Variable selection via the composite likelihood method for multilevel longitudinal data with missing responses and covariates

Abstract Longitudinal data with multilevel structures are commonly collected when following up subjects in clusters over a period of time. Missing values and variable selection issues are common for such data. Biased results may be produced if incompleteness of data is ignored in the analysis. On the other hand, incorporating a large number of irrelevant covariates into inferential procedures may lead to difficulty in computation and interpretation. A unified penalized composite likelihood framework is developed to handle data with missingness and variable selection issues. It is flexible to handle the situation where responses and covariates are missing not simultaneously under the assumption of missing not at random. The method is justified both rigorously with theoretical results and numerically with simulation studies. The method is also applied to the Waterloo Smoking Prevention Project data.

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