TY - JOUR
T1 - Fit Adequacy of Dichotomous Logit Response Models of the Regressor Bernoulli and Binomial Probability Distributions
AU - Ugwuanyim, G. Uzodinma
AU - Ogbonna, Chukwudi Justin
JF - Bulletin of Mathematical Sciences and Applications
VL - 16
SP - 38
EP - 48
SN - 2278-9634
PY - 2016
PB - SciPress Ltd
DO - 10.18052/www.scipress.com/BMSA.16.38
UR - https://localhost:44305/BMSA.16.38
KW - Base Rate
KW - Bernoulli Distribution
KW - Binomial Distribution
KW - Goodness-of-Fit
KW - Logit Models
KW - Quantal Variables
AB - Logit models belong to the class of probability models that determine discrete probabilities over a limited number of possible outcomes. They are often called ‘Quantal Variables’ or ‘Stimulus and Response Models’ in Biological Literature. The conventional R2 measure of goodness-of-fit is problematic in logit models. This has therefore led to the proposal of several alternative goodness-of-fit measures. But researchers in this area have identified the base rate problem in using these several alternative goodness-of-fit measures. This research is an extension of work done by people in this area. Specifically, this research is aimed at investigating the goodness-of-fit performances of eight statistics using the Bernoulli and Binomial distributions as explanatory variables under various scenarios. The study will draw conclusions on the “best” fit. The data for the study was generated through simulation and analysed using the multiple correlation analysis. The findings clearly show that for the Bernoulli Distribution, the goodness-of-fit statistics to use are: RO2, RC2, RM2 and λp; and for the Binomial Distribution, the goodness-of-fit statistics to use are: and RN2 and λp. RO2 stood out as the “best” goodness-of-fit statistics.
ER -