A multinomial and rank-ordered logit model with inter- and intra-individual heteroscedasticity

The heteroscedastic logit model is useful to describe choices of individuals when the randomness in the choice-making varies over time. For example, during surveys individuals may become fatigued and start responding more randomly to questions as the survey proceeds. Or when completing a ranking amongst multiple alternatives, individuals may be unable to accurately assign middle and bottom ranks. The standard heteroscedastic logit model accommodates such behavior by allowing for changes in the signal-to-noise ratio via a time-varying scale parameter. In the current literature, this time-variation is assumed equal across individuals. Hence, each individual is assumed to become fatigued at the same time, or assumed to be able to accurately assign exactly the same ranks. In most cases, this assumption is too stringent. In this paper, we generalize the heteroscedastic logit model by allowing for differences across individuals. We develop a multinomial and a rank-ordered logit model in which the time-variation in an individual-specific scale parameter follows a Markov process. In case individual differences exist, our models alleviate biases and make more efficient use of data. We validate the models using a Monte Carlo study and illustrate them using data on discrete choice experiments and political preferences. These examples document that inter- and intra-individual heteroscedasticity both exist.