Estimable functions of mixed models Choi, Jaesung;
This paper discusses how to establish estimable functions when there are fixed and random effects in design models. It proves that estimable functions of mixed models are not related to random effects. A fitting constants method is used to obtain sums of squares due to random effects and Hartley`s synthesis is used to calculate coefficients of variance components. To test about the fixed effects the degrees of freedom associated with divisor are determined by means of the Satterthwaite approximation.
mixed model;estimable function;fitting constants method;Type I sum of squares;synthesis;
Choi, J. S. (2011). Type I analysis by projections, The Korean Journal of Applied Statistics, 24, 373-381.
Choi, J. S. (2012). Type II analysis by projections, Journal of the Korean Data & Information Science Society, 23, 1155-1163.
Choi, J. S. (2014). Projection analysis for two-way variance components, Journal of the Korean Data & Information Science Society, 23, 547-554.
Corbeil, R. R. and Searle, S. R. (1976). A comparison of variance component estimators, Biometrics, 32, 779-791.
Elswick, K. R., Gennings, C. Jr., Chinchilli, M. V., and Dawson, S. K. (1991). A simple approach for finding estimable functions in linear models, The American Statistician, 45, 51-53.
Graybill, F. A. (1976). Theory and Application of the Linear Model, Wadsworth, California.
Hartley, H. O. (1967). Expectations, variances and covariances of ANOVA means squares by "synthesis", Biometrics, 23, 105-114.
Henderson, C. R. (1953). Estimation of variance and covariance components, Biometrics, 9, 226-252.
Hicks, C. R. (1973). Fundamental Concepts in the Design of Experiments, Holt, Rinehart and Winston, New York.
Milliken, G. A. and Johnson, D. E. (1984). Analysis of Messy Data, Van Nostrand Reinhold, New York.
Satterthwaite, F. E. (1946). An approximate distribution of estimates of variance components, Biometrics Bulletin, 2, 110-114.
Searle, S. R., Casella, G., and McCulloch, C. E. (1971). Linear Models, John Wiley and Sons, New York.
Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance Components, John Wiley and Sons, New York.