Abstract
We focus on the development of model selection criteria in linear mixed models. In particular, we propose the model selection criteria following the Mallows’ Conceptual Predictive Statistic (Cp) [1] [2] in linear mixed models. When correlation exists between the observations in data, the normal Gauss discrepancy in univariate case is not appropriate to measure the distance between the true model and a candidate model. Instead, we define a marginal Gauss discrepancy which takes the correlation into account in the mixed models. The model selection criterion, marginal Cp, called MCp, serves as an asymptotically unbiased estimator of the expected marginal Gauss discrepancy. An improvement of MCp, called IMCp, is then derived and proved to be a more accurate estimator of the expected marginal Gauss discrepancy than MCp. The performance of the proposed criteria is investigated in a simulation study. The simulation results show that in small samples, the proposed criteria outperform the Akaike Information Criteria (AIC) [3] [4] and Bayesian Information Criterion (BIC) [5] in selecting the correct model; in large samples, their performance is competitive. Further, the proposed criteria perform significantly better for highly correlated response data than for weakly correlated data.
Highlights
With the development in data science over the past decades, people become more aware of the complexity ofHow to cite this paper: Wenren, C., Shang, J.F. and Pan, J.M. (2016) Marginal Conceptual Predictive Statistic for Mixed Model Selection
We observe that corresponding to each φ, the IMCp outperforms the MCp, and both outperform marginal AIC (mAIC) and mBIC in selecting the correct model for small samples
The simulation results illustrate that the proposed criteria MCp and IMCp outperform mAIC and mBIC when the observations are highly correlated in small samples
Summary
With the development in data science over the past decades, people become more aware of the complexity ofHow to cite this paper: Wenren, C., Shang, J.F. and Pan, J.M. (2016) Marginal Conceptual Predictive Statistic for Mixed Model Selection. (2016) Marginal Conceptual Predictive Statistic for Mixed Model Selection. In longitudinal data, observations are usually recorded from the same individual over time. It is reasonable to assume that correlation exists among the observations from the same individual and linear mixed models are appropriately utilized for modeling such data. Since linear mixed models are extensively used, mixed model selection plays an important role in statistical literature. The aim of mixed model selection is to choose the most appropriate model from a candidate pool in the mixed model setting. To facilitate this task, a variety of model selection criteria are employed to implement the selection process
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