Some topics in the Details: CALIS Procedure section are intended primarily for references—you consult them only when you encounter specific problems in the PROC CALIS modeling or when you need to know the very fine technical details in certain special situations. Many of these reference topics in the Details: CALIS Procedure section are not required for practical applications of structural equation modeling. The following technical topics are discussed:

• Measures of multivariate kurtosis and skewness
  This is covered in the section Measures of Multivariate Kurtosis.

• Estimation criteria and the mathematical functions for estimation
  The section Estimation Criteria presents formulas for various estimation criteria. The relationships among these criteria are shown in the section Relationships among Estimation Criteria. To optimize an estimation criterion, you usually need its gradient and Hessian functions. These functions are detailed in the section Gradient, Hessian, Information Matrix, and Approximate Standard Errors, where you can also find information about the computation of the standard error estimates in PROC CALIS.

• Initial estimation
  Initial estimates are necessary for all kinds of iterative optimization techniques. They are described in section Initial Estimates.

• Use of optimization techniques
  Optimization techniques are covered in section Use of Optimization Techniques. See this section if you need to fine-tune the optimization.

• Output displays and control
  The output displays in PROC CALIS are listed in the section Displayed Output. General requirements for the displays are also shown.
  With the ODS system, each table and graph has a name, which can be used on the ODS OUTPUT or ODS SELECT statement. See the section ODS Table Names for the ODS table and graph names.

• Input and output files
  PROC CALIS supports several input and output data files for data, model information, weight matrices, estimates, fit indices, and estimation and descriptive statistics. The uses and the structures of these input and output data files are described in the sections Input Data Sets and Output Data Sets.