SAS describes their approach as follows: ...The normal equations are solved using a modified sweep routine that produces a generalized (g2) inverse (X'X)^- and a solution b = (X'X)^-X'y (Pringle and Raynor 1971)(1). For each effect in the model, a matrix L is computed such that the rows of L are estimable. Tests of the hypothesis are then made by first computing SS(LB=0)=(Lb)'(L(X'X)^-L')^-1(Lb) and then computing the associated F value using the mean squared error. ... and ...The Type III hypotheses are precisely the hypotheses being tested by programs that reparameterize using the usual assumptions (for example, all parameters for an effect summing to zero). When no missing cells exist in a factorial model, Type III SS coincide with Yates' weighted squares-of-means technique. When cells are missing in factorial models, the Type III SS coincide with those discussed in Harvey (1960)(2) and Henderson (1953)(3). ... (1). Pringle, R.M. and Raynor, A.A. (1971), Generalized Inverse Matrices with Applications to Statistics, New York: Hafner Publishing Co. (2). Harvey, W. R. (1960),"Least-Squares Analysis of Data with Unequal Subclass Frequencies," USDA, Agriculture Research Service, ARS 20-8, reprinted with corrections as ARS H-4, 1975, also reprinted 1979. (3) Henderson, C. R. (1953), "Estimation of Variance and Covariance Components," Biometrics, 9, 226 -252. ---------------------------------------------------------------------- Message: 1 Date: Tue, 21 Oct 2003 08:09:10 -0400 From: "Subramanian Karthikeyan" <subramanian_karthikeyan@hc-sc.gc.ca> Subject: [BioC] Type III Sum of Squares Calculation To: bioconductor@stat.math.ethz.ch Message-ID: <of41129209.407d90e2-on85256dc6.00429d83@hc-sc.gc.ca> Content-Type: text/plain; charset=us-ascii HI All: Can anyone give me the formulae/steps for calculating the type III sum of squares for an unbalanced 2-way ANOVA design? Eg. we are looking at 8 treatments x 4 doses, with unequal numbers of replications within the groups. I really need the stepwise calculation, as I would try to put it in my own code (possibly in Visual Basic) to automate the task. Thanks very much. Karth.