07AlternativeParameterizations

# The most common constraints are set rst to zero 1 0 r

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Unformatted text preview: ro” τ1 = 0 R default “set last to zero” τ3 = 0 SAS effective default “sum to zero” τ1 + τ2 + τ3 = 0 Copyright c 2010 Dept. of Statistics (Iowa State University) Statistics 511 4 / 14 Such constraints are not necessary. Placing such constriants on the parameters can be viewed as equivalent to choosing a particular full column rank design matrix. Set ﬁrst to zero: 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 Copyright c 2010 Dept. of Statistics (Iowa State University) µ = τ2 τ 3 µ µ µ + τ2 µ + τ2 µ + τ3 µ + τ3 Statistics 511 5 / 14 Set last to zero: 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 µ τ1 = τ2 Sum to zero: τ1 + τ2 + τ3 = 0 ⇐⇒ τ3 1 1 0 1 0 1 µ 0 1 1 τ1 = 0 1 1 1 −1 −1 τ 2 1 −1 −1 Copyright c 2010 Dept. of Statistics (Iowa State University) µ + τ1 µ + τ1 µ + τ2 µ + τ2 µ µ = −τ1 − τ2 µ + τ1 µ + τ1 µ + τ2 µ + τ2 µ − τ1 − τ2 µ − τ1 − τ2 Statistics 511 6 / 14 Instead of viewing “identiﬁability constraints” as constraints on parameters, we can view them as constraints on our solutions to the norma...
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## This document was uploaded on 03/27/2014.

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