Example 29.2 Estimating Covariances and Means Simultaneously
This example uses the same data set that is used in Example 29.1 and estimates the means and covariances. Use the MSTRUCT model specification as shown in the following statements:
proc calis data=sales meanstr nostand;
mstruct var=q1-q4;
run;
In the PROC CALIS statement, specify the MEANSTR option to request the mean structure analysis in addition to the default covariance structure analysis. If you are not interested
in the standardized solution, specify the NOSTAND option in the PROC CALIS statement to suppress computation of the standardized estimates. Without further model specification
(such as the MATRIX statement), PROC CALIS assumes a saturated structural model with all means, variances, and covariances
as model parameters.
Output 29.2.1 shows the modeling information. With the MEANSTR option specified in the PROC CALIS statement, the current analysis type
is Means and Covariances, instead of the default Covariances in Example 29.1.
Output 29.2.1: Modeling Information of the Saturated Mean and Covariance Structure Model for the Sales
Data
The CALIS Procedure
Mean and Covariance Structures: Model and Initial Values
WORK.SALES |
14 |
14 |
14 |
MSTRUCT |
Means and Covariances |
Output 29.2.2 shows the fit summary of the current model. Again, this is a perfect model fit with 0 chi-square value and 0 degrees of freedom.
Output 29.2.2: Fit Summary of the Saturated Mean and Covariance Structure Model for the Sales
Data
Output 29.2.3 shows the estimates of the means, together with the standard error estimates and the t values. These estimated means are exactly the same as the sample means, which are not shown here.
Output 29.2.3: Mean Estimates for the Sales
Data
1.36714 |
0.16132 |
8.47491 |
2.07429 |
0.13146 |
15.77902 |
2.20286 |
0.21596 |
10.20008 |
3.65500 |
0.45281 |
8.07176 |
Output 29.2.4 shows the variance and covariance estimates. These estimates are exactly the same as the elements in the sample covariance
matrix. In addition, these estimates match the estimates in Output 29.1.5 of Example 29.1, where only the covariance structures are analyzed.
Output 29.2.4: Variance and Covariance Estimates for the Sales
Data
These estimates are essentially the same as the sample means, variances, and covariances. This kind of analysis is much easier
using PROC CORR with the NOMISS option. However, the main purpose of Example 29.1 and Example 29.2 is to introduce the MSTRUCT modeling language and some basic but important options in PROC CALIS. You can apply the MSTRUCT
modeling language to more sophisticated situations that are beyond the saturated mean and covariance structure models. Example 29.3 and Example 29.4 fit some patterned covariance models that are nonsaturated. Also, options such as NOSE, NOSTAND, and MEANSTR are useful for all modeling languages in PROC CALIS.