Model Options
After you click Run in the Model Specification report, a Structural Equation Model report for the specified model appears. When you specify a Groups variable in the launch window, the model options show or hide elements in the reports for all levels of the Groups variable. This report has a red triangle menu that contains the following options:
Show Path Diagram
Shows or hides the path diagram in the model report.
Path Diagram Settings
Contains the following options to modify the path diagram for the model:
Customize Diagram
Enables you to customize many aspects of the path diagram. See Options to Customize the Path Diagram.
Layout
Contains two options that change the overall shape of the path diagram. You can choose between a Left to Right layout or a Top to Bottom layout.
Tip: You can also drag items in the path diagram to change the arrangement of specific items.
Copy Diagram
Saves an image of the path diagram to the clipboard. To retain the highest possible quality, paste the clipboard image as a vector graphic.
Copy Diagram Properties
Copies the current path diagram properties to the clipboard. You can then paste the properties into another SEM path diagram.
Paste Diagram Properties
Pastes the path diagram properties from the clipboard into the current SEM path diagram.
Summary of Fit
Shows or hides a report that contains details of the model fit.
Parameter Estimates
Shows or hides a report that contains the unstandardized parameter estimates for the model.
Standardized Parameter Estimates
Shows or hides a report that contains the standardized parameter estimates for the model.
Confidence Intervals
Shows or hides confidence intervals in the Parameter Estimates and Standardized Parameter Estimates reports.
Fit Indices
Shows or hides a report that contains a variety of index values that enable you to evaluate the fitted model. In addition to values that appear in the Summary of Fit report (see Structural Equation Model Fit Report), the Fit Indices report also contains the following index values:
BIC
The Bayesian information criterion. This value can be used to compare models, where a smaller number indicates a better model fit. See AICc, BIC, and BICu.
RNI
The relative noncentrality index (RNI) provides additional guidance for determining model fit. This value is equivalent to the CFI, but it is not bounded at 1. Values greater than 0.90 are preferred. See RNI.
TLI
The Tucker-Lewis index (TLI) provides additional guidance for determining model fit. This index is also known as the non-normed fit index (NNFI). The TLI is bounded between 0 and 1. Values greater than 0.95 are preferred (West et al. 2012). See TLI.
NFI
The normed fit index (NFI) provides additional guidance for determining model fit. The NFI is bounded between 0 and 1. Values greater than 0.95 are preferred (West et al. 2012). See NFI.
Revised GFI
The revised goodness-of-fit index provides additional guidance for determining model fit. The revised GFI is bounded between 0 and 1. Values greater than 0.95 are preferred (West et al. 2012). See Revised GFI and Revised AGFI.
Revised AGFI
The revised adjusted goodness-of-fit index provides additional guidance for determining model fit. The revised AGFI is bounded between 0 and 1 (West et al. 2012). See Revised GFI and Revised AGFI.
RMR
The root mean square residual (RMR) provides additional guidance for determining model fit. The residuals for the RMR are from the differences between the observed and model-implied covariances. The RMR is positive and smaller values are preferred (West et al. 2012). See RMR and SRMR.
SRMR
The standardized root mean square residual (SRMR) provides additional guidance for determining model fit. The residuals for the SRMR are from the standardized differences between the observed and model-implied covariances. The SRMR is positive and smaller values are preferred (West et al. 2012). See RMR and SRMR.
Note: For a description of the other values in the Fit Indices report, see Structural Equation Model Fit Report.
Total Effects
(Available only when a model contains at least one regression or loading variable and the effects converge.) Shows or hides a table of unstandardized and standardized estimates of the total effects in the model. Standard errors are also included. The test for convergence of the effects is described in Bentler and Freeman (1983). The right side of the table contains a bar chart of the standardized estimates.
Indirect Effects
(Available only when a model contains mediating variables and the effects converge.) Shows or hides a table of unstandardized and standardized estimates of the indirect effects in the model. Standard errors are also included. The test for convergence of the effects is described in Bentler and Freeman (1983). The right side of the table contains a bar chart of the standardized estimates.
Tip: You can obtain bootstrap estimates of the values in the Indirect Effects table. To run a bootstrap analysis, right-click in a table column that contains the statistic that you want to bootstrap and select Bootstrap. See “Bootstrapping” in Basic Analysis.
Specific Indirect Effects
(Available only when a model contains mediating variables and the effects converge.) Shows a table of unstandardized and standardized estimates for each identified specific indirect effect between a selected predictor and outcome variable. Each row in the table corresponds to a unique mediating path. All possible indirect paths that connect the selected variables are identified and estimated individually. This enables you to isolate and interpret individual mediating pathways, which provides insight into how the influence of one variable is transmitted through intermediate variables in the model. The right side of the table contains a bar chart of the standardized estimates.
Tip: When you use the Specific Indirect Effects option multiple times, each set of selected paths is appended to the existing table. To remove the table from the report, use the Remove option from the Specific Indirect Effects red triangle menu.
Prediction Profiler
(Not available when MIIV Two-Stage Least Squares estimation method is selected.) Enables you to view the effects of a set of predictors on the conditional expected values of a set of outcome variables. When you select this option, a window appears in which you must select one or more predictors and one or more outcomes. The predictions and 95% confidence intervals are based on the model-implied covariance matrix. For more information about the prediction profiler, see “Profiler” in Profilers.
Note: The initial list of variables in the setup window is limited to variables that are consistent with the model. For example, the Select Predictors list contains only variables that predict something in the model and the Select Outcomes list contains only variables that are predicted by some other variable in the model. Check the Show All Variables box to see all model variables in both lists.
Model Implied Covariances
Shows or hides a report that contains the covariance matrix that is implied by the model.
Model Implied Correlations
Shows or hides a report that contains the correlation matrix that is implied by the model.
Model Implied Means
Shows or hides a report that contains the means for each variable that are implied by the model.
Residuals
Shows or hides a report that contains a matrix of the residuals for the model. This matrix is the difference between the model implied covariance matrix and the sample covariance matrix.
Normalized Residuals
Shows or hides a report that contains a matrix of the normalized residuals for the model.
RAM Matrices
Shows or hides a report that contains the model matrices used in reticular action model (RAM) notation.
Covariance of Estimates
Shows or hides a report that contains the covariance matrix of the parameter estimates for the model.
Correlation of Estimates
Shows or hides a report that contains the correlation matrix of the parameter estimates for the model.
R2 for Endogenous Variables
(Available only when the model is recursive and contains endogenous variables.) Shows or hides a report that contains the R2 values for each endogenous variable in the model. This value is calculated as 1 minus the ratio of the residual variance and the model-implied variance for each endogenous variable. The R2 values represent how much variance is explained by the model in an endogenous variable. An endogenous variable is one with a path directed toward it in the path diagram.
Heat Maps
Enables you to visualize the residuals, covariances, and correlations in the model.
Normalized Residuals Heat Map
Shows or hides a report that contains a heat map of the normalized residuals for the model.
Model Implied Covariances Heat Map
Shows or hides a report that contains a heat map of the covariance matrix that is implied by the model.
Model Implied Correlations Heat Map
Shows or hides a report that contains a heat map of the correlation matrix that is implied by the model.
Covariance of Estimates Heat Map
Shows or hides a report that contains a heat map of the covariance matrix of the parameter estimates for the model.
Correlation of Estimates Heat Map
Shows or hides a report that contains a heat map of the correlation matrix of the parameter estimates for the model.
Modification Indices
Enables you to show all or a subset of the estimates of model modification indices. These values can be used to determine which parameters might be added to the model to improve model fit. Each table is sorted by the ChiSquare column in descending order.
All Modification Indices
Shows or hides a table that contains the estimates of all the model modification indices. This table contains a column that indicates the parameter type for each estimate.
Modification Indices for Means
Shows or hides a table that contains the estimates of the model modification indices for the means and intercepts.
Modification Indices for Loadings
Shows or hides a table that contains the estimates of the model modification indices for the loading parameters.
Modification Indices for Regressions
Shows or hides a table that contains the estimates of the model modification indices for the regression parameters.
Modification Indices for Variances
Shows or hides a table that contains the estimates of the model modification indices for the variance parameters.
Modification Indices for Covariances
Shows or hides a table that contains the estimates of the model modification indices for the covariance parameters.
Assess Measurement Model
(Available only for confirmatory factor models) Shows or hides a variety of statistics and graphs for quantifying the reliability and validity of tests and measures, including indicator reliability, construct validity matrix, composite reliability (coefficient Omega), and construct maximal reliability (coefficient H).
The Indicator Reliability report shows the squared standardized loadings for each manifest variable. A bar chart shows the reliability values along with a suggested minimum threshold for acceptable reliability (0.25). Low values for a variable indicate that the variable does not do a very good job of capturing variability in the corresponding latent variable.
The Construct Validity Matrix report helps evaluate whether latent variables are measuring their intended constructs:
– The lower triangular entries contain correlations between latent variables. These entries enable you to check how strongly correlated the latent variables are with each other and compare that to the hypothesized strength of correlation.
– The upper triangular entries are the squared correlations between latent variables. These entries enable you to focus on the overlap in variance across latent variables and potential overlap in what they measure. These statistics are particularly valuable when compared against the diagonal entries in the matrix.
– The diagonal entries contain the Average Variance Extracted (AVE) for each latent variable. The AVE is computed as the ratio of the sum of squared standardized loadings to the sum of squared loadings plus corresponding error variances. This computation avoids overestimation in situations where indicators load on multiple factors (such as bi-factor or double-loading models). The AVE is equivalent to the average of the indicator reliabilities for standard CFA models. High AVE values imply that the latent variable is consistently captured by the indicators. The AVE for a latent variable must be greater than its squared correlations with other latent variables (entries above and to the right of the diagonal) in order for discriminant validity to be considered adequate.
The accompanying visualization of the construct validity matrix enables you to compare the diagonal entries to the upper triangular entries. High AVE values and lower squared correlations support discriminant validity.
The Composite Reliability report shows the standardized and unstandardized coefficient Omega (McDonald 1999) for each latent variable, accompanied by bar charts for visual interpretation. The Construct Maximal Reliability report shows the coefficient H (Hancock and Mueller 2001) for each latent variable, accompanied by a bar chart displaying coefficient H for each latent variable. The values for coefficient Omega and coefficient H range from 0 to 1, and it is recommended that they are about 0.70 or greater. Omega represents the proportion of variance of the composite score(s) that is explained by the latent variable(s). Unlike Cronbach's alpha, Omega reliability does not assume a unidimensional construct with equal factor loadings and is therefore more trustworthy. H represents the proportion of latent variable variance represented by the indicators. These estimates are model-dependent; if a one-factor model is fit, the resulting Omega is known as general omega. If a factor model with more than one latent variable is fit, the resulting omega estimates are known as subscale omegas. However, if a bi-factor model is fit, the omega for the general factor estimate is known as hierarchical omega, whereas the group factors are known as hierarchical subscale omegas (Rodriguez et al. 2015). The standardized Omega coefficient represents the ratio of true score variance to total variance. True score variance is model-dependent and calculated using squared standardized loadings, whereas total variance is derived from the variance of the composite score based on the sample correlation matrix (Kelley and Pornprasertmanit 2016). Unstandardized Omega is computed using unstandardized loadings and variances, making it particularly useful for assessing the reliability of raw (sum) scores obtained directly from observed indicators.
The suggested thresholds should be used in the context of the goals for the survey; if you plan to use composite scores to make decisions about individuals, then reliability should be higher than the suggested threshold (around 0.90 or greater) but if you plan to use composite scores for research purposes, then the lower end of the threshold is acceptable (Nunnally 1978).
See Example of the Assess Measurement Model Report.
Predicted Values Plot
Shows or hides a plot of the predicted values for the endogenous variables in the model. For longitudinal data, this plot shows the model-implied growth trajectories over time. By default, the predicted values are shown as a box plot. Select the Connect data points check box to switch the display to a line plot.
Save Columns
Enables you to save columns based on the fitted structural equation model to the data table.
Save Factor Scores
(Available only when there are latent variables in the model.) Saves a column with the factor score computed using the regression method for each latent variable to the data table. The factor scores are calculated in a hidden column that is also added to the data table. This hidden column uses the Estimate Factor Score() JSL function. For more information about this function, see Help > Scripting Index.
Save Bartlett Factor Scores
(Available only when there are latent variables in the model.) Saves a column with the factor score computed using the Bartlett method for each latent variable to the data table. The factor scores are calculated in a hidden column that is also added to the data table. This hidden column uses the Estimate Bartlett Factor Score() JSL function. For more information about this function, see Help > Scripting Index.
Save Prediction Formulas
(Available only when there is at least one endogenous or dependent variable in the model.) Saves a column with a formula for the predicted values of the observed outcomes for each variable to the data table. When there are latent variables in the model, factor scores computed using the Bartlett method are also saved to the data table.
Save Observational Residuals
(Available only when there is at least one endogenous or dependent variable in the model.) Saves a column with the residual values of the observed outcomes for each variable to the data table. When there are latent variables in the model, factor scores computed using the Bartlett method are also saved to the data table.
Copy Model Specification
Copies the current structural equation model specifications to the clipboard. You can then paste the model specifications into another SEM platform report.
Recall in Model Specification
Sets the model in the Model Specification report to the specified model.
Remove Fit
Removes the specified model report from the report window.