The CATMOD Procedure

Example 29.5 Log-Linear Model, Structural and Sampling Zeros

This example illustrates a log-linear model of independence, by using data that contain structural zero frequencies as well as sampling (random) zero frequencies.

In a population of six squirrel monkeys, the joint distribution of genital display with respect to active or passive role was observed. The data are from Fienberg (1980, Table 8-2). Since a monkey cannot have both the active and passive roles in the same interaction, the diagonal cells of the table are structural zeros. See Agresti (2002) for more information about the quasi-independence model.

The DATA step replaces the structural zeros with missing values, and the MISSING=STRUCTURAL option is specified in the MODEL statement to remove these zeros from the analysis. The ZERO=SAMPLING option treats the off-diagonal zeros as sampling zeros. Also, the row for Monkey 't' is deleted since it contains all zeros; therefore, the cell frequencies predicted by a model of independence are also zero. In addition, the CONTRAST statement compares the behavior of the two monkeys labeled 'u' and 'v'. See the section Structural and Sampling Zeros with Raw Data for information about how to perform this analysis when you have raw data. The following statements produce Output 29.5.1 through Output 29.5.8:

data Display;
   input Active $ Passive $ wt @@;
   if Active ne 't';
   if Active eq Passive then wt=.;
   datalines;
r r  0   r s  1   r t  5   r u  8   r v  9   r w  0
s r 29   s s  0   s t 14   s u 46   s v  4   s w  0
t r  0   t s  0   t t  0   t u  0   t v  0   t w  0
u r  2   u s  3   u t  1   u u  0   u v 38   u w  2
v r  0   v s  0   v t  0   v u  0   v v  0   v w  1
w r  9   w s 25   w t  4   w u  6   w v 13   w w  0
;

title 'Behavior of Squirrel Monkeys';
proc catmod data=Display;
   weight wt;
   model Active*Passive=_response_ /
         missing=structural zero=sampling
         freq pred=freq noparm oneway;
   loglin Active Passive;
   contrast 'Passive, U vs. V' Passive 0 0 0 1 -1;
   contrast 'Active,  U vs. V' Active  0 0 1 -1;
   title2 'Test Quasi-Independence for the Incomplete Table';
quit;

The results of the ONEWAY option are shown in Output 29.5.2. Monkey 't' does not show up as a value for the Active variable since that row was removed.

Sampling zeros are displayed as 0 in Output 29.5.4. The Response Number column corresponds to the value displayed in the "Response Profiles" table in Output 29.5.3.

The analysis of variance table (Output 29.5.5) shows that the model of independence does not fit since the likelihood ratio test for the interaction is significant. In other words, active and passive behaviors of the squirrel monkeys are dependent behavior roles.

If the model fit these data, then the contrasts in Output 29.5.6 show that monkeys 'u' and 'v' appear to have similar passive behavior patterns but very different active behavior patterns.

Output 29.5.7 displays the predicted response functions and Output 29.5.8 displays predicted cell frequencies (from the PRED=FREQ option), but since the model does not fit, these should be ignored. Note that, since the response function is the generalized logit with the 25th response as the baseline, the observed response functions for the sampling zeros are missing.

proc freq data=RawDisplay;
   tables Active*Passive / sparse out=Combos noprint;
run;

data Combos2;
   set Combos;
   if Active ne 't';
   if Active eq Passive then count=.; 
run;

proc catmod data=Combos2;
   weight count;
   model Active*Passive=_response_ /
         zero=sampling missing=structural
         freq pred=freq noparm noresponse;
   loglin Active Passive;
quit;