On Bayesian model and variable selection using MCMC
Statistics and Computing
Bayesian parsimonious covariance estimation for hierarchical linear mixed models
Statistics and Computing
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We reanalyze endogenous sample selection in the context of customer scoring, targeting, and influencing decisions. Scoring relies on ordered lists of probabilities that customers act in a way that contributes revenues, e.g., purchase something from the firm. Targeting identifies constrained sets of covariate patterns associated with high probabilities of these acts. Influencing aims at changing the probabilities that individual customers act accordingly through marketing activities. We show that successful targeting and influencing decisions require inference that controls for endogenous selection, whereas scoring can proceed relatively successfully based on simpler models that provide local approximations, capitalizing on spurious effects of observed covariates. To facilitate the type of inference required for targeting and influencing, we develop a prior that frees the analyst from having to specify often arbitrary exclusion restrictions for model identification a priori or to explicitly compare all possible models. We cover exclusions of observed as well as unobserved covariates that may cause the successive selections to be dependent. We automatically infer the dependence structure among selection stages using Markov chain Monte Carlo-based variable selection, before identifying the scale of latent variables. The adaptive parsimony achieved through our prior is particularly helpful in applications where the number of successive selections exceeds two, a relevant but underresearched situation.