The Analysis of Brain Size under the Logit Model for Categorical Explanatory Data and Mixed Data

Abstract

The data and the involved factors of this analysis came from website
http://lib.stat.cmu.edu/ on ???Brain Size Data and Intelligence?? which belongs to Willerman et al.
(1991). They collected a sample of 38 right-handed Ango introductory psychology students at
Southwestern University. The students had indicated no history of alcoholism, unconsciousness,
brain damage, epilepsy, or heart disease. The research was to study the effect of explanatory
variables on the dichotomous response of the student???s brain size, where one group had less than
900,000 pixels and the other had more than or equal to 900,000 pixels. The explanatory variables
were gender, full scale IQ scores (FSIQ), verbal IQ scores (VIQ), performance IQ scores (PIQ),
weight and height. The analysis of data was based on logit models that consisted of two cases: the
grouped explanatory variables and the ungrouped explanatory variables. The selection of models
under the stepwise method was performed using SAS version 9.1.
The results revealed that the significant effect factors at ?? = 0.05 to the brain size of the
students were Gender and Performance IQ scores (PIQ). The logit model in the case of categorical
explanatory variable (logit (P??(x)) = -4.003+4.581Gender-1.774PIQ_Group) was preferable to the
logit model in the case of ungrouped explanatory variable (logit (P??(x)) = 0.034+4.560Gender-
0.063PIQ_Group). The likelihood ratio (G2 ), AIC and BIC statistics of the first case were less than
those of the second case. Moreover, Somers???D, Gamma, and c statistics of the first case were also
outperformed, including the magnitude of residuals. The residual plots of both cases were found
independently scattered.

Keywords: Logit Models, Dichotomous, Categorical Explanatory