Example 28.4 Log-Linear Model, Three Dependent Variables

This analysis reproduces the predicted cell frequencies for Bartlett’s data by using a log-linear model of no three-variable interaction (Bishop, Fienberg, and Holland; 1975, p. 89). Cuttings of two different lengths (Length=short or long) are planted at one of two time points (Time=now or spring), and their survival status (Status=dead or alive) is recorded.

As in the text, the variable levels are simply labeled 1 and 2. The following statements produce Output 28.4.1 through Output 28.4.3:

data bartlett;
   input Length Time Status wt @@;
   datalines;
1 1 1 156     1 1 2  84     1 2 1 84     1 2 2 156
2 1 1 107     2 1 2 133     2 2 1 31     2 2 2 209
;

title 'Bartlett''s Data';
proc catmod data=bartlett;
   weight wt;
   model Length*Time*Status=_response_ 
         / noparm pred=freq;
   loglin Length|Time|Status @ 2;
   title2 'Model with No 3-Variable Interaction';
quit;

The analysis of variance table shows that the model fits since the likelihood ratio test for the three-variable interaction is nonsignificant. All of the two-variable interactions, however, are significant; this shows that there is mutual dependence among all three variables.

The predicted values table (Output 28.4.2) displays observed and predicted values for the generalized logits.

The predicted frequencies table (Output 28.4.3) displays observed and predicted cell frequencies, their standard errors, and residuals.