In Example 7.9, include a predictor selection mechanism (see Chapter 3) in the MNAR version of the missing data logit regression for \(\eta_{i}\) (under a selection model approach). How does this affect inferences about \(\Delta\)?

Data from Example 7.9

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To illustrate contrasting inferences under selection and pattern mixture models consider data on milk yields (thousands of litres) for n = 107 dairy cows and T = 2 years (Kenward, 1998). In the first year there is complete response, but in the second year, when some cows became infected with mastitis, there are 26 cows with missing yields. Of substantive interest is the change in average yield between the two years as this may be affected by the mastitis infection. Inferences are in all examples based on the second half of two chain runs of 20 000 iterations. Initially a selection model is adopted with a bivariate normal likelihood assumed for the two readings, yi = (Vil, Yiz) yi~ N (u,). The missing data indicators are R; = 1 if year 2 yields are observed, and R = 0 otherwise. The missing data model R; ~ Bern(ni) could allow dependence on both the known first year yield alone (i.e. in line with MAR), or on both the first year yield and the possibly missing second year yield: logit(n) Bo+Byil + B2y12.