International Journal of Nonlinear Analysis and Applications

Expected mean square rate estimation of repeated measurements model

Document Type : Research Paper

Authors

1 Department of Economics, College of Administration and Economics, Thi-Qar University, Thi-Qar, Iraq

2 Department of mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq

Abstract

In this paper, we obtained the estimation corresponding to the expected mean square rate of repeated measurement model depend on maximum likelihood method (MLM), restricted maximum likelihood method (REMLM) and modified restricted maximum likelihood method (MREMLM), and got eight cases that were classified into three types.

Keywords

[1] A. H. S. Al-Mouel and J. M. Jassim, Two-way multivariate repeated model, J. Basrah Res. Sci. 32(1) (2006) 17–31.
[2] A. H. S. AL-Mouel and H. A. Kori , Conditional and unconditional of repeated measurements model, J. Phys. Conf. Ser. 1818 012107, (2021) pp.1–11.
[3] A. H. S. AL-Mouel and H. I. Mustafa, The sphericity test for one-way multivariate repeated measurements analysis of variance mode, J. Kufa Math. Compu. 2(2) (2014) 107–115.
[4] A. H. S. AL-Mouel and H. Z. Naji , Two random covariates in repeated measurement model, Basrah J. Sci. 32(1) (2014) 130–140.
[5] A. H. S. AL-Mouel and H. R. Showel, A note on estimation of variance components by maximization, IJPRET. 5(3) (2016) 1–10.
[6] A. J. Baranchick, Inadmissibility of maximum likelihood estimators in some multiple regression problems with three or more independent variables, Ann. Stat., 1 (1972) :312–321.
[7] E. Brunner and F. Langer , Nonparametric analysis of ordered categorical data in designs with longitudinal observations and small sample sizes, Biomet. J. 42 (2000) 663–675.
[8] D. A. Harville, Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems. Journal of the American Statistical Association , (1977),72: 320-340.
[9] H. J. Keselman , J. Algina and R. K. Kowalchuk . The analysis of repeated measures designs: A review, British J. Math. Stat. Psy. 54 (2001) 1–20.
[10] E. B. Moser and R. E. Macchiavelli , Model selection techniques for repeated measures covariance structures, Appl. Stat. Agric. 14 (2002) 17–31.
[11] A. Ozg¨ur, B. David, J. D. Peter and W. Jonas, ¨ Linear mixed-effects models for non-Gaussian repeated measurement data, Appl. Stat. 69(5) (2020) 1015—1065.
[12] H. D. Patterson and R. Thompson, Maximum likelihood estimation components of variance, Proc. 8th Int. Biometric Conf. (1974) 297–207.
[13] G. W. Snedecor and W. G. Cochran, Statistical Methods, Edition, Ames, Iowa State University press, Iowa. 1967.
[14] E. F. Vonesh and V. M. Chinchill, Linear and Non-linear Models for the Analysis of Repeated Measurements, Marcel Dakker Inc., New York, 1997.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 75-83
  • Receive Date: 03 March 2021
  • Revise Date: 21 April 2021
  • Accept Date: 30 April 2021