An adaptation of pseudo-score confidence interval method for linear mixed models

Yıl 2020, Cilt: 49 Sayı: 2, 902 - 913, 02.04.2020

Hatice Tul Kubra Akdur , Deniz Ozonur , Hulya Bayrak

https://doi.org/10.15672/hujms.510261

Öz

We adapt a confidence interval method based on a generalized Chi-Square test for fixed effect parameters of linear mixed models. Under different correlation structure of a response variable of a linear mixed model, the performances of the adaptation method pseudo-score and some of the existing confidence interval methods are investigated by carrying out a Monte Carlo simulation study. The simulation study suggests that pseudo-score method provides better results for small to moderate sample size cases with dependent observations in terms of coverage probability rates and average expected lengths. A depression study is analyzed for demonstrating the adaptation method.

Anahtar Kelimeler

linear mixed models, pseudo-score, profile likelihood

Kaynakça

• [1] A. Agresti and E. Ryu, Pseudo-score confidence intervals for parameters in discrete statistical models, Biometrika 97 (1), 215-222, 2010.
• [2] H.T.K. Akdur, D. Ozonur and H. Bayrak, A Comparison of Confidence Interval Methods of Fixed Effect in Nested Error Regression Model, SDU J Nat Appl Sci 20 (2), 2016.
• [3] M.K. Bahçecitapar, Some factors affecting statistical power of approximate tests in the linear mixed model for longitudinal data, Comm. Statist. Simulation Comput. 47 (1), 2018.
• [4] D. Bates, M. Machler, B. Bolker and S. Walker, Fitting linear mixed-effects models using lme4, arXiv preprint 1406.5823, 2014.
• [5] A.T. Beck, R.A. Steer and G.K. Brown, Beck depression inventory-II, Psychological Corporation 78 (2), 490-498, San Antonio, TX, 1996.
• [6] D.K. Bhaumik, A. Roy, S. Aryal, K. Hur, N. Duan, S.L.T. Normand, C.H. Brown, and R.D. Gibbons, Sample size determination for studies with repeated continuous outcomes, Psychiatr. Ann 38 (12), 2008.
• [7] A. R. De Leon and K. C. Chough, Analysis of mixed data: methods and applications, CRC Press, 2013.
• [8] D. Eugene, Mixed Models: Theory and Applications, Hoboken: Wiley, 2004.
• [9] G.M. Fitzmaurice, N.M. Laird and J.H.Ware Applied longitudinal analysis (Vol. 998), John Wiley and Sons, 2012.
• [10] A. Genz, F. Bretz, T. Miwa, ... , and M.T. Hothorn, Package mvtnorm, J. Stat. Softw. 11, 950-971, 2020.
• [11] U. Halekoh and S. Højsgaard, A kenward-roger approximation and parametric bootstrap methods for tests in linear mixed modelsthe R package pbkrtest, J. Stat. Softw. 59 (9), 1-30, 2014.
• [12] P.R. Houck, S. Mazumdar, T. Koru-Sengul, G. Tang, B.H. Mulsant, B.G. Pollock and C.F. Reynolds III, Estimating treatment effects from longitudinal clinical trial data with missing values: comparative analyses using different methods, Psychiatry Research 129 (2), 209-215, 2004.
• [13] R.N. Kackar and D.A. Harville, Approximations for standard errors of estimators of fixed and random effects in mixed linear models, J. Am. Stat. Assoc 79 (388), 853-862, 1984.
• [14] M. G. Kenward and J. H. Roger, Small sample inference for fixed effects from restricted maximum likelihood, Biometrics 53 (3), 983-997, 1997.
• [15] S. Landau, A handbook of statistical analyses using SPSS, CRC, 2004.
• [16] J. Liu, Statistical inference for functions of the parameters of a linear mixed model, Unpublished doctoral dissertation, Iowa State University, 2013.
• [17] G. Lovison, On rao score and pearson x2 statistics in generalized linear models, Statist. Papers 46 (4), 555-574, 2005.
• [18] J.C. Pinheiro and D.M. Bates, Mixed-effects models in S and S-Plus, Springer. New York. US, 2000.
• [19] J.C. Pinheiro, D.M. Bates, S. DebRoy, D. Sarkar, and R. C. Team, nlme: Linear and nonlinear mixed effects models. R package version, 3 (1), 111.
• [20] J. Proudfoot, D. Goldberg, A. Mann, B. Everitt, I. Marks and J. Gray, Computerized, interactive, multimedia cognitive-behavioural program for anxiety and depression in general practice, Psychol. Med. 33 (2), 217-227, 2003.
• [21] V.S. Staggs, Parametric bootstrap interval approach to inference for fixed effects in the mixed linear model, Unpublished doctoral dissertation, University of Kansas, 2009.
• [22] V.S. Staggs, Comparison of naive, kenwardroger, and parametric bootstrap interval approaches to small-sample inference in linear mixed models, Comm. Statist. Simulation Comput. 46 (3), 1933-1943, 2017.
• [23] G. Verbeke Linear mixed models for longitudinal data. In Linear mixed models in practice, 63153, Springer, 1997.
• [24] W. W. Stroup, G. A. Milliken, E. A. Claassen, R. D. Wolfinger, SAS for Mixed Models: Introduction and Basic Applications., SAS Institute, 2018.
• [25] B. Wu and A.R. de Leon Gaussian copula mixed models for clustered mixed outcomes, with application in developmental toxicology, J. Agric. Biol. Environ. Stat.19 (1), 39- 56, 2014.
• [26] J. Yan, Enjoy the joy of copulas: with a package copula, J. Stat. Softw. 21 (4), 1-21, 2007.