TEAM B -Day 10 Discriminant Analysis

Discriminant analysis is a technique for the multivariate study of group differences. More specifically, it provides a method of examining the extent to which multiple predictor variables are related to a categorical criterion, that is, group membership. Situations in which the technique is particularly useful include those in which the researcher wishes to assess which of a number of continuous variables best differentiates groups of individuals or in which he or she wishes to predict group membership on the basis of the discriminant function (analogous to a multiple regression equation) yielded by the analysis. The method is also useful as a follow-up to a significant analysis of variance.

DA multiple quantitative attributes are used to discriminate single classification variable. DA is different from the cluster analysis because prior knowledge of the classes, usually in the form of a sample from each class is required. The common objectives of DA are 

i) to investigate differences between groups

 ii)to discriminate groups effectively; 

iii) to identify important discriminating variables; 

iv) to perform hypothesis testing on the differences between the expected groupings;

 v) to classify new observations into pre-existing groups

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The ideas associated with discriminant analysis can be traced back to the 1920s and work completed by the English statistician Karl Pearson, and others, on intergroup distances, e.g., coefficient of racial likeness (CRL), (Huberty, 1994). In the 1930s R. A. Fisher translated multivariate intergroup distance into a linear combination of variables to aid in intergroup discrimination. Methodologists from Harvard University contributed much to the interest in application of discriminant analysis in education and psychology in the 1950s and 1960s .

Many previous posts have clearly depicted what a discriminant analysis is. In this post i would like to highlight how factor analysis is different from discriminant analysis.

Discriminant analysis helps to identify the independent variables that discriminate a nominally scaled dependent variable of interest. The linear combination of independent variables indicates the discriminating function showing the large difference that exists in the two group means. In other words the independent variables measured on an interval or ratio scale discriminate the groups of interest to study.

Factor analysis helps to reduce a vast number of variables to a meaningful, interpretable, and manageable set of factors. A principle component analyses transform all the variables into a set of composite variables that are not correlated to one another. Suppose we have measured in a questionnaire the four concepts of mental health, job satisfaction, life satisfaction, and job involvement with seven questions tapping each. When we factor analyze these 28 items, we should find four factors with the right variables loading on each factor, confirming that we have measured the concepts correctly.The cluster analysis is used to classify objects or individuals into mutually exclusive and collectively exhaustive groups with high homogeneity within clusters and low homogeneity between clusters. In other words cluster analysis helps to identify objects that are similar to one another, based on some specified criterion. Cluster analysis will cluster individuals by their preferences for each of the different brands.

To Obtain a Discriminant Analysis

From the menus choose:

Analyze
Classify
Discriminant...

Select an integer-valued grouping variable and click Define Range to specify the categories of interest.

Select the independent, or predictor, variables. (If your grouping variable does not have integer values, Automatic Recode on the Transform menu will create a variable that does.)

Select the method for entering the independent variables.

• Enter independents together. Simultaneously enters all independent variables that satisfy tolerance criteria.
• Use stepwise method. Uses stepwise analysis to control variable entry and removal.