The SURVEYLOGISTIC Procedure |
Testing the Parallel Lines Assumption
For an ordinal response, PROC SURVEYLOGISTIC performs a test of the parallel lines assumption. In the displayed output, this test is labeled "Score Test for the Equal Slopes Assumption" when the LINK= option is NORMIT or CLOGLOG. When LINK=LOGIT, the test is labeled as "Score Test for the Proportional Odds Assumption" in the output. This section describes the methods used to calculate the test.
For this test, the number of response levels,
, is assumed to be strictly greater than 2. Let
be the response variable taking values
. Suppose there are
explanatory variables. Consider the general cumulative model without making the parallel lines assumption:
where
is the link function, and
is a vector of unknown parameters consisting of an intercept
and
slope parameters
. The parameter vector for this general cumulative model is
Under the null hypothesis of parallelism
, there is a single common slope parameter for each of the
explanatory variables. Let
be the common slope parameters. Let
and
be the MLEs of the intercept parameters and the common slope parameters. Then, under
, the MLE of
is
and the chi-squared score statistic
has an asymptotic chi-square distribution with
degrees of freedom. This tests the parallel lines assumption by testing the equality of separate slope parameters simultaneously for all explanatory variables.
Copyright © SAS Institute, Inc. All Rights Reserved.