Browse > Article
http://dx.doi.org/10.7465/jkdi.2014.25.4.799

Type III sums of squares by projections  

Choi, Jaesung (Department of Statistics, Keimyung University)
Publication Information
Journal of the Korean Data and Information Science Society / v.25, no.4, 2014 , pp. 799-805 More about this Journal
Abstract
This paper deals with a method for getting the Type III sums of squares on the basis of projections under the assumption of two-way fixed effects model. For unbalanced data in general total sum of squares is not equal to the sum of componentwise Type III sums of squares. There are some differencies between two quantities. The suggested method using projections can detect where the differences occur and how much they are different. The traditional ANOVA method could not explain clearly the differences. It also discusses how eigenvectors and eigenvalues of the projection matrices can be used to get the Type III sums of squares.
Keywords
Eigenvalue; eigenvector; projection; projection matrix; Type III sums of squares;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 Montgomery, D. C. (1976). Design and analysis of experiments, John Wiley and Sons, Inc., New York.
2 Searle, S. R., Casella, G. and McCulloch, C. E. (1992). Variance components, John Wiley and Sons, Inc., New York.
3 Choi, J. S. (2011). Type I analysis by projections. The Korean Journal of Applied Statistics, 24, 373-381.   과학기술학회마을   DOI   ScienceOn
4 Choi, J. S. (2012). Type II analysis by projections. Journal of the Korean Data & Information Science Society, 23, 1155-1163.   과학기술학회마을   DOI   ScienceOn
5 Cochran, G. W. and Cox, M. G. (1957). Experimental designs, John Wiley and Sons, Inc., New York.
6 Choi, J. S. (2013). Estimable functions of less than full rank linear model Journal of the Korean Data & Information Science Society, 24, 333-339.   과학기술학회마을   DOI   ScienceOn
7 Corbeil, R. R. and Searle, S. R. (1976). A comparison of variance component estimators. Biometrics, 32, 779-791.   DOI   ScienceOn
8 Graybill, F. A. (1976). Theory and application of the linear model, Wadsworth, Inc., California.
9 Huynh, H. and Feldt, L. S. (1970). Conditions under which mean square ratios in repeated measures designs have exact F-distributions. Journal of the American Statistical Association, 65, 1582-1589.   DOI   ScienceOn
10 Milliken, G. A. and Johnson, D. E. (1984). Analysis of messy data, Van Nostrand Reinhold, New York.
11 Steel, R. G. and Torrie, J. H. (1980). Principles and procedures of statistics, McGraw-Hill, Inc., New York.