{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

07AlternativeParameterizations

# However it is important to understand the design

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: olumn space of the design matrix for the model as originally speciﬁed. However, it is important to understand the design matrix used so that the parameter estimates corresponding to coefﬁcients in the linear combination of the columns of the design matrix can be properly interpreted. Copyright c 2010 Dept. of Statistics (Iowa State University) Statistics 511 11 / 14 For example, suppose E(yij ) = µ + τi for i = 1, 2, 3 and j = 1, . . . , ni What does the parameter τ2 represent? Constraints none set ﬁrst to zero set last to zero sum to zero Interpretation of τ2 non-estimable trt 2 mean − trt 1 mean trt 2 mean − trt 3 mean trt 2 mean − average of trt 1, 2, 3 means opyright c 2010 Dept. of Statistics (Iowa State University) Statistics 511 12 / 14 Recall that all linear functions of E(y) are the only estimable quantities; i.e., the estimable quantities are given by {AE(y) : A an n-column matrix of constants}. Thus, as long as models restrict E(y) to the same column space, the estimable quantities are identical. Copyright c 2010 Dept. of Statistics (Iowa State University) Statistics 511 13 / 14 Then why, in the treatment effects formulation of the model, is it that τ2 is estimable under “set ﬁrst to zero” constraint but not estimable without constraints? Under “set ﬁrst to zero” constraint, τ2 is the estimable quantity “treatment 2 mean − treatment 1 mean.” With no constraints, that same quantity is also estimable, but it is τ2 − τ1 . Copyright c 2010 Dept. of Statistics (Iowa State University) Statistics 511 14 / 14...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online