{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

07AlternativeParameterizations

# Such constraints have no impact on what linear

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: and only if C (X ) ∩ C (M ) = {0} and rank(M) = p − rank(X). Such constraints have no impact on what linear functions of β are estimable or on inferences about estimable functions of β . Thus, the same analysis results are obtained with or without constraints. Copyright c 2010 Dept. of Statistics (Iowa State University) Statistics 511 9 / 14 In 511, we often start with a non-full-rank design matrix for ease and symmetry when specifying a model. For example, it is nice to be able to write yijk = µ + αi + βj + ijk for i = 1, 2, 3; j = 1, 2, 3, 4; k = 1, . . . , 10 if we want to specify a two-factor additive model. The design matrix that matches this model speciﬁcation does not have full-column rank. R (and other statistical software) will automatically pick a full-column-rank design matrix, which is equivalent to placing certain constraints on the solutions to the normal equations. Copyright c 2010 Dept. of Statistics (Iowa State University) Statistics 511 10 / 14 It does not matter which full-column-rank design matrix (or corresponding constraint set) is chosen as long as the column space of the selected design matrix is the same as the c...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online