The benefits of incorporating utility dependencies in finite mixture probit models

We propose an application of a new finite mixture multinomial conditional probit (FM-MNCP) model that accommodates preference heterogeneity and explicitly accounts for utility dependencies between choice alternatives considering both local and background contrast effects. The latter is accomplished by using a one-factor structure for segment-specific covariance matrices allowing for nonzero off-diagonal covariance elements. We compare the model to a finite mixture multinomial independent probit (FM-MNIP) model that as well accommodates heterogeneity but assumes independence. That way, we address the potential benefits of a model that additionally accounts for dependencies over a model that accommodates heterogeneity only. Our model comparison is based on empirical data for smoothies and is assessed in terms of fit, holdout validation, and market share predictions. One of the main findings of our empirical study is that allowing for utility dependencies may counterbalance the effects of considering heterogeneity, and vice versa. Additional findings from a simulation study indicate that the FM-MNCP model outperforms the FM-MNIP model with respect to parameter recovery.