An empirical comparison of the validity of a neural net based multinomial logit choice model to alternative model specifications

Abstract

Applications of choice models to brand purchase data as a rule specify a linear deterministic utility function. We estimate deterministic utility by means of a neural net able to approximate any continuous multivariate function and its derivatives to a desired level of precision. We compare this model to related alternatives both with linear and nonlinear utility functions. Alternatives with nonlinear utility functions are based on generalized additive modeling and Taylor series expansion, respectively. We analyze purchase data of the six largest brands in terms of market share for two product groups. Neural choice models outperform the alternative models studied w.r.t. posterior probabilities. They also attain the best crossvalidated log-likelihood values. These results demonstrate that the increase in complexity caused by the neural choice model is justified by higher validity. In the empirical study the neural choice models imply elasticities different from those obtained by linear utility multinomial logit models for several predictors. Neural choice models discover inversely S-shaped, saturation and interaction effects on utility.