The Effect Of Divisive Analysis Clustering Technique on Goodness-Of-Fit Test for Multinomial Logistic Regression

Abstract

The relationship between a categorical dependent variable and independent variable(s) are usually modelled using the logistic regression method. There are three types of logistic regression: binary, multinomial, and ordinal. When there is two cayegories of  dependent variable, binary logistic regression is used while when there is more than two nominal categories of dependent variable, multinomial logistic regression is employed. Ordinal logistic regression is used when the dependent variable contains more than two ordinal categories. All regression models should be checked after being fitted to the data to see whether it matches the data or not. For multinomial logistic regression, there are numbers of goodness-of-fit test proposed and can be used to evaluate the fit of the model. One of the proposed tests is based on clustering partitioning strategy. Howevert, the proposed test  only considered agglomerative nesting (AGNES) hierarchical clustering technique, which is Ward’s to group the data. The performance of the test using divisive analysis (DIANA) hierarchical clustering technique is remain unknown. Thus, this study attempts to examine the power of the test using divisive analysis clustering technique. Simulation technique is used to evaluate the performance of the test. The results showed that that the test using DIANA clustering technique has managed type I error and the mean are close to hypothesized values. It also has almost equivalent power with the test using Ward’s clustering technique in detecting omission of a quadratic term. However, the test using Ward’s clustering technique shows noticeably higher power in detecting omission of an interaction term.