Question

Discuss the major issues relating to types of variables used and sample size required in the application of discriminant analysis.

Answer 1

Discriminant analysis is a technique that is used by the researcher to analyze the research data when the criterion or the dependent variable is categorical and the predictor or the independent variable is interval in nature. The term categorical variable means that the dependent variable is divided into a number of categories. For example, three brands of computers, Computer A, Computer B and Computer C can be the categorical dependent variable.

The objective of discriminant analysis is to develop discriminant functions that are nothing but the linear combination of independent variables that will discriminate between the categories of the dependent variable in a perfect manner. It enables the researcher to examine whether significant differences exist among the groups, in terms of the predictor variables. It also evaluates the accuracy of the classification.

Discriminant analysis is described by the number of categories that is possessed by the dependent variable.

As in statistics, everything is assumed up until infinity, so in this case, when the dependent variable has two categories, then the type used is two-group discriminant analysis. If the dependent variable has three or more than three categories, then the type used is multiple discriminant analysis. The major distinction to the types of discriminant analysis is that for a two group, it is possible to derive only one discriminant function. On the other hand, in the case of multiple discriminant analysis, more than one discriminant function can be computed.

There are many examples that can explain when discriminant analysis fits. It can be used to know whether heavy, medium and light users of soft drinks are different in terms of their consumption of frozen foods. In the field of psychology, it can be used to differentiate between the price sensitive and non price sensitive buyers of groceries in terms of their psychological attributes or characteristics. In the field of business, it can be used to understand the characteristics or the attributes of a customer possessing store loyalty and a customer who does not have store loyalty.

For a researcher, it is important to understand the relationship of discriminant analysis with Regression and Analysis of Variance (ANOVA) which has many similarities and differences. Often we can find similarities and differences with the people we come across. Similarly, there are some similarities and differences with discriminant analysis along with two other procedures. The similarity is that the number of dependent variables is one in discriminant analysis and in the other two procedures, the number of independent variables are multiple in discriminant analysis. The difference is categorical or binary in discriminant analysis, but metric in the other two procedures. The nature of the independent variables is categorical in Analysis of Variance (ANOVA), but metric in regression and discriminant analysis

Unequal group size does not influence the direct solution of the discriminant analysis problem. However, unequal group size can cause subtle changes during the classification phase. Normally, the sampling frequency of each group (the proportion of the total sample that belongs to a particular group) is used during the classification stage. If the relative group sample sizes are not representative of their sizes in the overall population, the classification procedure will be erroneous

Discriminant analysis does not make the strong normality assumptions that MANOVA does because the emphasis is on classification. A sample size of at least twenty observations in the smallest group is usually adequate to ensure robustness of any inferential tests that may be made. Outliers can cause severe problems that even the robustness of discriminant analysis will not overcome. You should screen your data carefully for outliers using the various univariate and multivariate normality tests and plots to determine if the normality assumption is reasonable. You should perform these tests on one group at a time.

Multicollinearity occurs when one predictor variable is almost a weighted average of the others. This collinearity will only show up when the data are considered one group at a time. Forms of multicollinearity may show up when you have very small group sample sizes (when the number of observations is less than the number of variables). In this case, you must reduce the number of independent variables.