## Example 25.2 Estimating Covariances and Means Simultaneously

This example uses the same data set that is used in Example 25.1 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 25.2.1 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 25.1.

**
Output 25.2.1
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 25.2.2 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 25.2.2
Fit Summary of the Saturated Mean and Covariance Structure Model for the Sales Data**

Output 25.2.3 shows the estimates of the means, together with the standard error estimates and the values. These estimated means are exactly the same as the sample means, which are not shown here.

**
Output 25.2.3
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 25.2.4 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 25.1.5 of Example 25.1, where only the covariance structures are analyzed.

**
Output 25.2.4
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 25.1 and Example 25.2 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 25.3 and Example 25.4 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.