A comparison of some link functions for binomial regression models with application to school drop-out rates in East Java

Abstract

Classical linear regression is inadequate when the response variable is the number of success in a sequence of experiments. However, the binomial regression is considered more suitable. Binomial regression can be analyzed through the Generalized Linear Model (GLM) with a specifics link functions. Some of link functions usually used in binomial regressions are logit, probit, and complimentary log-log (cloglog). Both logit and probit are symmetrical links functions, while cloglog is asymmetrical. This study aims to compare all three link functions and evaluate them by employing the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) index. All three link function will be applied for binomial regression models using simulation and real data on school drop-out rates in East Java Indonesia. Based on the AIC and BIC index, it is evidenced that the cloglog gives the best performance than the logit and probit link function for the school drop-out rates model. Therefore, this case is considered appropriate using the asymmetrical assumptions.