Multinomial Regression in Insect choice studies: A case of Leaf miner Parasitoids' choices

Abstract

Researchers are often confronted with multinomial data in insect choice studies. Common choice models available to researchers for analysis of multinomial data include multinomial logit (MNL) and multinomial probit model (MNP). MNL relies on the Independence from Irrelevant Alternatives (IIA) assumption which is violated when choices are correlated resulting in overestimating the probability of selecting correlated alternatives. The more flexible MNP model relaxes IIA assumption and allows modelling correlated errors. Little evidence exists on the performance of multinomial logit and multinomial probit models on insect choice data. This study investigated the performance of the two models in terms of predictive accuracy and goodness of fit on choice data collected in a laboratory experiment involving leaf miner parasitoids. Sum of squared deviations of predicted probabilities from observed probabilities was used to evaluate predictive accuracy. Akaike Information Criterion and Bayesian Information Criterion were used to evaluate goodness of fit. The findings indicated that MNP resulted in a higher predictive accuracy than MNL. The observed predictive accuracy for MNP came with a cost on the goodness of fit since MNL had a better fit to the data than MNP model from the Bayesian Information Criterion statistics despite violation of IIA assumption. There was little evidence that imposing homoskedastic restriction on the covariance matrix of the MNP model improved predictive accuracy and goodness of fit. MNL and MNP models resulted in qualitatively similar predicted probabilities. These findings suggest recommending use of the more analytically-tractable MNL in modelling insect choice data when IIA assumption is violated