Testing Built-In Covariance Patterns in PROC CALIS
Some covariance patterns are well-known in multivariate statistics. For example, testing the diagonal pattern for a covariance
matrix in the preceding section is a test of uncorrelatedness between the observed variables. Under the multivariate normal
assumption, this test is also a test of independence between the observed variables. This test of independence is routinely
applied in maximum likelihood factor analysis for testing the zero common factor hypothesis for the observed variables. For
testing such a well-known covariance pattern, PROC CALIS provides an efficient way of specifying a model. With the COVPATTERN= option, you can invoke the built-in covariance patterns in PROC CALIS without the MSTRUCT model specifications, which could
become laborious when the number of variables are large.
For example, to test the diagonal pattern (uncorrelatedness) of the motor skills, you can simply use the following specification:
proc calis data=motor covpattern=uncorr;
run;
The COVPATTERN=UNCORR option in the PROC CALIS statement invokes the diagonally patterned covariance matrix for the motor
skills. PROC CALIS then generates the appropriate free parameters for this built-in covariance pattern. As a result, the MATRIX
statement is not needed for specifying the free parameters, as it is if you use explicit MSTRUCT model specifications. Some
of the output for using the COVPATTERN= option is shown in Figure 17.3.
In the second table of Figure 17.3, the estimates of variances and their standard errors are the same as those shown in Figure 17.2. The only difference is that the parameter names (for example, _varparm_1
) for the variances in Figure 17.3 are generated by PROC CALIS, instead of being specified as those in Figure 17.2.
However, the current chi-square test for the model fit is 8.8071 (df=3, p=0.0320), which is different from that in Figure 17.2 for testing the same covariance pattern. The reason is that the chi-square correction due to Bartlett (1950) has been applied automatically to the current built-in covariance pattern testing. Theoretically, this corrected chi-square
value is more accurate. Therefore, in addition to its efficiency in specification, the built-in covariance pattern with the
COVPATTERN= option offers an extra advantage in the automatic chi-square correction.
The COVPATTERN= option supports many other built-in covariance patterns. For details, see the COVPATTERN= option. See also the MEANPATTERN= option for testing built-in mean patterns.