Alzheimer’s disease (AD) is a neurodegenerative disease with an increasing rate of prevalence in the United States. There is currently no cure for AD, and there is therefore interest in characterizing AD in order to develop disease modifying therapies. Characterization of AD can be facilitated by Bayesian feature selection models, which allow us to identify (possibly high-dimensional) patient feature data that are associated with longitudinal AD outcome data (e.g., cognitive scores over time). However, current Bayesian feature selection models are limited by salient complexities arising in the study of longitudinal AD outcome data. In particular, there are no Bayesian feature selection models that can simultaneously account for irregularly-spaced longitudinal outcome data, account for feature data group structure, and specify time-varying feature parameters. Accounting for these complexities can lead to a feature selection model with superior performance. We therefore developed a Bayesian linear mixed model for feature selection which addresses these complexities. We applied our novel approach to analyze longitudinal cognitive scores in the Alzheimer's Disease Neuroimaging Initiative participants with multimodal feature data, including neuroimaging, cerebrospinal fluid biomarkers, genetic markers, neurological diagnoses, and demographics. We found that our model identifies a parsimonious subset of patient feature data associated with rate of cognitive decline, and moreover by accounting for these aforementioned complexities, provides improved precision of feature parameter estimates. Our model therefore represents an effective tool that researchers can use to perform feature selection given complexities arising in the longitudinal study of AD.