A Comparative Analysis of Some Link Functions for Binomial Regression Models with Applications to Bioassay Data

Abstract

The response variable that represents the number of successes in a series of trials is too complex for classical linear regression to handle. On the other hand, binomial regression is seen to be more suitable, especially when dealing with bioassay data. In the context of the Generalised Linear Model (GLM), binomial regression is examined using certain link functions. The link functions logit, probit, complementary log-log (cloglog), Laplace, and Cauchy are frequently used for binomial regressions. While clog log, Laplace, and Cauchy are asymmetrical link functions, logit and probit are symmetrical. The study thereby aims to evaluate the performance of these link functions according to the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) indices. The study sheds light on how well these link functions work in the field of bioassays for modelling reactions with a binary result by expanding the analysis to the particular application of bioassay data. Additionally, the study incorporates the dose-response model that is frequently used in bioassay investigations. This approach examines the link between administered dosages and observed reactions during a set time period by exposing various groups to varying quantities of toxins or drugs.