Model Specification Report

The Model Specification report in the Structural Equation Models platform contains controls for specifying your model. When you click OK in the launch window, the default model of independence appears in the Diagram and Lists tabs of the Model Specification report. The independence model includes all means and variances of the specified Model Variables.

Specification Panel

The Specification panel contains controls for building your model.

Model Name

Enables you to specify a name for the model. When you click Run in the Action panel, a model report that uses the text in Model Name is created.

From List

Lists the model variables that were specified in the launch window as well as a Constant term. The Constant term estimates means of any observed or latent variable by regressing each variable on the Constant. Select one or more variables in this list and one or more variables in the To List before clicking one of the arrow buttons to add terms to the model. If you create a latent variable, the latent variable is added to the From List and the To List. You can filter the items in this list using the search filter controls at the top of the list. See Search Filter Options.

To List

Lists the model variables that were specified in the launch window as well as a Constant term. The Constant term estimates means of any observed or latent variable by regressing each variable on the Constant. Select one or more variables in the From List and one or more variables in this list before clicking one of the arrow buttons to add terms to the model. If you create a latent variable, the latent variable is added to the From List and the To List. Variables in the To List must be selected to add latent variables to the model. You can filter the items in this list using the search filter controls at the top of the list. See Search Filter Options.

Unidirectional Arrow

Specifies the type of relationship between the selected variables in the From List and the To List. The unidirectional arrow is equivalent to a regression effect.

Bidirectional Arrow

Specifies the type of relationship between the selected variables in the From List and the To List. The bidirectional arrow is equivalent to a covariance effect.

Add Latent

Adds a latent variable to the From and To lists. The variable is named based on the text in the box to the left of the button.

Note: You must select indicators for the latent variable in the To List prior to clicking the button.

Remove Latent

Removes any latent variables that are currently selected in either the From List or the To List. Removing a latent variable from the From and To lists also removes the latent variable from the model.

Model Shortcuts

Contains three categories of options to quickly build common models. Note that when you select one of these options, all current model specifications are cleared.

Specification Assist

Contains options that shortcut the process of adding covariances for either exogenous or endogenous variables. Additionally, the Switch Latent Scale option enables you to change the scale of the latent variables, which is useful when fitting confirmatory factor analyses.

Covary Exogenous Variables

Enables you to quickly specify all possible covariances among the existing exogenous variables. Exogenous variables are variables that are not predicted by any other variables in the model. In most cases, these variables are expected to have nonzero covariation with each other for proper model specification.

Covary Endogenous Variables

Enables you to quickly specify all possible covariances among the existing endogenous variables. Endogenous variables are variables that are predicted by one or more other variables in the model. In some instances, residual variances of endogenous variables are expected to covary with each other for proper model specification. This shortcut is most often useful for path models that have one set of predictors for one set of outcomes but no mediators nor latent variables.

Switch Latent Scale

Switches between two common approaches for setting the scale of the latent variables in the model. To estimate models with latent variables, the scale of the latent variables must be set. The following two options are the most common approaches to set the scale: fix the first loading to 1 or fix the variance of the latent variable to 1. The first approach sets the scale of the latent variable to that of the indicator that has its loading fixed to 1. The second approach ensures the latent variable has a variance of 1, which can be paired with a mean of 0 to ensure the latent variable has a z-score metric.

Cross-Sectional Classics

Contains options for confirmatory factor analysis and mediation analysis.

Confirmatory Factor Analysis

Enables you to select the indicators of latent variables and customize their names. An option is provided for selecting between orthogonal (non-correlated) or oblique (correlated) specifications.

Mediation Analysis

Enables you to test causal theories where a mediator variable is hypothesized to transmit the effect of a causal predictor onto an outcome. A key aspect of these models involves the significance of the indirect (or mediated) effect of the predictor on the outcome through the mediator. This shortcut enables specification of a simple mediation model by allowing you to specify variables for the causal, mediator, and outcome roles. A check box can be used to specify a multiple mediation model by selecting more than one mediator variable.

Longitudinal Analysis

Contains options for common latent growth curve models. Latent growth curve models are a family of longitudinal models that are used to characterize trajectories of observational units over time. The standard specification of these models enables you to obtain an estimate of the average trajectory in the population and measures of dispersion from that average. Four common growth curve shortcuts are provided; the Intercept-only Latent Growth Curve, Linear Latent Growth Curve, Quadratic Latent Growth Curve, and Latent Basis Growth Curve.

Note: If variables in the To List are selected when you select one of the latent growth curve options, the model is applied only to the selected variables. Otherwise, the model is applied to all of the variables in the To List.

Intercept-only Latent Growth Curve

Specifies a model that implies flat trajectories for the observational units. This model has one latent variable that can be interpreted as an intercept for the given process. The intercept has an estimated mean and variance, which characterizes the average level of the process in the population and the departure of individual units from that average, respectively. This model is often used as a baseline for comparison with other latent growth curve models. For example, if a linear latent growth curve model fits better than an intercept-only model, you can establish the presence of a linear trend.

Linear Latent Growth Curve

Specifies a model that implies linear trajectories for the observational units. The model has two latent variables: an intercept and a linear slope. Each of these latent variables has a mean and a variance, which enables you to interpret the average level and change across the observational units and the departures from that average, respectively. All latent variables, or growth factors, are allowed to covary. The first loading of the slope is fixed to 0, which centers the intercept at the first time point. Note that this shortcut assumes that the variables are in time-ascending order, such that loadings for the slope factor start at 0 and increment by 1 unit for each variable.

Quadratic Latent Growth Curve

Specifies a model that implies quadratic trajectories for the observational units. The model has three latent variables: an intercept, a linear slope, and a quadratic slope. Each of these latent variables has a mean and a variance, which enables you to interpret the average quadratic trajectory and individual departures from that average, respectively. All latent variables, or growth factors, are allowed to covary. The first loading of the linear and quadratic slopes is fixed to 0, which centers the intercept at the first time point. Note that this shortcut assumes that the variables are in time-ascending order, such that loadings for the linear slope factor start at 0 and increment by 1 unit for each variable. Loadings for the quadratic slope factor are the squared values of the loadings for the linear slope factor.

Latent Basis Growth Curve

Specifies a growth curve without a known functional form. This model is often used for nonlinear trajectories. The model has two latent variables: an intercept and a nonlinear slope, each with a mean and a variance to enable interpretation of an average trajectory and individual departures from that average. These latent variables, or growth factors, are allowed to covary. The first loading of the nonlinear slope is fixed to 0, which centers the intercept at the first time point. The last loading of the nonlinear slope is fixed to 1, and all intermediate loadings are freely estimated. This specification enables you to interpret the loading estimates as proportions of change. Note that this shortcut assumes that the variables are in time-ascending order.

Fit and Compare Growth Models

(Not available for multiple group analysis.) Enables you to compare the fits of intercept-only, linear, and quadratic growth curve models using a chi-square difference test. A common goal in longitudinal analysis is to characterize the patterns of change in the data. Comparing the fits of these three models accomplishes this goal by identifying which type of trajectory best fits the data. All fitted model reports are collapsed by default so that the best fitting model can be identified prior to examining the specific model results.

Multivariate Latent Growth Curve

Enables quick specification of multivariate growth curve models. A subset of variables for a given process can be selected along with a choice for the type of growth curve that will be specified for that process. A button enables you to add each of the univariate models that are specified. By default, all latent variables are allowed to covary, which enables you to make inferences about the associations between growth factors. Note that this shortcut assumes that the variables for each process are in time-ascending order.

Action Panel

The buttons in the Action panel operate on the lists of specified model variables in the Lists tab. The following operations are available:

Fix To

Enables you to fix the parameter value of the currently selected effect to a constant value. When you fix the parameter value for a variable, the fixed value appears in parentheses after the name of the term.

Note: If you keep the default value of 0 when you click OK, the selected effects are removed from the model.

Set Equal

Enables you to constrain the parameter values of two or more selected effects to be equal. When you set two or more effects to have equal parameter values, an arbitrary alphanumeric label (“c1”) appears in parentheses after the names of the terms. In the case of multiple sets of effects that have parameter values that are set equal to each other, sequential numbering is used (“c1”, “c2”, and so on).

Note: Equality constraints are allowed only within the same type of parameters.

Free

Enables you to remove restrictions on the selected effects in the model. Restrictions include effects that have been set to a fixed value or effects that have been set equal to other effects.

Remove

Removes the selected effects from the model.

Undo

Undoes the last modification to the model.

Redo

Redoes the last undone modification to the model.

Run

Fits and creates a report for the currently specified model.

Reset

Resets the model specification to the independence model, which is the default.

Diagram Panel

The Diagram panel contains buttons that enable you to adjust the layout of the model diagram. The first button enables you to rotate the manifest variables (represented by rectangles) in the diagram. The second button enables you to cycle through two different arrangements of the diagram. The third button enables you to customize the diagram. See Customize the Path Diagram.

Details Panel

The Details panel contains information about the model that is currently specified in the Model Specification report. Information about the model includes the number of manifest variables, number of latent variables, number of freely estimated parameters, and number of degrees of freedom. You can also adjust the maximum number of iterations.

Diagram Tab

The Diagram tab contains a model diagram that enables you to visualize the currently specified model. Latent variables are represented by circles, and manifest variables are represented by rectangles. Unidirectional arrows represent loadings and regressions. Bidirectional arrows represent variances and covariances. A variance is specified by a bidirectional arrow from one variable to itself. A covariance is specified by a bidirectional arrow between two variables.

The path diagram is interactive, so you can drag items to arrange them. You can also use the arrow keys to move selected items in the path diagram. You can use the buttons in the Diagram panel to rearrange items in the path diagram. You can use the options in the path diagram pop-up menu to add or remove items in the path diagram. The path diagram pop-up menu appears when you right-click in the path diagram itself. The contents of the pop-up menu differs based on whether you click on part of the blank canvas or on an element of the path diagram. You can also zoom in or out in the path diagram by adjusting the zoom setting in the upper left corner of the path diagram. The path diagram also contains a Lock button in the top left corner that enables you to lock the positions of the items in the path diagram. When the path diagram is locked, the Lock button is blue. After making a selection in the path diagram, you can hide the selection by selecting the Selection > Hide Selection option in the pop-up menu. When items in the path diagram are hidden, an Unhide All button appears at the top of the path diagram that enables you to show all hidden items.

Note: When you specify a Groups variable in the launch window, the Diagram tab is nested within multiple group tabs. You can navigate between these tabs using the panel tabs on the left side of the Diagram tab. There is a Union tab that shows the set of group models and a panel tab for each level of the Groups variable.

See Customize the Path Diagram for more information about path diagram customization options. See Diagram Panel, Details Panel, and Path Diagram Settings.

Tip: To copy the path diagram as an image, right-click the diagram and select Copy Diagram. To retain the highest possible quality, paste the clipboard image as a vector graphic.

Lists Tab

The Lists tab contains lists for each type of variable in the model. They are categorized by the arrows that are used to represent them in the model diagram. Unidirectional arrows are used to designate means or intercepts, loadings, and regressions. Bidirectional arrows are used to designate variances and covariances. Means and intercepts for the model appear only in the Lists tab and not in the Diagram tab.

Note: When you specify a Groups variable in the launch window, the Lists tab is nested within multiple group tabs. You can navigate between these tabs using the panel tabs on the left side of the Lists tab. There is a Union tab that shows Lists tab for the set of group models and a panel tab for each level of the Groups variable.

You can filter the items in each list using the search filter controls at the top of each list. See Search Filter Options.

Status Tab

The Status tab contains checks for model identifiability. Structural equation models must be identified to obtain reliable estimates. Identification in the context of SEM means that one can derive unique solutions for every parameter in the model based on the population covariance matrix of the input data. Because you can specify such a variety of models in the SEM framework, there are a variety of rules for identifiability. The Status tab consists of three panels of information: Identification Rules, Model Details, and Data Details.

• The Identification Rules panel contains a list of up to eight rules that are appropriate for a specified model. Some rules are necessary and others are sufficient to guarantee model identification. If necessary rules fail, steps must be taken to correct them before fitting the model. If sufficient rules fail, you do not necessarily need to address any issues. Sometimes sufficient rules can fail without being evidence of anything wrong with the model. Note that all of the rules assume a positive definite covariance matrix. If the covariance matrix is not positive definite, a warning appears below the Model Details panel.

Tip: For more information about a particular identification rule, click on the row of the table for the rule and a description of the rule appears to the right of the table.

• The Model Details panel contains a list of descriptive values for the currently specified model. These values can be used to detect potential issues with the model.

• The Data Details panel contains a list of descriptive values for the input data. These values can be used to detect potential issues with the data.

If there are singularities in the specified data columns, the report contains a Singularity Details table.

Note: When you specify a Groups variable in the launch window, the Status tab is nested within multiple group tabs. You can navigate between these tabs using the panel tabs on the left side of the Status tab. There is a Union tab that shows Lists tab for the set of group models and a panel tab for each level of the Groups variable.

The Status tab itself contains a dynamic icon that shows the current status of the specified model. The icon designates the status:

Figure 8.5 Example Status Tab 

Search Filter Options

The From List, To List, and the list boxes that appear in the Lists tab in the Model Specification report contain search filters that enable you to filter the items in a specific list.

Click the down arrow button next to the search box to refine your search.

Contains Terms

Returns items that contain a part of the search criteria. A search for “ease oom” returns messages such as “Release Zoom”.

Contains Phrase

Returns items that contain the exact search criteria. A search for “text box” returns entries that contain “text” followed directly by “box” (for example, “Context Box” and “Text Box”).

Starts With Phrase

Returns items that start with the search criteria.

Ends With Phrase

Returns items that end with the search criteria.

Whole Phrase

Returns items that consist of the entire string. A search for “text box” returns entries that contain only “text box”.

Regular Expression

Enables you to use the wildcard (*) and period (.) in the search box. Searching for “get.*name” looks for items that contain “get” followed by one or more words. It returns “Get Color Theme Names”, “Get Name Info”, and “Get Effect Names”, and so on.

Invert Result

Returns items that do not match the search criteria.

Match All Terms

Returns items that contain both strings. A search for “t test” returns elements that contain either or both of the search strings: “Pat Test”, “Shortest Edit Script” and “Paired t test”.

Ignore Case

Ignores the case in the search criteria.

Match Whole Words

Returns items that contain each word in the string based on the Match All Terms setting. If you search for “data filter”, and Match All Terms is selected, entries that contain both “data” and “filter” are returned.

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