A Review of Some Goodness-of-Fit Tests for Logistic Regression Model

Abstract

Some goodness-of-fit statistic (Likelihood ratio test, Pseudo (R2) test, Hosmer-lemeshow test and Chi-square test) were used to determine model fit in binary logistic regression, their estimates were compared to each other, to determine their performances.  From our analysis the likelihood ratio test, the pseudo (R2) test and the chi-square test, produced results that are similar and shows the presences of poor fit, with  model1 being the most fit of the three models. Even though hosmer-lemeshow test produced a P-value that is very low, indicating the presence of poor fit in all three models, the differences between these models were not revealed, because the test produced the same estimates for the three models. The likelihood ratio test produced results that are similar to the chi-square test. We also observed that the goodness-of-fit parameters (Null Deviances, Residual Deviance and the Alkaike Information Criteria (AIC)), that accompany model formation in R-statistical software produced result that align with the goodness-of-fit statistic used, the set back is that the summary provided by this parameters, does not reveal model similarities.