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Unformatted text preview: HW 4 for Stat 7249  Spring 2009 Due March 19 Reading in text for this assignment • Chapter 8 Datasets • posted on class web page 1. Show that the complementary loglog model discussed in class (i.e., the Proportional hazards model) is equivalent to the ’continuationratio’ model given by g { π j ( x ) / (1 γ j 1 ( x )) } = α j β T x. (1) if g ( · ) is the complementary loglog link. Also, express α j in terms of the cutpoints θ 1 ,...,θ k 1 appearing in the PH model. 2. Consider the proportional odds model, logit γ j ( x i ) = θ j βx i with x and β both scalars. Denote by ˆ θ j and ˆ π j the fitted parameters and probabilities under the hypothesis that β = 0. Show that the derivative of the log likelihood with respect to β at β = 0, θ j = ˆ θ j , is given by T = X R ij x i s j where R ij = Y ij m i ˆ π j is the residual under independence and s j = ˆ γ j + ˆ γ j 1 . [Note: This is the score test of the hypothesis that β = 0 in the PO model].= 0 in the PO model]....
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This note was uploaded on 01/15/2012 for the course STA 7249 taught by Professor Daniels during the Spring '08 term at University of Florida.
 Spring '08
 Daniels

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