In Example 7.3 investigate whether an improved fit results from making all the lag coefficients random (including lags 1 and 3 ), and with all mean lag coefficients unknown (including the mean of \(ho_{5 i}\) ).

Data from Example 7.3

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This example demonstrates options for representing varying autoregressive dependence in data on the percentage protein content y(t = 1, ..., T;) of cow milk according to diet regime. This may be an alternative to polynomial growth models in the face of diversity in the shapes of individual trajectories. 52 cows were observed for a maximum of T; = 19 weeks, though some were observed for less than this - the numbers of weeks vary from 14 to 19. There are also a few missing cases in intervening weeks, before the end of the observation period on particular cows. These are assumed to be missing at random. Following Rahiala (1999), a lag 5 model is fitted which conditions on the first five obser- vations, with lags assumed at 1, 2, 3 and 5 weeks, varying coefficients at lag 2 and 5, and with the mean lag at 5 taken as zero. Thus Yit~ N(Vit, s), Vit = Poi + P1yit-1 + P2iVit-2 + P3Yit-3 + P5iVit-5+X;B,