Component-Based Regularization of Multivariate Generalized Linear Mixed Models

References

• Anderson, D. A., and Aitkin, M. (1985), “Variance Component Models with Binary Response: Interviewer Variability,” Journal of the Royal Statistical Society, Series B, 47, 203–210. DOI:10.1111/j.2517-6161.1985.tb01346.x.
   Google Scholar
• Bates, D., Mächler, M., Bolker, B., and Walker, S. (2015), “Fitting Linear Mixed-effects Models Using lme4,” Journal of Statistical Software, 67, 1–48.
   Web of Science ®Google Scholar
• Breslow, N. E., and Clayton, D. G. (1993), “Approximate Inference in Generalized Linear Mixed Models,” Journal of the American Statistical Association, 88, 9–25. DOI:10.1080/01621459.1993.10594284.
   Web of Science ®Google Scholar
• Bry, X., Trottier, C., Mortier, F., and Cornu, G. (2018), “Component-based Regularisation of a Multivariate GLM With a Thematic Partitioning of the Explanatory Variables,” Statistical Modelling, in press. DOI:10.1177/1471082X18810114.
   PubMedGoogle Scholar
• Bry, X., Trottier, C., Mortier, F., Cornu, G., and Verron, T. (2014), “Extending SCGLR to Multiple Regressor-groups: The Theme-SCGLR Method,” in Proceedings of the eighth International Conference on Partial Least Squares and Related Methods, Paris, France.
   Google Scholar
• Bry, X., Trottier, C., Mortier, F., Cornu, G., and Verron, T. (2016), The Multiple Facets of Partial Least Squares and Related Methods, Chapter Supervised Component Generalized Linear Regression with Multiple Explanatory Blocks: THEME-SCGLR, pp. 141–154. Springer International Publishing.
   Google Scholar
• Bry, X., Trottier, C., Verron, T., and Mortier, F. (2013), “Supervised Component Generalized Linear Regression Using a PLS-extension of the Fisher Scoring Algorithm,” Journal of Multivariate Analysis, 119, 47–60. DOI:10.1016/j.jmva.2013.03.013.
   Web of Science ®Google Scholar
• Bry, X. and Verron, T. (2015). THEME: THEmatic Model Exploration Through Multiple Co-structure Maximization,” Journal of Chemometrics, 29, 637–647. DOI:10.1002/cem.2759.
   Web of Science ®Google Scholar
• Clayton, D. G. (1996), “Generalized Linear Mixed Models,” in Markov chain Monte Carlo in practice, eds. W. R. Golks, S. Richardson, and D. J. Spiegelhalter, New York: Springer/Chapman and Hall/CRC. Springer, pp. 275–301.
   Google Scholar
• Cornu, G., Mortier, F., Trottier, C., and Bry, X. (2018), SCGLR: Supervised Component Generalized Linear Regression. R package version 3.0.
   Google Scholar
• Eliot, M., Ferguson, J., Reilly, M. P., and Foulkes, A. S. (2011), “Ridge Regression for Longitudinal Biomarker Data,” The International Journal of Biostatistics, 7, 1–11. DOI:10.2202/1557-4679.1353.
   Google Scholar
• Fahrmeir, L. and Tutz, G. (1994), Multivariate Statistical Modelling Based on Generalized Linear Models, Springer Series in Statistics, London: Springer-Verlag.
   Google Scholar
• Groll, A. (2017), glmmLasso: Variable Selection for Generalized Linear Mixed Models by L1-Penalized Estimation, R package version 1.5.1.
   Google Scholar
• Groll, A., and Tutz, G. (2014), “Variable Selection for Generalized Linear Mixed Models by L1 -penalized Estimation,” Statistics and Computing, 24, 137–154. DOI:10.1007/s11222-012-9359-z.
   Web of Science ®Google Scholar
• Hadfield, J. D. (2010), “MCMC Methods for Multi-Response Generalized Linear Mixed Models: The MCMCglmm R Package,” Journal of Statistical Software, 33, 1–22.
   PubMed Web of Science ®Google Scholar
• Henderson, C. R. (1975), “Best Linear Unbiased Estimation and Prediction Under a Selection Model,” Biometrics, 31, 423–447. DOI:10.2307/2529430.
   PubMed Web of Science ®Google Scholar
• Hoerl, A. E., and Kennard, R. W. (1970), “Ridge Regression: Biased Estimation for Nonorthogonal Problems,” Technometrics, 12, 55–67. DOI:10.1080/00401706.1970.10488634.
   Web of Science ®Google Scholar
• Knudson, C. (2016), Monte Carlo Likelihood Approximation for Generalized Linear Mixed Models, PhD thesis, University of Minnesota.
   Google Scholar
• McCullagh, P., and Nelder, J. (1989), Generalized Linear Models (2nd ed.), Chapman & Hall/CRC Monographs on Statistics & Applied Probability. London: Taylor & Francis.
   Google Scholar
• McCulloch, C. E. (1997), “Maximum Likelihood Algorithms for Generalized Linear Mixed Models,” Journal of the American Statistical Association, 92, 162–170. DOI:10.1080/01621459.1997.10473613.
   Web of Science ®Google Scholar
• Nelder, J. A., and Wedderburn, R. W. M. (1972), “Generalized Linear Models,” Journal of the Royal Statistical Society, Series A, 135, 370–384. DOI:10.2307/2344614.
   Web of Science ®Google Scholar
• Pinheiro, J. C., and Bates, D. M. (1995), “Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model,” Journal of Computational and Graphical Statistics, 4, 12–35. DOI:10.2307/1390625.
   Google Scholar
• R Core Team (2017), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Schall, R. (1991), “Estimation in Generalized Linear Models With Random Effects,” Biometrika, 78, 719–727. DOI:10.1093/biomet/78.4.719.
   Web of Science ®Google Scholar
• Schelldorfer, J., Meier, L., and Bühlmann, P. (2014), “GLMMLasso: An Algorithm for High-Dimensional Generalized Linear Mixed Lodels Using ℓ1 -Penalization,” Journal of Computational and Graphical Statistics, 23, 460–477. DOI:10.1080/10618600.2013.773239.
   Web of Science ®Google Scholar
• Shun, Z., and McCullagh, P. (1995), “Laplace Approximation of High Dimensional Integrals,” Journal of the Royal Statistical Society, Series B, 57, 749–760. DOI:10.1111/j.2517-6161.1995.tb02060.x.
   Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection Via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288. DOI:10.1111/j.2517-6161.1996.tb02080.x.
   Google Scholar
• Zeger, S. L., and Karim, M. R. (1991), “Generalized Linear Models With Random Effects; A Gibbs Sampling Approach,” Journal of the American Statistical Association, 86, 79–86. DOI:10.1080/01621459.1991.10475006.
   Web of Science ®Google Scholar
• Zhang, Y., Zhou, H., Zhou, J., and Sun, W. (2017), “Regression Models for Multivariate Count Data,” Journal of Computational and Graphical Statistics, 26, 1–13. DOI:10.1080/10618600.2016.1154063.
   PubMed Web of Science ®Google Scholar
• Zou, H., and Hastie, T. (2005). “Regularization and Variable Selection Via the Elastic Net,” Journal of the Royal Statistical Society, Series B, 67, 301–320. DOI:10.1111/j.1467-9868.2005.00503.x.
   Google Scholar