Model Comparison Report
The Model Comparison report in the Structural Equation Models platform contains a table of all the models that have been fit. Use the icons in the second column to control which model reports appear below the Model Comparison report. The rest of the columns to the right of Model Name enable you to compare models based on various criteria.
The AICc Weight value for a model can be interpreted as the probability that a particular model is the true model given that one of the fitted models is the truth. Therefore, the model with the AICc weight closest to one is the best fit. The AICc weights are calculated using only nonmissing AICc values and are defined as follows:
AICcWeight = exp[-0.5(AICc-min(AICc))] / sum(exp[-0.5(AICc-min(AICc))])
where min(AICc) is the smallest AICc value among the fitted models.
For information about the other criteria in the Model Comparison report, see Structural Equation Model Fit Report.
Note: If a model does not converge, an asterisk appears at the beginning of the model name in the Model Comparison report.
To provide context for the performance of the fitted models, the following two models are shown by default in the Model Comparison report:
Unrestricted (Saturated)
Fits all means, variances, and covariances of the specified Model Variables without imposing any structure on the data.
Independence
Fits all means and variances of the specified Model Variables and fixes all covariances to zero.
Model Comparison Table Options
The following options are available in the pop-up menu in the Model Comparison table after a row in the table has been selected.
Rename Model
(Applies only when you have selected a model in the table other than Unrestricted (Saturated) or Independence.) Enables you to change the name of a model that has already been fit. When you change the name of the model in the Model Comparison table, the name of the model in the corresponding outline in the report is also updated.
Set as Independence Model
(Applies only when you have selected a model in the table other than Unrestricted (Saturated) or Independence.) Replaces the Independence model with the selected model in the report. This option is particularly useful for longitudinal models. When you change the Independence model, the comparative fit indices in the Model Comparison table are updated.
Caution: Specifying the incorrect independence model can lead to invalid fit indices.
Reset Default Independence Model
(Available only when a model other than the default independence model has been set as the independence model.) Restores the default independence model as the Independence model for model comparisons. This option also updates the comparative fit indices in the Model Comparison table to their original values.
Model Comparison Report Options
Two options appear below the Model Comparison table. These options are available after you click on rows to highlight them in the Model Comparison table.
Compare Selected Models
(Available only when two or more rows of the table are highlighted.) Computes nested chi-square difference tests between all nested model combinations of the selected rows.
Tip: If any of the models that you select are not nested, a warning appears and the non-nested combination of models does not appear in the Chi-Square Difference Test report.
Clear Selection
(Available only when one or more rows of the table are highlighted.) Clears all selections from the rows of the table.
Chi-Square Difference Test Report
The Chi-Square Difference Test report in the Structural Equation Models platform contains a table of nested chi-square tests. The table contains two columns that define the models. The first column contains the more constrained of the two models, and the second column contains the less constrained of the two models. The smaller model is nested within the larger model. The remaining columns show the differences in chi-square values, degrees of freedom, CFI, and RMSEA, as well as the p-values for the nested chi-square tests. The Δ notation in the column names indicates differences. A significant Δ chi-square value indicates that the additional constraints in the nested model produce a statistically significant increase in misfit and that the less constrained model should be retained. Because chi-square tests are influenced by sample size, such that they are more likely to be significant as sample sizes increase, the ΔCFI and ΔRMSEA should also be considered; ideally, the ΔCFI should not exceed –0.01 and ΔRMSEA should not exceed 0.015 (Chen 2007).
Caution: Difference tests in this report are meaningful only for nested models.
You can remove any row of the report by clicking the red X button. To remove the report entirely, you must remove all of the rows of the table. If you remove a Structural Equation Model node in the main report, any difference tests involving that model are removed from the table.