This dissertation addresses the problem of simultaneous variable selection and estimation in the random-intercepts model with the first-order lag response. This type of model is commonly used for analyzing longitudinal data obtained through repeated measurements on individuals over time. This model uses random effects to cover the intra-class correlation and the first lagged response to address the serial correlation, which are the two common sources of dependency in longitudinal data. We demonstrate that the conditional likelihood approach by ignoring the correlation among random effects and initial responses can lead to biased regularized estimates. In addition, we demonstrate that joint modeling of initial responses and subsequent observations in the structure of the dynamic random-intercepts model leads to both consistency and Oracle properties of regularized estimators. We present theoretical results in both low and high-dimensional settings and eva‎luate regularized estimators’ performances by conducting simulation studies and analysis of a real data set. Moreover, a solution is presented to obtain consistent estimates in random intercept models with q-order lag responses, which can be used to address the issue of variable selection in these models.

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ايرج كاظمي , عبدالرحمن راسخ , صفيه محمودي