The CALIS Procedure

where functions are either parameters in the model or parametric functions computed in the SAS programming statements.

When the estimates in a model are asymptotically multivariate-normal, any continuous and differentiable function of the estimates is also normally distributed. In the TESTFUNC statement, you can test these parametric functions using z-tests. The form of the null hypothesis is as follows:

:

where is the set of model parameters (independent or dependent) in the analysis and is a continuous and differentiable function of the model parameters.

For example, if , , and are parameters in the model, and you want to test whether and are the same and whether is the same as the average of and , you can use the following statements:

testfunc   t1_t2_diff t3_t1t2_diff;
t1_t2_diff   = theta1 - theta2;
t3_t1t2_diff = theta3 - (theta1 + theta2)/2;

In the TESTFUNC statement, you test two functions: t1_t2_diff and t3_t1t2_diff. These two functions are defined in the SAS programming statements that follow after the TESTFUNC statement. Thus, t1_t2_diff represents the difference between and , and t3_t1t2_diff represents the difference between and the average of and .

See the SIMTESTS statement if you want to test several null hypotheses simultaneously.