Goodness-of-fit tests of generalized linear mixed models for repeated ordinal responses

References

• A. Agresti, Modelling ordered categorical data: recent advances and future challenges, Stat. Med. 18 (1999), pp. 2191–2207. doi: 10.1002/(SICI)1097-0258(19990915/30)18:17/18<2191::AID-SIM249>3.0.CO;2-M
   PubMed Web of Science ®Google Scholar
• A. Alonso, S. Litiere, and G. Molenberghs, A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models, Comput. Stat. Data Anal. 52 (2008), pp. 4474–4486. doi: 10.1016/j.csda.2008.02.033
   Web of Science ®Google Scholar
• D.M. Berridge and R. Crouchley, Multivariate Generalized Linear Mixed Models Using R, Chapman & Hall, New York, 2011.
   Google Scholar
• N.E. Breslow and D.G. Clayton, Approximate inference in generalized linear mixed models, J. Am. Statist. Assoc. 88 (1993), pp. 9–25.
   Web of Science ®Google Scholar
• C.C. Clogg and E.S. Shihadeh, Statistical Models for Ordinal Data, Thousand Oaks, New York, 1994.
   Google Scholar
• D.R. Cox and D.V. Hinkley, Theoretical Statistics, Chapman & Hall, London, 1974.
   Google Scholar
• D.S. Elliot, D. Huizinga, and S. Menard, Multiple Problem Youth: Delinquency, Substance Use and Mental Health Problems, Springer, New York, 1989.
   Google Scholar
• G.M. Fitzmaurice, N.M. Laird, and J.H. Ware, Applied Longitudinal Analysis, Wiley Series, Hoboken, NJ, 2004.
   Google Scholar
• D.W. Hosmer, T. Hosmer, S.L. LeCessie, and S. Lemeshow, A comparison of goodness-of-fit tests for the logistic regression model, Stat. Med. 16 (1997), pp. 965–980. doi: 10.1002/(SICI)1097-0258(19970515)16:9<965::AID-SIM509>3.0.CO;2-O
   PubMed Web of Science ®Google Scholar
• X.Z. Huang, Diagnosis of random-effect model misspecification in generalized linear mixed models for binary response, Biometrics 65 (2009), pp. 361–368. doi: 10.1111/j.1541-0420.2008.01103.x
   PubMed Web of Science ®Google Scholar
• X.Z. Huang, Detecting random-effects model misspecification via coarsened data, Comput. Stat. Data Anal. 55 (2011), pp. 703–714. doi: 10.1016/j.csda.2010.06.012
   Web of Science ®Google Scholar
• N.L. Johnson and S. Kotz, Distributions in Statistics, Continuous Univariate Distributions, Houghton-Mifflin, Boston, 1970.
   Google Scholar
• N.M. Laird and J.H. Ware, Random-effects models for longitudinal data, Biometrics 38 (1982), pp. 963–974. doi: 10.2307/2529876
   PubMed Web of Science ®Google Scholar
• D.Y. Lin, L.J. Wei, and Z. Ying, Model-checking techniques based on cumulative residuals, Biometrics 58 (2002), pp. 1–12. doi: 10.1111/j.0006-341X.2002.00001.x
   PubMed Web of Science ®Google Scholar
• K.-C. Lin, Goodness-of-fit tests for modeling longitudinal ordinal data, Comput. Stat. Data Anal. 54 (2010), pp. 1872–1880. doi: 10.1016/j.csda.2010.02.013
   Web of Science ®Google Scholar
• K.-C. Lin and Y.-J. Chen, Detecting misspecification in the random-effects structure of cumulative logit models, Comput. Stat. Data Anal. 92 (2015), pp. 126–133. doi: 10.1016/j.csda.2015.07.002
   Web of Science ®Google Scholar
• K.-C. Lin, Y.-J. Chen, and Y. Shyr, A nonparametric smoothing method for assessing GEE models with longitudinal binary data, Stat. Med. 27 (2008), pp. 4428–4439. doi: 10.1002/sim.3315
   PubMed Web of Science ®Google Scholar
• S. Litière, A. Alonso, and G. Molenberghs, Type I and type II error under random-effects misspecification in generalized linear mixed models, Biometrics 63 (2007), pp. 1038–1044. doi: 10.1111/j.1541-0420.2007.00782.x
   PubMed Web of Science ®Google Scholar
• S. Litière, A. Alonso, and G. Molenberghs, The impact of a misspecification random-effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models, Stat. Med. 27 (2008), pp. 3125–3144. doi: 10.1002/sim.3157
   PubMed Web of Science ®Google Scholar
• L.C. Liu and D. Hedeker, A mixed-effects regression model for longitudinal multivariate ordinal data, Biometrics 62 (2006), pp. 261–268. doi: 10.1111/j.1541-0420.2005.00408.x
   PubMed Web of Science ®Google Scholar
• P. McCullagh, Regression models for ordinal data, J. R. Statist. Soc. B42 (1980), pp. 109–142.
   Google Scholar
• P. McCullagh and J.A. Nelder, Generalized Linear Models, Chapman and Hall, London, 1989.
   Google Scholar
• C.E. McCulloch, S.R. Searle, and J.M. Neuhaus, Generalized, Linear, and Mixed Models, 2nd ed., Wiley, New York, 2008.
   Google Scholar
• G. Molenberghs and G. Verbeke, Models for Discrete Longitudinal Data, Springer, New York, 2005.
   Google Scholar
• W. Pan, Goodness-of-fit tests for GEE with correlated binary data, Scand. J. Stat. 29 (2002), pp. 101–110. doi: 10.1111/1467-9469.00091
   Web of Science ®Google Scholar
• Z. Pan and D.Y. Lin, Goodness-of-fit methods for generalized linear mixed models, Biometrics 61 (2005), pp. 1000–1009. doi: 10.1111/j.1541-0420.2005.00365.x
   PubMed Web of Science ®Google Scholar
• J. Pan and R. Thompson, Gauss–Hermite quadrature approximation for estimation in generalized linear mixed models, Comput. Stat. 18 (2003), pp. 57–78.
   Web of Science ®Google Scholar
• B. Rowan, S.W. Raudenbush, and Y.F. Cheong, Teaching as a nonroutine task: implications for the management of schools, Educ. Adm. Q. 29(4) (1993), pp. 479–500. doi: 10.1177/0013161X93029004005
   Web of Science ®Google Scholar
• R. Schall, Estimation in generalized linear models with random effects, Biometrika 78 (1991), pp. 719–727. doi: 10.1093/biomet/78.4.719
   Web of Science ®Google Scholar
• R. Stiratelli, N. Laird, and J.H. Ware, Random-effects models for serial observations with binary response, Biometrics 40 (1984), pp. 961–971. doi: 10.2307/2531147
   PubMed Web of Science ®Google Scholar
• R.X. Sturdivant, J.J. Rotella, and R.E. Russell, A smoothed residual based goodness-of-fit statistic for nest-survival models, Stud. Avian Biol. 34 (2007), pp. 45–54.
   Google Scholar
• G. Verbeke and G. Molenberghs, Linear Mixed Models for Longitudinal Data, Springer, New York, 2009.
   Google Scholar
• E.F. Vonesh, V.M. Chinchilli, and K. Pu, Goodness-of-fit in generalized nonlinear mixed-effects models, Biometrics 52 (1996), pp. 572–587. doi: 10.2307/2532896
   PubMed Web of Science ®Google Scholar
• J.M. Williamson, H.M. Lin, and H.X. Barnhart, A classification statistic for GEE categorical regression models, J. Data Sci. 1 (2003), pp. 149–165.
   Google Scholar
• S.L. Zeger and M.R. Karim, Generalized linear models with random effects: a Gibbs sampling approach, J. Am. Statist. Assoc. 86 (1991), pp. 79–86. doi: 10.1080/01621459.1991.10475006
   Web of Science ®Google Scholar
• S.L. Zeger, K.-Y. Liang, and P.S. Albert, Models for longitudinal data: a generalized estimating equation approach, Biometrics 44 (1988), pp. 1049–1060. doi: 10.2307/2531734
   PubMed Web of Science ®Google Scholar