Linear mixed models (LMM) (Laird and Ware, 1982) are widely used in longitudinal data analysis as they incorporate random effects to deal with group-specific heterogeneity. Data involving repeated observations of the same variables are common in epidemiology, medical statistics and many other fields. Likelihood-based methods are often used to make inference for (generalized) linear mixed models (Bates et al., 2000; Gumedze and Dunne, 2011). Schelldorfer et al. (2011) and Groll and Tutz (2014) introduced separately the L1-penalized estimation for high-dimensional linear mixed models. Fong et al. (2010) argued that for small sample sizes likelihood-based inference can be unreliable with variance components being difficult to estimate and suggested to use the Bayesian method. When the random effects distribution is misspecified, the resulting maximum likelihood estimators are inconsistent and biased (Neuhaus et al., 1992; Heagerty and Kurland, 2001; Litière et al., 2008). Fahrmeir and Lang (2001) presented a fully Bayesian inference via Markov Chain Monte Carlo (MCMC) simulation in generalized additive and semiparametric mixed models. Rosa et al. (2003) described a normal/independent residual distributions for robust inference and suggested also the Bayesian framework. Bayesian inference for mixed models can be conducted with for example BayesX, a program with MCMC simulation techniques (Lang and Brezger, 2000).