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Effect of misspecification of random effects distribution on the performance of parameters estimation methods in binary logistic mixed models. (English. French summary) Zbl 1445.62169
Summary: We empirically compared a Bayesian estimation method (Integrated Nested Laplace Approximation, INLA) to three classical estimation methods (Penalized Quasi-Likelihood, PQL; Hierarchical Likelihood Method, HLM and Adaptive Gauss-Hermite Quadrature, AGHQ) under six random effect distributions in binary logistic mixed models. Results revealed that AGHQ and HLM had best performance for all distributions considered in the case of fixed effects. For the random effects, classical methods showed best performance for the symmetric distributions (normal, uniform and mixture-normal). AGHQ, HLM and INLA outperform PQL for normal and uniform distributions whatever the sample considered.
62J05 Linear regression; mixed models
62J12 Generalized linear models (logistic models)
62F15 Bayesian inference
65C05 Monte Carlo methods
Full Text: DOI Euclid
[1] Agresti, A., Caffo, B. and Ohman-Strickland, P. 2004. Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies.Comput. Stat. Data Anal.47, 639-653. · Zbl 1429.62483
[2] Bolker, B. M., Brooks, M. E., Clark, C. J., Geange, S. W., Poulsen, J. R., Stevens, M. H. H., White, J. S. 2009. Generalized linear mixed models: a practical guide for ecology and evolution.Trends in Ecology and Evolution24, 127-135
[3] Breslow N. E. and Lin X. 1995. Bias correction in generalized linear mixed models with a single component of dispersion.Biometrika, 82, 81-91. · Zbl 0823.62059
[4] Capanu M., G¨onen M. and Begg C. B. 2013. An assessment of estimation methods for generalized linear mixed models with binary outcomes.Statistics in Medicine, 32(26),45504566.
[5] Casals M., Langohr K., Carrasco J. L. and R¨onneg ˚ard L. 2015. Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles: a simulation study.Sort39 (2), 281-308. · Zbl 1396.62172
[6] Codd C. L. 2014. A Review and Comparison of Models and Estimation Methods for Multivariate Longitudinal Data of Mixed Scale Type. PhD thesis, Ohio State University, USA, 131p.
[7] Collins D. 2008. The performance of estimation methods for generalized linear mixed models. PhD thesis, School of Mathematics & Applied Statistics-Faculty of Informatics, University of Wollongong, Australia, 223 p.
[8] Drikvandi R., Verbeke G. and Molenberghs G. 2017. Diagnosing misspecification of the random-effects distribution in mixed models.Biometrics, 73, 63-71. · Zbl 1366.62213
[9] Efendi A., Drikvandi R., Verbeke G., Molenberghs G. 2014. A goodness of fit test for the random effects distribution in mixed models.Statistical Methods in Medicine Research, 26, 970-983.
[10] Faraway J. J. 2006. Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models. Second edition. Chapman and Hall/CRC. p. 332. · Zbl 1095.62082
[11] Gbur E. E., Stroup W. W., McCarter K. S., Durham S., Young L. J., Christman M., West M. and Kramer M. 2012. Analysis of Generalized Linear Mixed Models in the Agricultural
[12] B. E. Lokonon, M. Senou and R. Gl‘egl‘e Kaka¨ı, Afrika Statistika, Vol. 15 (1), 2020, pages
[13] 2247-2261. Effect of misspecification of random effects distribution on the performance · Zbl 1273.11083
[14] of parameters estimation methods in binary logistic mixed models.2261 and Natural Resources Sciences, edited by American Society of Agronomy Soil Science Society of America, Crop Science Society of America, 33 p.
[15] Heagerty P.J. and Kurland, B.F. 2001. Misspecified Maximum Likelihood Estimates and Generalised Linear Mixed Models.Biometrika88, 973-985. · Zbl 0986.62060
[16] Hernandez F., Usuga O. and Giampaoli V. 2014. A misspecification simulation study in Poisson mixed model, In: Kneib T, Sobotka F, Fahrenholz J and Irmer H,Proceedings of the 29th International Workshop on Statistical Modelling, (207-212)Gottingen, Germany, 14-18 July 2014.
[17] Hernandez F. and Giampaoli V. 2018. The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model.stats1, 48-76.
[18] Jang M. J., Lee Y., Lawson A. B. and Browne W. J. 2007. A comparison of the hierarchical likelihood and Bayesian approaches to spatial epidemiological modeling.Environmetrics, 18, 809-821.
[19] Kim, Y., Choi, Y.-K., Emery, S. 2013. Logistic regression with multiple random effects: a simulation study of estimation methods and statistical packages.The American Statistician, 67, 171-182
[20] Lee Y. and Nelder J. A. 2001. Hierarchical generalised linear models: a synthesis of generalised linear models, random-effect models and structured dispersions.Biometrika, 88, 987-1006. · Zbl 0995.62066
[21] Lee Y., Nelder J. A. and Pawitan Y. 2006. Generalized linear models with random effects: Unified analysis via H-likelihood.: CRC Press. · Zbl 1110.62092
[22] Liti‘ere S., Alonso A., Molenberghs G. 2008. The impact of a misspecified random-effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models.Statistics in Medicine27, 3125-3144.
[23] Lokonon B E., Beh Mba R., Gbeha M and Gl‘el‘e Kaka¨ı R. 2019. Parameters Estimation Methods in Generalized Linear Mixed Models Applied in Ecology: A Critical Review.International Journal of Engineering and Future Technology16(3), 12-27.
[24] McCulloch C.E. and Neuhaus J.M. 2011. Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter.Stat. Sci.26, 388-402. · Zbl 1246.62169
[25] McNeish D. M. 2016. Estimation Methods for Mixed Logistic Models with Few Clusters. Multivariate Behavioral Research, 51(6), 790-804.
[26] Neuhaus J.M., Hauck W.W. and Kalbfleisch J.D. 1992. The effects of mixture distribution misspecification when fitting mixed-effects logistic models.Biometrika79, 755-762.
[27] Rue H., Martino S. and Chopin N. 2009. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations.Journal of the Royal Statistical Society B, 71, 319-392. · Zbl 1248.62156
[28] Rue H., Riebler A., Sorbye S. H., Illian J. B., Simpson D. P. and Lindgren F. K. 2017. Bayesian computing with INLA: A review.Annual Review of Statistics and Its Application, 4, 395421.
[29] Verbeke G. and Lesaffre E. 1997. The effect of misspecifiying the random-effects distribution in linear mixed models for longitudinal data.Comput. Stat. Data Anal.23, 541-556. · Zbl 0900.62374
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