Bayesian approach to inference and variable selection for misclassified and under-reported response models.

Response partial missingness is a problem in studies conducted in a variety of disciplines. We investigate the impact ignoring response partial missingness has on determining a subset of significant covariates in non-linear regression. In particular, we consider non-differential misclassification in logistic regression and non-differential under-reporting in Poisson regression. Differential misclassification and differential under-reporting are also addressed but in less detail. We then develop a Bayesian approach to select significant covariates while accounting for the partial missingness. Examples of response partial missingness in which the variable selection method is applied include determining the factors that contribute to whether or not an individual will stop smoking and how many days an individual is absent from work.