# hw5 - ﬁnal model 2 Conditional random coeﬃcient models...

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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: ﬁnal model. 2. Conditional random coeﬃcient models Now let’s assume each child has his/her own probability trajectory that’s linear on the log-odds scale: logit π ij = β + β 1 s i + β 2 t j + b i + b i 1 t j , b i iid ∼ N 2 ( , Σ ) . Fit this model in PROC GLIMMIX; use method=laplace . Interpret the model. 3. Assume a quadratic mean eﬀect, but only child-speciﬁc random intercepts: logit π ij = β + β 1 s i + β 2 t j + β 3 t 2 j + b i b i iid ∼ N (0 ,σ 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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