Research Methodology - Dr. Krishan K. Pandey
Research Methodology - Dr. Krishan K. Pandey Research Methodology - Dr. Krishan K. Pandey
Multivariate Analysis Techniques 317 the data are quantitative, collected on interval or ratio scale, or whether the data are qualitative, collected on nominal or ordinal scale. The technique to be used for a given situation depends upon the answers to all these very questions. Jadish N. Sheth in his article on “The multivariate revolution in marketing research” 3 has given the flow chart that clearly exhibits the nature of some important multivariate techniques as shown in Fig. 13.1. Thus, we have two types of multivariate techniques: one type for data containing both dependent and independent variables, and the other type for data containing several variables without dependency relationship. In the former category are included techniques like multiple regression analysis, multiple discriminant analysis, multivariate analysis of variance and canonical analysis, whereas in the latter category we put techniques like factor analysis, cluster analysis, multidimensional scaling or MDS (both metric and non-metric) and the latent structure analysis. Multiple regression One Is it metric? All multivariate methods Are some variables dependent? Yes No Dependence methods How many variables are dependent? Several Yes No Yes No Multiple discriminant analysis Are they metric? Multivariate analysis of variance Fig. 13.1 Interdependence methods Are inputs metric? Yes No Factor analysis Canonical analysis Clustre analysis Non-metric MDS Metric MDS Latent structure analysis 3 Journal of Marketing, American Marketing Association, Vol. 35, No. 1 (Jan. 1971), pp. 13–19.
318 Research Methodology VARIABLES IN MULTIVARIATE ANALYSIS Before we describe the various multivariate techniques, it seems appropriate to have a clear idea about the term, ‘variables’ used in the context of multivariate analysis. Many variables used in multivariate analysis can be classified into different categories from several points of view. Important ones are as under: (i) Explanatory variable and criterion variable: If X may be considered to be the cause of Y, then X is described as explanatory variable (also termed as causal or independent variable) and Y is described as criterion variable (also termed as resultant or dependent variable). In some cases both explanatory variable and criterion variable may consist of a set of many variables in which case set (X 1 , X 2 , X 3 , …., X p ) may be called a set of explanatory variables and the set (Y 1 , Y 2 , Y 3 , …., Y q ) may be called a set of criterion variables if the variation of the former may be supposed to cause the variation of the latter as a whole. In economics, the explanatory variables are called external or exogenous variables and the criterion variables are called endogenous variables. Some people use the term external criterion for explanatory variable and the term internal criterion for criterion variable. (ii) Observable variables and latent variables: Explanatory variables described above are supposed to be observable directly in some situations, and if this is so, the same are termed as observable variables. However, there are some unobservable variables which may influence the criterion variables. We call such unobservable variables as latent variables. (iii) Discrete variable and continuous variable: Discrete variable is that variable which when measured may take only the integer value whereas continuous variable is one which, when measured, can assume any real value (even in decimal points). (iv) Dummy variable (or Pseudo variable): This term is being used in a technical sense and is useful in algebraic manipulations in context of multivariate analysis. We call X i ( i = 1, …., m) a dummy variable, if only one of X i is 1 and the others are all zero. IMPORTANT MULTIVARIATE TECHNIQUES A brief description of the various multivariate techniques named above (with special emphasis on factor analysis) is as under: (i) Multiple regression * : In multiple regression we form a linear composite of explanatory variables in such way that it has maximum correlation with a criterion variable. This technique is appropriate when the researcher has a single, metric criterion variable. Which is supposed to be a function of other explanatory variables. The main objective in using this technique is to predict the variability the dependent variable based on its covariance with all the independent variables. One can predict the level of the dependent phenomenon through multiple regression analysis model, given the levels of independent variables. Given a dependent variable, the linear-multiple regression problem is to estimate constants B , B , ... B and A such that the expression Y = B X + B X + ... + B X + A pare rovides 1 2 k 1 1 2 2 k k a good estimate of an individual’s Y score based on his X scores. In practice, Y and the several X variables are converted to standard scores; z , z , z , ... z ; each y l 2 k z has a mean of 0 and standard deviation of 1. Then the problem is to estimate constants, βi , such that z′ = β z + β z + + β z y 1 1 2 2 ... k k * See Chapter 7 also for other relevant information about multiple regression.
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Multivariate Analysis Techniques 317<br />
the data are quantitative, collected on interval or ratio scale, or whether the data are qualitative,<br />
collected on nominal or ordinal scale. The technique to be used for a given situation depends upon the<br />
answers to all these very questions. Jadish N. Sheth in his article on “The multivariate revolution in<br />
marketing research” 3 has given the flow chart that clearly exhibits the nature of some important<br />
multivariate techniques as shown in Fig. 13.1.<br />
Thus, we have two types of multivariate techniques: one type for data containing both dependent<br />
and independent variables, and the other type for data containing several variables without dependency<br />
relationship. In the former category are included techniques like multiple regression analysis, multiple<br />
discriminant analysis, multivariate analysis of variance and canonical analysis, whereas in the latter<br />
category we put techniques like factor analysis, cluster analysis, multidimensional scaling or MDS<br />
(both metric and non-metric) and the latent structure analysis.<br />
Multiple<br />
regression<br />
One<br />
Is it metric?<br />
All multivariate methods<br />
Are some<br />
variables<br />
dependent?<br />
Yes No<br />
Dependence<br />
methods<br />
How many<br />
variables<br />
are dependent?<br />
Several<br />
Yes No Yes<br />
No<br />
Multiple<br />
discriminant<br />
analysis<br />
Are they<br />
metric?<br />
Multivariate<br />
analysis of<br />
variance<br />
Fig. 13.1<br />
Interdependence<br />
methods<br />
Are inputs metric?<br />
Yes No<br />
Factor<br />
analysis<br />
Canonical analysis<br />
Clustre<br />
analysis<br />
Non-metric<br />
MDS<br />
Metric<br />
MDS<br />
Latent<br />
structure<br />
analysis<br />
3 Journal of Marketing, American Marketing Association, Vol. 35, No. 1 (Jan. 1971), pp. 13–19.