Year 2020,
Volume: 49 Issue: 2, 902 - 913, 02.04.2020
Hatice Tul Kubra Akdur
,
Deniz Ozonur
,
Hulya Bayrak
References
-
[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Unpublished doctoral dissertation, Iowa State University, 2013.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.
An adaptation of pseudo-score confidence interval method for linear mixed models
Year 2020,
Volume: 49 Issue: 2, 902 - 913, 02.04.2020
Hatice Tul Kubra Akdur
,
Deniz Ozonur
,
Hulya Bayrak
Abstract
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.
References
-
[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.