Programming the statistical procedures from SAS

GLM: Type I, II, III and IV ESTIMABLE FUNCTIONS

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GLM: Type I, II, III and IV ESTIMABLE FUNCTIONS

Hi everyone,

I'm estimating a simple unbalanced GLM model with no empty cells defined as y= intercept + A + B +A*B  (Factor A has three levels A1, A2, A3),  Factor B has 2 levels B1 and B2)) with

n11=2, n12=1, n21=1, n22=2, n31=2, n32=1.

I'm trying to understand how the generating sets corresponding to Intercept, A, B and A*B for Type I, II, III and V Estimable Functions are formed in SAS. According to SAS USER GUIDE

a formalized representation of Type I generating sets for B1, B2, and B3, (regression model Y = X1 ×B1+X2 ×B2+X3 ×B3) respectively, is

G_1 & = & ( & X_1'X_1 & | & X_1'X_2 & | & X_1'X_3 & ) \  G_2 & = & ( & 0 & | & ... ..._2 & | & X_2'M_2{X}_3 & ) \  G_3 & = & ( & 0 & | & 0 & | & X_3'M_3{X}_3 & ) \

where

M_1 & = & I - X_1(X_1'X_1)^-X_1'

and

M_2 & = & M_1 - M_1{X}_2(X_2'M_1{X}_2)^-X_2'M_1

In the GLM procedure, the Type I estimable functions displayed symbolically when the E1 option is requested are

G_1^* & = & (X_1' X_1)^-G_1 \  G_2^* & = & (X_2'M_1{X}_2)^-G_2 \  G_3^* & = & (X_3'M_2{X}_3)^-G_3

Question 1: Are X1 , X2, X3, X4 etc the columns of the Design Matrix associated with Intercept, A, B, A*B

Question 2: How M3 (for G4 --> A*B) will be computed?

Question 3: When I tried to compute Type I estimable functions for Intercept, A, B, A*B using syntax commands in SAS I didn't manage to replicate the results. Am I wrong in syntax programming or the above definition of the generating sets is applicable only for regression models not containing factors such as Y = X1 ×B1+X2 ×B2+X3 ×B3? How the code for Type I Estimable functions will look like?

Cheers

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