Discriminant Function Analysis in Dissertation & Thesis Research
As the name implies, discriminant function analysis is used in research that wants to predict group membership (dependent variable) from several independent variables. In dissertation and thesis research, discriminant function analysis often is used when all of the independent variables are continuous and well-distributed. Logit analysis is used in papers that have all discrete independent variables. Logistic regression is used when the independent variables are a combination of discrete and continuous variables and/or when the independent variables are poorly distributed.
When to Use Sequential Discriminant Function Analysis
To use a one-way discriminant function, the goal must be to predict group membership (dependent variable) from several independent variables. For example, your goal may be to correctly identify a subject's profession (dependent variable) from other independent variables such as attitudes toward music, reading material, and scores on extroversion subscales.
As you may have noticed, discriminant function analysis answers the same questions as a MANOVA, but in reverse. Group membership is the independent variable in a MANOVA, but the dependent variable in discriminant function analysis. Just like a MANOVA, you can analyze the contribution of your independent variables to the prediction of group membership. To illustrate, your results may indicate that the major variable that discriminates between professions is attitude toward reading material, while the variables music and extroversion don't contribute much to discrimination between professions.
Sequential one-way discriminant function is used in research when you assign priorities to the independent variables. Continuing with the example, let's say your dissertation wanted to predict profession from several attitudinal independent variables. These independent variables could be attitude toward music, reading, vacation destination, and recreational activities. These variables might be prioritized according to their expected prediction contributions. That is, you might order these variables starting with the independent variable you think will contribute most to the dependent variable (profession) down to the independent variable you think will contribute least to the dependent variable (profession). The order of your variables should be based in your paper's literature, but let's say here the order from highest contribution to lowest is attitude toward reading material, vacation destination, music, and finally recreational activities. The sequential discriminant function analysis will first examine the degree to which profession (dependent variable) is reliably predicted from attitudes toward reading material (independent variable). Then, it will assess if there is a gain in prediction of profession by adding attitudes toward vacation destination, then music, and so on.
So, how do you determine the priority order of your predictor variables? Much the same way you prioritize the importance of dependent variables in a MANOVA, the independent variables in a multiple regression, and the independent and dependent variables in canonical correlations, you can look at the correlations between predictors and the discriminant functions. A second method can be used by examining how well the predictors separate each group from the others, although this procedure won't be discussed here.
Benefits of Sequential Discriminant Function Analysis
There are two main benefits to using sequential discriminant function analysis. First, it allows you to get rid of predictors that don't contribute any more than predictors already entered into the equation. You can drop them from future analyses. Second, as sequential discriminant function analysis is a covariance analysis, it allows you to evaluate the contribution of a predictor variable while removing the influence of other predictors.
If your predictors discriminate among groups, then your results should report how the groups differ on those variables. The best way to do this is to report the groups' means on the predictor variables. Going back to our example, say attitude toward reading material reliably discriminated between blue-collar and white-collar professions. In your results section, you should report the blue-collar group's mean reading attitude score and the white-collar group's mean reading attitude score.
It should be noted that in research, discriminant function analysis is often used to predict membership in naturally occurring groups, not groups that arise from random assignment. However, if the paper is designed so that sufficient experimental controls are in effect, then the discriminant function analysis can be used to reliably separate groups on the basis of the predictor variables (i.e. the predictor variables caused the ability to discriminate between groups).
As with most other statistics, there are certain assumptions which underlie the discriminant function analysis and limitations to its use. In general, the assumptions and limitations are similar to those of the MANOVA, but see a statistics book for details.