Standard ordinary linear model cannot handle grouping structure data. This induces a correlation structure through the error term in this model. Therefore mixed effect models often allow the modeling of such structural data setting. This study proposes different estimation algorithms in linear and nonlinear mixed effects models when the grouping structure data are available. I in fact prove a consistency and oracle optimality result in these grounds, and develop algorithms with provable numerical convergence. Further, I demonstrate the performance of the different proposed algorithms on the Landsat ETM+ scene data set.