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Bias‐reduced marginal Akaike information criteria based on a Monte Carlo method for linear mixed‐effects models

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  • Wataru Sakamoto

Abstract

In linear mixed‐effects (LME) models, if a fitted model has more random‐effect terms than the true model, a regularity condition required in the asymptotic theory may not hold. In such cases, the marginal Akaike information criterion (AIC) is positively biased for (−2) times the expected log‐likelihood. The asymptotic bias of the maximum log‐likelihood as an estimator of the expected log‐likelihood is evaluated for LME models with balanced design in the context of parameter‐constrained models. Moreover, bias‐reduced marginal AICs for LME models based on a Monte Carlo method are proposed. The performance of the proposed criteria is compared with existing criteria by using example data and by a simulation study. It was found that the bias of the proposed criteria was smaller than that of the existing marginal AIC when a larger model was fitted and that the probability of choosing a smaller model incorrectly was decreased.

Suggested Citation

  • Wataru Sakamoto, 2019. "Bias‐reduced marginal Akaike information criteria based on a Monte Carlo method for linear mixed‐effects models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(1), pages 87-115, March.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:1:p:87-115
    DOI: 10.1111/sjos.12339
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    Cited by:

    1. Benjamin Säfken & Thomas Kneib, 2020. "Conditional covariance penalties for mixed models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 990-1010, September.
    2. Cantoni, Eva & Jacot, Nadège & Ghisletta, Paolo, 2024. "Review and comparison of measures of explained variation and model selection in linear mixed-effects models," Econometrics and Statistics, Elsevier, vol. 29(C), pages 150-168.

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