Abstarct: ‎Longitudinal ‎data are ‎those ‎observations ‎in ‎which ‎measurements ‎of ‎each ‎experiment ‎unit‎s repeats over the time. Linear mixed model is one of the tools used to analyze such data. However, pre sense of multicolinearity causes to use shrinkage methods for analysis. In this dissertation, the combination of linear mixed elliptical models with shrinkage methods such as ridge and Liu is considered for analysis purposes. The performance of the proposed estimators is evaluated using simulation and real data analysis.