Abstract
It is common to encounter data that have a hierarchical or nested structure. Examples include patients within hospitals within cities, students within classes within schools, factories within industries within states, or families within neighborhoods within census tracts. These structures have become increasingly common in recent times and include variability at each level which must be taken into account. Hierarchical models which account for the variability at each level of the hierarchy, allow for the cluster effects at different levels to be analyzed within the models (Shahian et al. in Ann Thorac Surg, 72(6):2155–2168, 2001). This chapter discusses how the information from different levels can be used to produce a subject-specific model. However, there are often cases when these models do not fit as additional random intercepts and random slopes are added to the model. This addition of additional parameters often leads to non-convergence. We present a simulation study as we explore the cases in these hierarchical models which often lead to non-convergence. We also used the 2011 Bangladesh Demographic and Health Survey data as an illustration.
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References
Austin, P. C. (2010). Estimating multilevel logistic regression models when the number of clusters is low: A comparison of different statistical software procedures. The International Journal of Biostatistics, 6(1), 1–20.
Austin, P. C., Manca, A., Zwarenstein, M., Juurlink, D. N., & Stanbrook, M. B. (2010). A substantial and confusing variation exists in handling of baseline covariates in randomized controlled trials: a review of trials published in leading medical journals. Journal of Clinical Epidemiology, 63(2), 142–153.
Ene, M., Leighton, E. A., Blue, G. L., & Bell, B. A. (2015). Multilevel models for categorical data using SAS PROC GLIMMIX: The Basics. SAS Global Forum 2015 Proceedings.
Hartzel, J., Agresti, A., & Caffo, B. (2001). Multinomial logit random effects models. Statistical Modelling, 1(2), 81–102.
Hedeker, D., Mermelstein, R. J., & Demirtas, H. (2008). An application of a mixed effects location scale model for analysis of Ecological Momentary Assessment (EMA) data. Biometrics, 64(2), 627–634.
Hedeker, D., Mermelstein, R. J., & Demirtas, H. (2012). Modeling between- and within subject variance in Ecological Momentary Assessment (EMA) data using mixed-effects location scale models. Statistics in Medicine, 31(27), 3328–3336.
Hox, J. J. (2002). Multilevel analysis: Techniques and applications. Mahwah: Lawrence Erlbaum Associates Inc.
Irimata, K. M., & Wilson, J. R. (2017). Identifying Intraclass correlations necessitating hierarchical modeling. Journal of Applied Statistics, accepted.
Kiernan, K., Tao, J., & Gibbs, P. (2012). Tips and strategies for mixed modeling with SAS/STAT procedures. SAS Global Forum 2012 Proceedings.
Kuss, O. (2002). Global goodness-of-fit tests in logistic regression with sparse data. Statistics in Medicine, 21, 3789–3801.
Kuss, O. (2002). How to use SAS for logistic regression with correlated data. In SUGI 27 Proceedings (pp. 261–27).
Lesaffre, E., & Spiessens, B. (2001). On the effect of the number of quadrature points in a logistic random effects model: An example. Journal of the Royal Statistical Society. Series C (Applied Statistics), 50(3), 325–335.
Longford, N. T. (1993). Random coefficient models. Oxford: Clarendon Press.
Maas, C. J. M., & Hox, J. J. (2004). The influence of violations of assumptions on multilevel parameter estimates and their standard errors. Computational Statistics & Data Analysis, 46(3), 427–440.
McMahon, J. M., Pouget, E. R., & Tortu, S. (2006). A guide for multilevel modeling of dyadic data with binary outcomes using SAS PROC NLMIXED. Computational Statistics & Data Analysis, 50(12), 3663–3680.
National Institute of Population Research and Training (NIPORT). (2013). Bangladesh demographic and health survey 2011. NIPORT, MItra and Associates, ICF International: Dhaka Bangladesh, Calverton MD.
Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society. Series A (General) 135(3), 370–384.
Newsom, J. T. (2002). A multilevel structural equation model for dyadic data. Structural Equation Modeling: A Multidisciplinary Journal, 9(3), 431–447.
Rasbash, J., Steele, F., Browne, W. J., & Goldstein, H. (2012). User’s guide to WLwiN, Version 2.26. Centre for Multilevel Modelling, University of Bristol. Retrieved from http://www.bristol.ac.uk/cmm/software/mlwin/download/2-26/manual-web.pdf.
Raudenbush, S. W. (1992). Hierarchical linear models. Newbury Park: Sage Publications.
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods. Thousand Oaks: Sage Publications.
Rodriquez, G., & Goldman, N. (1995). An assessment of estimation procedures for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A (Statistics in Society) 158(1), 73–89.
SAS Institute Inc. (2013). Base SAS \(^{\textregistered }\) 9.4 Procedure guide: Statistical procedures (2nd ed.). Cary, NC: SAS Institute Inc.
Schabenberger, O. (2005). Introducing the GLIMMIX procedure for generalized linear mixed models. SUGI 30 Proceedings, 196–30.
Shahian, D. M., Normand, S. L., Torchiana, D. F., Lewis, S. M., Pastore, J. O., Kuntz, R. E., et al. (2001). Cardiac surgery report cards: Comprehensive review and statistical critique. The Annals of Thoracic Surgery, 72(6), 2155–2168.
Smyth, G. K. (1989). Generalized linear models with varying dispersion. Journal of the Royal Statistical Society, Series B, 51, 47–60.
Snijders, T. A. B., & Bosker, R. J. (1998). Multilevel analysis: An introduction to basic and advanced multilevel modeling. Thousand Oaks: Sage Publications.
Three-level multilevel model in SPSS. (2016). UCLA: Statistical Consulting Group. http://www.ats.ucla.edu/stat/spss/code/three_level_model.htm.
Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models and the Gauss-Newton method. Biometrika, 61(3), 439–447.
Xie, L., & Madden, L. V. (2014). %HPGLIMMIX: A high-performance SAS macro for GLMM Estimation. Journal of Statistical Software, 58(8).
Wilson, J. R., & Lorenz, K. A. (2015). Modeling Binary correlated responses using SAS, SPSS and R. New York: Springer International Publishing.
Wolfinger, D. (1999). Fitting nonlinear mixed models with the new NLMIXED procedure. In Sugi 24 Proceedings (pp. 278–284).
Acknowledgements
This work is funded in part by the National Institutes of Health Alzheimer’s Consortium Fellowship Grant, Grant No. NHS0007. The content in this paper is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
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Irimata, K.M., Wilson, J.R. (2017). Monte-Carlo Simulation in Modeling for Hierarchical Generalized Linear Mixed Models. In: Chen, DG., Chen, J. (eds) Monte-Carlo Simulation-Based Statistical Modeling . ICSA Book Series in Statistics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3307-0_13
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