References
- Goldstein H. Multilevel cross-classified models. Sociol Methods Res. 1994;22:364–375. doi: 10.1177/0049124194022003005
- Leckie G. Cross-classified multilevel models – concepts. LEMMA VLEModule 12, 2013. p. 1–60 [cited 2015 Nov 4]. Available from: http://www.bristol.ac.uk/cmm/learning/course.html
- Browne WJ, Goldstein H, Rasbash J. Multiple membership multiple classification (MMMC) models. Statist Model. 2001;1:103–124. doi: 10.1191/147108201128113
- Rasbash J, Goldstein H. Efficient analysis of mixed hierarchical and cross-classified random structures using a multilevel model. J Educ Behav Statist. 1994;19:337–350. doi: 10.3102/10769986019004337
- Van den Noortgate W, de Boeck P, Meukders M. Cross-classification multilevel logistic models in psychometrics. J Educ Behav Statist. 2003;28:369–386. doi: 10.3102/10769986028004369
- Luo W, Kwok O. The impacts of ignoring a crossed factor in analyzing cross-classified data. Multivariate Behav Res. 2009;44:182–212. doi: 10.1080/00273170902794214
- Meyers JL, Beretvas SN. The impact of inappropriate modeling of cross-classified data structures. Multivariate Behav Res. 2006;41:473–497. doi: 10.1207/s15327906mbr4104_3
- Shi Y, Leite W, Algina J. The impact of omitting the interaction between crossed factors in cross-classified random effects modelling. Br J Math Stat Psychol. 2010;63:1–15. doi: 10.1348/000711008X398968
- Clayton DG, Rasbash J. Estimation in large crossed random effect models by data augmentation. J Roy Statist Soc Ser A. 1999;162:425–436. doi: 10.1111/1467-985X.00146
- Fielding A, Goldstein H. Cross-classified and multiple membership structures in multilevel models: an introduction and review. Research Report RR791. London: Department for Education and Skills; 2006.
- Goldstein H. Nonlinear multilevel models, with an application to discrete response data. Biometrika. 1991;78:45–51. doi: 10.1093/biomet/78.1.45
- Breslow NE, Clayton DG. Approximate inference in generalized linear mixed models. J Amer Statist Assoc. 1993;88:9–25.
- Raudenbush SW, Yang M, Yosef M. Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. J Comput Graph Statist. 2000;9:141–157.
- Rabe-Hesketh S, Skrondal A, Pickles A. Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects. J Econom. 2005;128:301–323. doi: 10.1016/j.jeconom.2004.08.017
- Joe H. Accuracy of Laplace approximation for discrete response mixed models. Comput Statist Data Anal. 2008;52:5066–5074. doi: 10.1016/j.csda.2008.05.002
- McCulloch CE. Maximum likelihood variance components estimation for binary data. J Amer Statist Assoc. 1994;89:330–335. doi: 10.1080/01621459.1994.10476474
- Cho SJ, Rabe-Hesketh S. Alternating imputation posterior estimation of models with crossed random effects. Comput Statist Data Anal. 2011;55:12–25. doi: 10.1016/j.csda.2010.04.015
- Browne WJ, Draper D. A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Anal. 2006;1:473–514. doi: 10.1214/06-BA117
- Karim MR, Zeger SL. Generalized linear models with random effects: salamander mating revisited. Biometrics. 1992;48:631–644. doi: 10.2307/2532317
- Rue H, Martino S, Chopin N. Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). J R Stat Soc Ser B. 2009;71:319–392. doi: 10.1111/j.1467-9868.2008.00700.x
- Grilli L, Metelli S, Rampichini C. Bayesian estimation with integrated nested Laplace approximation for binary logit mixed models. J Statist Comput Simul. 2015;85:2718–2726. doi: 10.1080/00949655.2014.935377
- Fong Y, Rue H, Wakefield J. Bayesian inference for generalized linear mixed models. Biostatistics. 2010;11:397–412. doi: 10.1093/biostatistics/kxp053
- McCullagh P, Nelder JA. Generalized linear models. 2nd ed. London: Chapman & Hall/CRC; 1989.
- Martins TG, Simpson D, Lindgren F, et al. Bayesian computing with INLA: new features. Comput Statist Data Anal. 2013;67:68–83. doi: 10.1016/j.csda.2013.04.014
- Rue H, Riebler A, Sørbye SH, et al. Bayesian computing with INLA: a review; 2016. arXiv:1604.00860 [stat.ME].
- Gelman A. Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal. 2006;1:515–534. doi: 10.1214/06-BA117A
- Martino S, Rue H. Implementing approximate Bayesian inference using integrated nested Laplace approximation: a manual for the INLA program. Technical report. Trondheim: Norwegian University of Science and Technology; 2008.
- Bates DM. lme4: mixed-effects modeling with R. Springer; 2010.
- Ferkingstad E, Rue H. Improving the INLA approach for approximate Bayesian inference for latent Gaussian models. Electron J Stat. 2015;9:2706–2731. doi: 10.1214/15-EJS1092
- Fielding A. Teaching groups as foci for evaluating performance in cost-effectiveness of GCE advanced level provision: some practical methodological innovations. Sch Effect Sch Improv. 2002;13:225–246. doi: 10.1076/sesi.13.2.225.3435
- Rabe-Hesketh S, Skrondal A. Multilevel and longitudinal modeling using stata. College Station (TX): Stata Press; 2012.
- Roos M, Held L. Sensitivity analysis in Bayesian generalized linear mixed models for binary data. Bayesian Anal. 2011;6:259–278. doi: 10.1214/11-BA609
- Roos M, Martins TG, Held L, et al. Sensitivity analysis for Bayesian hierarchical models; 2013. arXiv:1312.4797 [stat.ME].
- Simpson DP, Rue H, Martins TG, et al. Penalising model component complexity: a principled, practical approach to constructing priors. Trondheim (Norway): Norwegian University of Sciences and Technology; 2014. arxiv:1403.4630 (revised in 2015).
- Guo J, Riebler A, Rue H. Bayesian bivariate meta-analysis of diagnostic test studies with interpretable priors; 2015. arXiv:1512.06217 [stat.ME].