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Several multivariate measurements require variables selection and ordering. Stepwise procedures ensure a step by step method through which these variables are selected and ordered usually for discrimination and classification purposes. Stepwise procedures in discriminant analysis show that only important variables are selected, while redundant variables (variables that contribute less in the presence of other variables) are discarded. The use of stepwise procedures is employed as to obtain a classification rule with a low error rate. Here in this work, variables are selected based on Wilks’ lambda Ù and partial F. The variable with the minimum Ù and maximum F is included in the model first, followed by the next most important variable as can be observed from the forward selection. Backward elimination deletes the variable with the smallest F and the largest Ù in a step by step fashion. SPSS is used to illustrate how stepwise procedures can be employed to identify the most important variable to be included in the model based on Wilks’ Ù and partial F. The analysis revealed that only variables X1, head width at the widest dimension and X4, eye-to-top-of-head measurement are the most important variables that are worthy of inclusion into the discriminant function.
1.1 DISCRIMINANT ANALYSIS
Discriminant Analysis or D.A is a multivariate technique used to classify cases into distinct groups. It separates distinct sets of objects (or observations) and allocates new objects (or observations) to previously defined groups. Discriminant analysis is concerned with the problem of classification, which arises when a researcher having made a number of measurements on an individual, wishes to classify the individual into one of several categories on the basis of these multivariate measurements (Onyeagu, 2003).
Discriminant analysis will help us analyze the differences between groups and provide us with a means to assign or classify any case into the groups which it most closely resembles.
There are two aspects of discriminant analysis,
1. Predictive Discriminant Analysis (PDA) or Classification, which is concerned with classifying objects into one of several groups and
2. Descriptive Discriminant Analysis (DDA) which focused on revealing major differences among the groups (Stevens 1996).
According to Huberty (1994), Descriptive discriminant analysis includes the collection of techniques involving two or more criterion variables and a set of one or more grouping variables, each with two or more levels. “Whereas in predictive discriminant analysis (PDA) the multiple response variables play the role of predictor variables. In descriptive discriminant analysis (DDA) they are viewed as outcome variables and the grouping variable(s) as the explanatory variable(s). That is, the roles of the two types of variables involved in a multivariate multigroup setting in DDA are reversed from the role in PDA.
1.2 STEPWISE DISCRIMINANT ANALYSIS
A researcher may wish to discard variables that are redundant (in the presence of other variables) when a large number of variables are available for groups separation. Here (in discriminant analysis), variables (say y’s) are selected and, the basic model does not change. Unlike regression, where independent variables are selected and consequently, the model is altered.
Stepwise selection is a combination of forward and backward variables selection methods. In forward selection, the variable entered at
each step is the one that maximizes the partial F-Statistic based on Wilks’Ù. The maximal additional separation of groups above and beyond the
separation already attained by the other variables is thus obtained. The proportion of these F’s that exceed Fα is greater than α. While in backward
selection (elimination), the variable that contributes least is deleted at each step as shown by the partial F.
The variables which are selected one at a time, and at each step, are re-examined to see if any variable that entered earlier has become redundant in the presence of recently added variables. When the largest partial F among the variables available for entry fails to exceed a preset threshold value, the procedure stops.
Stepwise discriminant Analysis is a form of discriminant analysis. During the selection process no discriminant functions are calculated. However, after the completion of the subset selection, discriminant function is calculated for the selected variables. These variables can also be used in the construction of classification functions.
1.3 STEPS INVOLVED IN DISCRIMINANT ANALYSIS
1. Construct the discriminant function.
2. Evaluate the discriminant function for population one (1) by substituting the mean values of X1, X2, ….., Xp into Y = L1X1 + L2 X2+…+LP
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