Using a heterogeneous multinomial probit model with a neural net extension to model brand choice

The multinomial probit model introduced here combines heterogeneity across households with flexibility of the (deterministic) utility function. To achieve flexibility deterministic utility is approximated by a neural net of the multilayer perceptron type. A Markov Chain Monte Carlo method serves to estimate heterogeneous multinomial probit models which fulfill economic restrictions on signs of (marginal) effects of predictors (e.g., negative for price). For empirical choice data the heterogeneous multinomial probit model extended by a multilayer perceptron clearly outperforms all the other models studied. Moreover, replacing homogeneous by heterogeneous reference price mechanisms and thus allowing price expectations to be formed differently across households also leads to better model performance. Mean utility differences and mean elasticities w.r.t. price and price deviation from reference price demonstrate that models with linear utility and nonlinear utility approximated by a multilayer perceptron lead to very different implications for managerial decision making.