The expected mean squares for unbalanced mixed effect interactive
model were derived using Brute Force Method. From the expected mean squares,
there are no obvious denominators for testing for the main effects when the
factors are mixed. An expression for F-test for testing for the main effects
was derived which was proved to be unbiased.
References
[1]
Peretz, C., Goren, A., Smid, T. and Kromhout, H. (2002) Application of Mixed-Effect Models for Exposure Assessment. Annals of Occupational Hygiene, 46, 69-77. http://dx.doi.org/10.1093/annhyg/mef009
[2]
Edward, F.V. and Randy, L.C. (1992) Mixed-Effect Nonlinear Regression for Unbalanced Repeated Measures. Biometrics, 48, 1-17. http://dx.doi.org/10.2307/2532734
[3]
Ofversten, J. (1993) Exact Tests for Variance Components in Unbalanced Mixed Linear Models. Biometrics, 49, 45- 57. http://dx.doi.org/10.2307/2532601
[4]
Khuri, A.I. and Littell, R.C. (1987) Exact Tests for the Main Effects Variance Components in an Unbalanced Random Two-Way Model. Biometrics, 43, 545-560. http://dx.doi.org/10.2307/2531994
[5]
Ananda, M.M.A. and Weerahandi, S. (1997) Two-Way ANOVA with Unequal Cell Frequencies and Unequal Variances. Statistica Sinica, 7, 631-646.
[6]
Dawn, I. (1995) Analysis of Variance for Unbalanced Data. Marketing, Theory and Practice, 6, 337-343.
Eze, F.C. and Chigbu, P.E. (2012) Unbalanced Two-Way Random Model with Integer-Value Degrees of Freedom. Journal of Natural Sciences Research, 2, 100-107.
[9]
Neter, J., Kutner, M.H. and Wasserman, W. (1996) Applied Linear Statistical Models. WCB/McGraw-Hill, 696-700.