Optimal Procedures for Certain Crossed Repeated Measures Model

Authors: Sami D. Gabbara1 & Ghadah A. AL-Sakkal2
1 Department of Mathematics, College of Science, Salahaddin University, Erbil, Iraq
2 Department of Computer, Faculty of Engineering, Tishk International University, Erbil, Iraq

Abstract:In this paper, we develop a general method to analyze several different kinds of certain crossed repeated measures models (CRMM) which represent many situations occurring in repeated measurements on the same experimental units (individuals). Let Yi=(Y1111,,Yidrc) be the vector of observations of the ith individuals. It is assumed that the Yi are jointly normally distributed with mean µi . We want to test hypotheses about µi . In order to get powerful tests we make the simplifying assumptions that all measurements have the same variance σ2 and every pair of measurements that comes from (i) different bulls and different cows (ii) different bulls but with the same cow (iii) the same bull with different cows; have covariance’s 0, σ 2 ρ 1 , σ 2ρ2 respectively. And every pair of measurements that comes from the same bull and the same cow with treatments of (a) different columns and different rows (b) the same column but different rows (c) different columns but the same row have covariance’s σ 2ρ 3 , σ 2ρ 4 and σ 2 ρ 5 , respectively. The results of this model can be used to analyze certain 4-way balanced mixed and/or random effects models. This procedure is also useful to analyze any of the mentioned 4-way models by adding any number of fixed effects to the model as long as those added effects do not interact with any random effects already in these models.

Keywords: Coordinate-Free, Mixed Models, Random Models, Repeated Measures Models

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doi: 10.23918/eajse.v5i1p1

References

Al-Sakkal, G.A. (1999). Optimal Procedures for Certain Crossed Repeated Measures Model. M.Sc. Thesis, Al-Mustansiriyah, University, Iraq.

Arnold, S. F. (1973). Application of the theory of Products of Problems to certain Patterned covariance matrices. Ann. Statist. 1,682-699.

Arnold, S. F. (1979). A Coordinate-Free Approach to Finding Optimal Procedures for Repeated Measures Designs. Ann. Statist. 7,812-822.

Baayen, R. H., Davidson D. J., & Bates D.M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59(4), 390-412.

Cox, G. M., & Cochran W. G. (1992). Experimental designs. New York: Wiley and Sons.

Gabbara, S. D. (1985). Nested and Crossed Repeated Measures Models. Unpublished, Ph. D. Thesis, The Pennsylvania State University, USA.

Hoshmand R. (2006). Design of experiments for agriculture and natural sciences. 2nd Edition, Taylor and Francis Group.

Lehman, E. L. (1959). Testing statistical hypotheses. New York: Wiley.

Rhonda, D., Szczesniak, D. L., & Raouf S. A. (2016). Semi parametric mixed models for nested repeated measures applied to ambulatory blood pressure monitoring data. The Journal of Modern Applied Statistical Methods, 15(1), 255-275.

Saarinen, F. (2004). Using mixed models in a cross-over study with repeated measurements within periods. Thesis submitted to the Dept. of Mathematical Statistics, Stockholm University, SE-106 91 Stockholm, Sweden.