Example 5 for PROC CATMOD: Log-Linear Model

This script analyzes the joint distribution of interactions (active role, passive role) within a population of 6 squirrel monkeys. Data comes from Fienberg (1980). The diagonal of the contingency table consists of structural zeros, as a monkey cannot interact with itself (have both active and passive roles simultaneously). The script uses PROC CATMOD to fit a quasi-independence model, which tests the independence of variables conditionally on the absence of structurally empty cells. Specific contrast tests are also performed to compare the behaviors of certain monkeys.

Data Analysis

Type : CREATION_INTERNE

The data is created directly in the script via a DATA step with a DATALINES statement. Interactions are read, and structural zeros are defined by setting the weight variable (wt) to a missing value when the 'active' and 'passive' monkeys are the same.

1 Code Block

DATA STEP Data

Explanation :
This DATA STEP block reads the interaction data. The `input` statement with the double at sign (`@@`) allows reading multiple observations on the same data line. The condition `if Active eq Passive then wt=.;` is crucial as it identifies the diagonal cells of the table and assigns a missing value to the `wt` weight, thereby marking them as structural zeros for the subsequent analysis.

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1	DATA Display;
2	INPUT Active $ Passive $ wt @code_sas_json/8_SAS_Intro_ReadFile_MultiCol_@@.json;
3	IF Active ne 't';
4	IF Active eq Passive THEN wt=.;
5	DATALINES;
6	r r 0 r s 1 r t 5 r u 8 r v 9 r w 0
7	s r 29 s s 0 s t 14 s u 46 s v 4 s w 0
8	t r 0 t s 0 t t 0 t u 0 t v 0 t w 0
9	u r 2 u s 3 u t 1 u u 0 u v 38 u w 2
10	v r 0 v s 0 v t 0 v u 0 v v 0 v w 1
11	w r 9 w s 25 w t 4 w u 6 w v 13 w w 0
12	;

2 Code Block

PROC CATMOD

Explanation :
The CATMOD procedure is used for categorical data analysis. `weight wt;` specifies the frequency variable. The `model` statement defines the complete interaction model. The `missing=structural` option tells the procedure that missing values for `wt` correspond to structural zeros and should be excluded from the analysis, while `zero=sampling` treats other zeros as sampling zeros. `loglin Active Passive;` fits a log-linear model with only main effects, which corresponds to a quasi-independence test. Finally, the `contrast` statements allow performing specific hypothesis tests on the model parameters, here to compare monkeys 'u' and 'v'.

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1	PROC CATMOD DATA=Display;
2	weight wt;
3	model Active*Passive=_response_ /
4	missing=structural zero=sampling
5	freq pred=freq noparm oneway;
6	loglin Active Passive;
7	contrast 'Passive, U vs. V' Passive 0 0 0 1 -1;
8	contrast 'Active, U vs. V' Active 0 0 1 -1;
9	title2 'Test Quasi-Independence for the Incomplete Table';
10	QUIT;

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