ALGORITMA FORWARD DAN BACKWARD BERDASARKAN ENTROPI SEBAGAI ALTERNATIF UNTUK ALGORITMA SEGMENTASI CHAID (Chi-squared Automatic Interaction Detection); FORWARD AND BACKWARD ALGORITHMS BASED ON ENTROPY AS ALTERNATIVES FOR CHAID SEGMENTATION ALGORITHM

Siti Nurul Hasana, Suryo Guritno

2013 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

CHAID (Chi-squared Automatic Interaction Detection), proposed by Kass in 1980, is an algorithm to detect, in automatic way, the interaction between two or more predictors and its role in the explanation of the dependent variable. But, this is not always true when Simpson’s paradox is present. This is due to the fact that CHAID is a forward selection algorithm based on the marginal counts rather than in considering the conditional independent. In other words, CHAID uses marginal information by examination of the table of marginal totals formed by summing over the remaining factors, but it is well known that collapsibility is not always licit. This paper will propose alternative algorithms, they are Forward and Backward algorithms based on entropy. The Forward algorithm is generated by procedure in which is similar to the classic CHAID procedure, except that it uses the likelihood ratio to test for independence and entropy to evaluate the changes. The Backward algorithm is started with the full set of predictors and then continued with eliminating the predictors progressively. The elimination procedure is based on conditional independence and the use of entropy to test it. From both algorithms, the Backward is the suggested algorithm as alternative for CHAID segmentation algorithm, because it is more possible to elude the phenomenon of Simpson’s Paradox.

Kata Kunci : CHAID; Paradoks Simpson; Pelipatan Tabel (Collapsibility); Entropi; Algoritma Forward; Algoritma Backward