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 interand intra-individual heteroscedasticity both exist.

We develop a dynamic Bayesian model for clickthrough and conversion probabilities of paid search advertisements. These probabilities are subject to changes over time, due to e.g. changing consumer tastes or new product launches. Yet, there is little empirical research on these dynamics. Gaining insight into the dynamics is crucial for advertisers to develop effective search engine advertising (SEA) strategies. Our model deals with dynamic SEA environments for a large number of keywords: it allows for time-varying parameters, seasonality, data sparsity and position endogeneity. The model also discriminates between transitory and permanent dynamics. Especially for the latter case, dynamic SEA strategies are required for long-term profitability. We illustrate our model using a 2 year dataset of a Dutch laptop selling retailer. We find persistent time variation in clickthrough and conversion probabilities. The implications of our approach are threefold. First, advertisers can use it to obtain accurate daily estimates of clickthrough and conversion probabilities of individual ads to set bids and adjust text ads and landing pages. Second, advertisers can examine the extent of dynamics in their SEA environment, to determine how often their SEA strategy should be revised. Finally, advertisers can track ad performances to timely identify when keywords' performances change.

In this paper, we develop a general method for heterogeneous variable selection in Bayesian nonlinear panel data models. Heterogeneous variable selection refers to the possibility that subsets of units are unaffected by certain variables. It may be present in applications as diverse as health treatments, consumer choice-making, macroeconomics, and operations research. Our method additionally allows for other forms of cross-sectional heterogeneity. We consider a two-group approach for the model's unitspecific parameters: each unit-specific parameter is either equal to zero (heterogeneous variable selection) or comes from a Dirichlet process (DP) mixture of multivariate normals (other cross-sectional heterogeneity). We develop our approach for general nonlinear panel data models, encompassing multinomial logit and probit models, poisson and negative binomial count models, exponential models, among many others. For inference, we develop an efficient Bayesian MCMC sampler. In a Monte Carlo study, we find that our approach is able to capture heterogeneous variable selection whereas a "standard" DP mixture is not. In an empirical application, we find that accounting for heterogeneous variable selection and non-normality of the continuous heterogeneity leads to an improved in-sample and out-of-sample performance and interesting insights. These findings illustrate the usefulness of our approach.