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Abstract:
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A crucial problem in building a multiple regression model is the selection of predictors to include. Here, we develop two strategies for variable selection in logistic and probit regression models with missing values on explanatory variables. One approach, which we call "impute, then select" (ITS), involves initially performing multiple imputation and then applying Bayesian variable selection to the multiply imputed data sets. The second strategy, which we call "simultaneously impute and select" (SIAS), is to conduct Bayesian variable selection and missing data imputation simultaneously within one Markov Chain Monte Carlo (MCMC) process. For illustration purposes, ITS and SIAS are applied to a data set from Los Angeles Foster Care Study where some explanatory variables have a substantial amount of missing data.
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