scales, also known as categorical scale,
sociological, psychological and other         provide the number of occurrences in
types of behavioral data. Almost any          each class or category of the variable
research problem is easily analyzed by        being studied. Ordinal scales, on the
any number of statistical programs on         other hand, are the next higher level of
microcomputers.                               measurement precision. Variables can be
This article tries to know, at a     ordered or ranked with ordinal scales in
glance, what are multivariate data            relation to the amount of the attribute
analysis and its application on research      possessed.
activities.                                           Metric measurement can be made
with either interval or ratio scales. The
What is Multivariate Analysis?                most familiar interval scales, for
Multivariate analysis is not easy     example, are the Fahrenheit and Celsius
to define. However, some experts in the       temperature scales. Each has a different
area of data analysis, such as Hair,          arbitrary zero point, and either indicates
Anderson, Tatham and Black, said that         a zero amount or lack of temperature
broadly speaking, multivariate analysis       because we can register temperatures
refers to all statistical methods that        below the zero point on each scale. Ratio
simultaneously      analyze      multiple     scales represent the highest form of
measurements on each individual or            measurement precision because they
An Overview of Multivariate Data Analysis ….. (Steph Subanidja)
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possess the advantages of all lower
scales plus an absolute zero point.            The objective of the multiple regression
analysis is to predict the changes in the
Application of Multivariate Data               dependent variable in response the
Analysis (MDA)                                 change in the independent variables. So,
There are at least 11 applications     it is suggested, do not using the
of MDA, namely 1) principal                    regression, if you do not want to predict
components and factor analysis, 2)             the changes in the dependent variable.
multiple regressions and correlations, 3)              Multiple discriminant analysis
multiple discriminant analysis, 4)             (MDA) is the appropriate multivariate
multivariate analysis of variance and          technique if the single dependent
covariance, 5) conjoint analysis, 6)           variable is dichotomous such as male-
canonical correlation, 7) cluster analysis,    female or multichotomous such as high-
8)    multidimensional      scaling,    9)     medium- low. Therefore, the dependent
correspondence analysis, 10) linear            variable is non-metric scale. The primary
probability models and 11) structural          objectives of MDA are to understand
equation modeling.                             group differences and to predict values
Principal components and factor        of group based on several metric
analysis are a statistical approach that       independent variables. So, the equation
can be used to analyze interrelationships      of MDA is:
among a large number of variables. This
approach is appropriate to analyze, for        y (for non-metric scale) = f (X1, X2, …,
example, market segmentation. So, we           Xn ) for non-metric scale.
have independent variable with a large
number of indicators or factors, with                 Multivariate analysis of variance
either nominal, ordinal, interval or ratio     (MANOVA) is a statistical technique to
scales.                                        simultaneously explore the relationship
Multiple       regression        is    between several categorical independent
appropriate method to analyze a single         variables and two or more metric
metric dependent variable related to two       dependent variables. The mathematical
or more metric independent variables.          equation of MANOVA is:
By using mathematical equation, the
regression is:                                 y1 + y2 + … + yn (for metric scale) = X1
+ X2 + …+ Xn (for non-metric scale).
y (for metric scale) = f (X1, X2, …, Xn)
for metric scale.
Ingenious, Vol. 1, No. 1, August 2003: 3 - 6
5

Whereas, multivariate analysis of               of mutually exclusive groups based on
covariance (MANCOVA) can be used to             the similarities among the entities that is
remove the effect of any uncontrolled           individuals or objects.
metric dependent variables toward the                   Multidimensional scaling (MDS)
dependent     variables.       ANOVA,           is usually used to transform consumer
furthermore, represents a single metric         judgments or similarity or preference
dependent variable based on several             into      distances      represented     in
non-metric independent variables.               multidimensional space. MDS is also
Conjoint    analysis    is  the         called as perceptual mapping of the
relationship between a single non-metric        similarities.
dependent variable and several non-                     Correspondence analysis (CA) is
metric independent variables. The               a special form of MDS. In the basic
mathematical function as follows                form, CA employs a contingency table,
which is a cross-tabulation of two
y (for non-metric or metric scale) = X1 +       categorical variables. It provides a
X2 + …+ Xn (for non-metric scale).              multivariate        representation       of
interdependence for non-metric data that
Canonical correlations analysis         is not possible with other methods.
can be viewed as a logical extension of                 Linear probability models, which
multiple regression analysis in order to        often referred to as logit -analysis, are a
correlate simultaneously several metric         combination of multiple regressions and
or non-metric dependent variables and           multiple discriminant analysis. The
several metric or non-metric independent        technique to analyze the data is similar
variables. So that the equation of the          to multiple regression analysis.
relationship of the canonical correlation               Structural equation modeling
is:                                             (SEM), often called as LISREL (the
name of one of software packages), is a
y1 + y2 + … + yn (for metric and non            technique      that     allows     separate
metric scale) = X1 + X2 + …+ Xn (for            relationship for each of a set of
metric and non-metric scale).                   dependent variables. There are two basic
component of SEM: the structural model
Cluster analysis is a statistical       and the measurement model. The
technique to develop meaningful                 structural model is usually called as the
subgroups of individuals or objects. The        Path Analysis model, which relates
objective of cluster analysis is to classify    independent to dependent variables.
a sample of entities into a small number        Whereas, measurement model allows to
An Overview of Multivariate Data Analysis ….. (Steph Subanidja)
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use several variables for a single
independent or dependent variables. The
mathematical equation of the SEM is
shown as follows:

y1 = X11 + X12 + …+ X1n
y2 = X21 + X22 + …+ X2n
………………………….
Ym = Xm1 + Xm2 + …+ Xmn

Variable y is for metric scale and
variable X for both metric and or non-
metric scale.
From the information above, it
can be seen that multivariate data
analysis is a comprehensive method of a
statistical    technique     to   analyze
relationship among variables. The types
of the techniques can be used for almost
all relationships based on the objectives
of the researchers or decision makers.
So, the problem is, now, not how
to analyze the data, but how to construct
the relationship among variables based
on the exploring some literatures or
phenomena such as journals, books,
studies, or researcher’s managerial
experiences.

* is now a doctorate student of