hw5 - nal model. 2. Conditional random coecient models Now...

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Stat 771 Homework 5, due Monday, April 25 We will consider data from a longitudinal study at Harvard of effects of air pollution on respiratory illness in children. The children were examined annually at ages 7 through 10 and classified according to the presence of absence of respiratory illness. The only predictor is whether a kid’s mom smoked at the start of the study: s i = 1 for smoking regularly and s i = 0 otherwise. 1. Marginal model Fit the following marginal model in PROC GENMOD: logit π ij = β 0 + β 1 s i + β 2 t j + β 3 t 2 j + β 4 s i t j . Here, Y i = Y i 1 Y i 2 Y i 3 Y i 4 and t = 7 8 9 10 . Try AR(1), compound symmetry, and unstructured for the correlation matrices; choose one via QIC. If you can drop the smoking by time interaction, do so. Interpret your
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Unformatted text preview: nal model. 2. Conditional random coecient models Now lets assume each child has his/her own probability trajectory thats linear on the log-odds scale: logit ij = + 1 s i + 2 t j + b i + b i 1 t j , b i iid N 2 ( , ) . Fit this model in PROC GLIMMIX; use method=laplace . Interpret the model. 3. Assume a quadratic mean eect, but only child-specic random intercepts: logit ij = + 1 s i + 2 t j + 3 t 2 j + b i b i iid N (0 , 2 ) . Fit this model in PROC GLIMMIX; use method=laplace . Interpret the model. Which model (in 2 or 3) has lower AIC? 1...
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