Introduction to Structural Equation Modeling with Latent Variables

Testing Parametric Functions

Oftentimes, researchers might have a priori hypotheses about the parameters in their models. After knowing the model fit is satisfactory, they want to test those hypotheses under the model. PROC CALIS provides two statements for testing these kinds of hypotheses. The TESTFUNC statement enables you to test each parametric function separately, and the SIMTESTS statement enables you to test parametric functions jointly (and separately). For example, assuming that effect1, effect2, effect3, and effect4 are parameters in your model, the following SIMTESTS statement tests the joint hypothesis test1, which consists of two component hypotheses diff_effect and sum_effect:

SIMTESTS  test1 = (diff_effect sum_ffect);
diff_effect = effect1 - effect2;
sum_effect  = effect3 + effect4;

To make test1 well-defined, each of the component hypotheses diff_effect and sum_effect is assumed to be defined as a parametric function by some SAS programming statements. In the specification, diff_effect represents the difference between effect1 and effect2, and sum_effect represents the sum of effect3 and effect4. Hence, the component hypotheses being tested are:

\begin{eqnarray*}  H_{1}\colon & &  \mbox{diff}\_ \text {effect} = \mbox{effect1} - \mbox{effect2} = 0 \\ H_{2}\colon & &  \mbox{sum}\_ \text {effect} = \mbox{effect3} + \mbox{effect4} = 0 \end{eqnarray*}