Longitudinal data analysis using Bayesian-frequentist hybrid random effects model

The mixed random effect model is commonly used in longitudinal data analysis within either frequentist or Bayesian framework. Here we consider a case, in which we have prior knowledge on partial parameters, while no such information on the rest of the parameters. Thus, we use the hybrid approach on the random-effects model with partial parameters. The parameters are estimated via Bayesian procedure, and the rest of parameters by the frequentist maximum likelihood estimation (MLE), simultaneously on the same model. In practice, we often know partial prior information such as, covariates of age, gender, etc. These information can be used, and accurate estimations in mixed random-effects model can be obtained. A series of simulation studies were performed to compare the results with the commonly used random-effects model with and without partial prior information. The results in hybrid estimation (HYB) and MLE were very close to each other. The estimated θ values in with partial prior information model (HYB) were more closer to true θ values, and showed less variances than without partial prior information in MLE. To compare with true θ values, the mean square of errors are much less in HYB than in MLE. This advantage of HYB is very obvious in longitudinal data with a small sample size. The methods of HYB and MLE are applied to a real longitudinal data for illustration purposes.