 Structural Equation Modeling Results - Advanced Tab

Select the Advanced tab of the Structural Equation Modeling Results dialog box to access the options described here.

Model summary. Click the Model summary button to open the model summary spreadsheet, which presents model output in a spreadsheet form convenient for analysis. A variety of information is given for each path in the model. For a description of the spreadsheet, see Model Summary Spreadsheet.

Basic summary statistics. Click the Basic summary statistics button to produce a spreadsheet containing some of the basic summary statistics also presented in the Summary box. See Statistics in the Structural Equation Modeling Results Summary Box for more details on the information available there.

Iteration history. Click the Iteration history button to create a spreadsheet with iteration results. During iteration, STATISTICA saves the output that is displayed in the Iteration Window for the last executed sequence of iterations. By opening this spreadsheet, you can review these results. You can also save them to a data file or analyze them graphically. The statistics in this spreadsheet are described in Iteration Results.

Goodness-of-Fit Indices. Use the options under Goodness-of-Fit Indices to generate several of the best-known and most useful indices of fit for evaluating structural equation models. There are, literally, dozens of such indices, and we present only those which we think are very widely used, especially valuable, or both.

Noncentrality-based indices. Click the Noncentrality-based indices button to produce a spreadsheet with the non-centrality parameter and four goodness-of-fit indices. These indices are all based on the idea, first proposed by Steiger and Lind (1980), of basing goodness-of-fit assessment on an estimation of the population noncentrality parameter.  Instead of testing the hypothesis that the fit is perfect, we ask the questions (a) "How bad is the fit of our model to our statistical population?" and (b) "How accurately have we determined population badness-of-fit from our sample data." The indices presented here allow us to assess both questions, because they allow confidence interval assessment as well as the more traditional point estimates. As a result, they reward high sample size, and high power, with a narrower confidence interval expressing high precision of estimate. For more details, see the Noncentrality-Based, Goodness-of-Fit Indices spreadsheet.

Other single sample indices. Click the Other single sample indices button to create a spreadsheet with a sampling of some of the better known single sample indices of fit, and some related measures. For more details see the Single Sample, Goodness-of-Fit Indices spreadsheet.

Lagrange multiplier statistics. Click the Lagrange multiplier statistics button to produce a spreadsheet with Lagrange Multiplier statistics for each constraint required by the fitting procedure. In the Correlation option of Data to Analyze (see Analysis Parameters), each endogenous manifest variable has a dummy latent variable attached to it, with its variance constrained to one. If the New standardization method is employed, each endogenous latent variable has its variance constrained to one, and STATISTICA gives a Lagrange multiplier statistic for each variable.

The Lagrange Multiplier statistics should be zero, if the constraints serve (as they are meant to) solely as identification constraints. If any are non-zero, or significantly exceed the standard error, then the model has probably been miss-specified, or estimation did not converge properly.