Reduced bias estimation of variance for repeated measurements model

Mustafa, Hadeel Ismail; AL-Mouel, Abdul Hussein Saber

doi:10.47974/JSMS-1084

Open Access Research Article

Reduced bias estimation of variance for repeated measurements model

^*Hadeel Ismail MustafaCorresponding authorhadeelismu@gmail.comDepartment of Computer Information SystemCollege of Computer Science and Information TechnologyUniversity of BasrahBasrah, IraqView full profile → , Abdul Hussein Saber AL-Mouelabdulhusseinsaber@yahoo.comDepartment of MathematicsCollege of ScienceUniversity of BasrahBasrah, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 663–671Vol. 27Issue 3March 2024DOI: 10.47974/JSMS-1084XML

Received:: 15 Feb 2023
Published Online:: 27 Feb 2024
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1084
Pages:: 663–671

Abstract

This paper discusses two important points; the first part describes the one-way repeated measurements model, which had two random effects in addition to the random error and two fixed factors. The model was also written as a set of matrices, which showed how the random effects and fixed factors interacted. The second part shows the maximum likelihood method for determining the variance components for a one-way repeated measures model. In this method, it was seen that the estimates of the variance combinations have some bias. The goal of this study is to use the Mean bias reduction method of the one-way repeated measurements model to reduce the bias in the estimators of the variance components.

Keywords

One-way repeated measurements model Variance compounds Mean bias reduction Maximum likelihood method

Subject Classifications

62F1062G05

References

[1] Al-Mouel , A. H. S. and Wang, J. L.,.One –Way Multivariate Repeated Measurements Analysis of Variance Model. Applied Mathematics a Journal of Chinese Universities 19(4), pp. 435-448 (2004).
[2] AL-Mouel, A. H. S and Mustafa, H. I.,. The Sphericity Test for OneWay Multivariate Repeated Measurements Analysis of Variance Mode. Journal of Kufa for Mathematics and Computer Vol. 2, no. 2, Dec. 2014, pp 107-115 (2014).
[3] Al-Mouel, A.H.S., Multivariate Repeated Measures Models and Comparison of Estimators, Ph.D. Thesis, East China Normal University, China (2004).
[4] Jassim N. O. and Al-Mouel, A H S.,.Lasso Estimation for High-Dimensional Repeated Measurement Model, AIP Conf. Proc., 2292, 020002, pp. 1-10 (2020).
[5] Jiang, J., Linear and Generalized Linear Mixed Models and Their Applications. Springer Series in Statistics (2007).
[6] Kori H. A. and AL-Mouel, A. H. S,. Expected mean square rate estimation of repeated measurements model, Int. J. Nonlinear Anal. Appl. 12 (2021).
[7][7] Kosmidis I, Guolo A and Varin C., Improving the accuracy of likelihood-based inference in meta-analysis and metaregression. Biometrika; 104: 489–496. (2017).
[8] Kosmidis, I.,Bias in parametric Estimation: reduction and useful sideeffects. Wiley Interdisciplinary Reviews: Computational Statistics 6, 185–196 (2014).
[9] Vonesh, E.F. and Chinchilli, V.M.,Linear and Nonlinear Models for the Analysis of Repeated Measurements, Marcel Dakker, Inc., New York (1997).
[10] Wand, M., Fisher information for generalized linear mixed models. Journal of Multivariate Analysis 98, 1412–1416 (2007).
[11] Shubham Sharma & Ahmed J. Obaid. Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox, Journal of Interdisciplinary Mathematics, 23:4, 843-849 (2020), DOI: 10.1080/09720502.2020.1727611.
[12] Adi Raveh msraveh@huji.ac.il & Guy Leshem leshemg@cs.bgu.ac.il. Bias in estimation of classical statistical coefficient, Journal of Statistics and Management Systems, 14:1, 141-150 (2011), DOI: 10.1080/09720510.2011.10701548.

Views: 173Downloads: 75Citations: 0