hw4 - HW 4 for Stat 7249 - Spring 2009 Due March 19 Reading...

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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 log-log model discussed in class (i.e., the Proportional hazards model) is equivalent to the continuation-ratio model given by g { j ( x ) / (1- j- 1 ( x )) } = j- T x. (1) if g ( ) is the complementary log-log link. Also, express j in terms of the cutpoints 1 ,..., k- 1 appearing in the PH model. 2. Consider the proportional odds model, logit j ( x i ) = j- x i with x and both scalars. Denote by j and j the fitted parameters and probabilities under the hypothesis that = 0. Show that the derivative of the log likelihood with respect to at = 0, j = j , is given by T = X R ij x i s j where R ij = Y ij- m i j is the residual under independence and s j = j + j- 1 . [Note: This is the score test of the hypothesis that = 0 in the PO model].= 0 in the PO model]....
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hw4 - HW 4 for Stat 7249 - Spring 2009 Due March 19 Reading...

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