Stepwise Procedures In Discriminant Analysis

CHAPTER FIVE
RESULTS, CONCLUSION AND RECOMMENDATION
RESULTS
As can be observed from the results of the analysis, when discriminant analysis was employed, the variable CIRCUM(X2) has the highest Wilks’ lambda of 0.999 followed by FBEYE (X2) (0.959). The variable EYEHD (X4) has the least Wilks’ lambda of 0.517 followed by EARHD (X5) (0.705). Also the least F-value was recorded with the variable CIRCUM (X2) (0.074) followed by the variable FBEYE (X2) (2.474), while the variable EYEHD (X4) has the highest F-value of 54.207 followed by the variable EARHD (X5) (24.325).
The standardized canonical discriminant function obtained is:
Y    =    -0.603X1 – 0.010X2 + 0.082X3 + 0.823X4 + 0.338X5
After the substitution of the values into the above functions, it is found that 90% of the original grouped cases are correctly classified. With cross validation, 86.7% of Cross-validated cases are correctly classified.
In the stepwise procedures on the other hand, where the redundant variables are not included in the model, the Standardized Canonical discriminant functions obtained is:
Y       =       -0.550X1 + 1.012X4
After the substitution of the values into the discriminant functions formed, we noticed that about 88.3% of the original grouped cases are correctly classified. While 86.7% of cross-validated grouped cases are correctly classified.

CONCLUSION
From the interpretation of the results above, it is clear to see that the percentage of correct classification of the original grouped cases with discriminant analysis (all independent variables) (90.0%) is greater than that obtained from stepwise procedures (88.3%). This may be due to the possibility of the removal of an important variable during the stepwise selection process or due to sampling error encountered during the choice of samples.
This problem is seen solved when cross-validation is employed as both methods yield equal percentage of 86.7% of cross-validated grouped cases correctly classified. It can also be observed from the two discriminant functions obtained with discriminant analysis (all independent variables) and stepwise discriminant analysis, the variables X1 and X4 have the highest absolute standardized canonical discriminant function coefficients (X1 = 0.603 and X4 = 0.823 for discriminant analysis, X1 = 0.550 and X4 = 1.012
for stepwise discriminant analysis). It can therefore be concluded that the variables, X1 and X4 , are the most important variables necessary for the groups description. Having seen this, it is worthy of note that the stepwise procedures even with the reduced variables model, convey the required information.

RECOMMENDATION
Since the reduction of the number of variables to a manageable size is sometimes warranted as a preliminary analysis, stepwise procedures in discriminant analysis are recommended. The use of cross validation method is also necessary for obtaining a classification rule with a low error rate. The problems associated with the use of stepwise procedures have alternatives. It is therefore the function of the researcher to design his/her study with statistical procedures that will enable him/her to obtain sensible results from the computer printouts.