By José Pinheiro, Douglas Bates
This ebook offers an outline of the idea and alertness of linear and nonlinear mixed-effects types within the research of grouped info, comparable to longitudinal info, repeated measures, and multilevel information. Over one hundred seventy figures are integrated within the booklet.
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Extra info for Mixed Effects Models in S and S-Plus
Example text
4 —Three times the difference between T4 and the average of T1, T2, and T3. Fitting the model in this form with lme produces > fm1Stool <+ lme(effort ~ Type, data = ergoStool, random = ~ 1 | Subject) > summary( fm1Stool ) . . 0035 16 T2 T3 1. 6314 Number of Observations: 36 Number of Groups: 9 By convention, the coefficient corresponding to the first column in the X i , which is the column of 1’s, is called the intercept. 4 where a straight-line model for each group is written in terms of its slope and its intercept with the y-axis.
This allows the overall pattern to vary between dogs in terms of the location of the peak, but not in terms of the curvature at the peak. The only difference between sides for the same dog will be a shift in the intercept. 42 1. 17. Pixel intensity on CT scans over time for lymph nodes on the left and the right sides of 10 dogs. 4349 est. 2998 Random Effects: Level: Dog lower est. 19138 Level: Side lower est. 173 Within-group standard error: lower est. 18 If we write the pixel intensity of the jth side’s on the ith dog at the kth occasion as yijk i = 1, .
It may be feasible to use a model with a common slope. 11 would lead us to expect. Furthermore, even though we have ordered the groups from the one with the smallest average distance (subject F10) to the one with the largest average distance (subject F11), this ordering is not reflected in the intercepts. Finally, we see that the pattern across subjects in the intervals for the intercepts is nearly a reflection of the pattern in the intervals for the slopes. Those with experience analyzing regression models may already have guessed why this reflection of the pattern occurs.