Nonlinear Effects in Brand Choice Models : Comparing Heterogeneous Latent Class to Homogeneous Nonlinear Models

We investigate whether the latent class multinomial logit choice model with segmentspecific linear utility functions implies effects that are similar to those of parametric homogeneous nonlinear models given that this latent class model performs at least as well. The two nonlinear models have higher-order polynomial (i.e. quadratic and cubic) and piecewise linear utility functions, respectively. Piecewise linear functions are represented by linear splines and can reproduce threshold, saturation and asymmetric effects. We evaluate models and their variants using a tenfold cross-validation. As criterion we use the geometric mean of choice probabilities across all purchases for the brand actually chosen. We measure the similarity of effects between two models by the absolute differences of choice probabilities implied by these models for varying values of a predictor. Logits of choice probabilities provide a more detailed insight into the effects implied by models. For the data set we analyze, the latent class model with linear utility is clearly superior to the two homogeneous nonlinear models. Overall, the effects implied by the latent class models are similar to those of the two parametric nonlinear models