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, 41 (9), 2001-2010

Longitudinal Data Analysis Using Bayesian-frequentist Hybrid Random Effects Model

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Longitudinal Data Analysis Using Bayesian-frequentist Hybrid Random Effects Model

Le Chen et al. J Appl Stat.

Abstract

The mixed random effect model is commonly used in longitudinal data analysis within either frequentist or Bayesian framework. Here we consider a case, we have prior knowledge on partial-parameters, while no such information on rest. 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 practices, we often know partial prior information such as, covariates of age, gender, and etc. These information can be used, and get accurate estimations in mixed random-effects model. 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 Maximum likelihood estimation (MLE) were very close each other. The estimated θ values in with partial prior information model (HYB) were more closer to true θ values, and shown less variances than without partial prior information in MLE. To compare with true θ values, the mean square of errors (MSE) are much less in HYB than in MLE. This advantage of HYB is very obvious in longitudinal data with small sample size. The methods of HYB and MLE are applied to a real longitudinal data for illustration.

Keywords: Hybrid; Longitudinal data; Simulation.

Figures

Figure 1
Figure 1
Estimated θ values (Y-axis) and Simulation data sets from 1 to 3000 (X-axis). The red dot lines presented true θ0, blue dots present estimated values in HYB model with partial prior information, Gray dots present estimated values in MLE model without prior information. From top to bottom presents number individuals of 5, 10, 25, 50, 100, 300, and 500, respectively
Figure 2
Figure 2
Mean square Error values (Y-axis) with true θ0 by using HYB (red) and MLE (blue) models. X-axis presents number of individuals in simulation studies. From left to right presents (θ0,1, …, θ0,5), respectively. (θ1, θ2, θ3) without prior information, and (θ4, θ5) with prior information
Figure 3
Figure 3
Ratio of MSE in MLE and MSE in HYB (Y-axis). X-axis presents (θ1, …, θ5). (θ1, θ2, θ3) without prior information, (θ4, θ5) with prior information

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