The data

For this example we are going to use a simulated dataset, present in the jamovi data library after installing SEMLj, in which we found six items. They are supposed to reflect two latent variables. As you open the data, jamovi recognizes the items as categorical variable, as shown by the little icon in the column name label.

These items will be transformed automatically in ordered variables by SEMLj. In general, SEMLj considers as ordered variables (ordinal) all observed variables that are defined as nominal or ordinal in the datasheet. If one has a variable that jamovi recognizes as continuous and wishes to treat it as ordinal in SEM, one simply changes its type in “Ordinal” in jamovi data tab.

The model

We start with a measurement model (CFA), in which item 1 to 3 load to the first latent variable (\(Y\)), and item 4 to 6 load to the second latent variable (\(X\)).

Output

As soon as we set the input, we obtain the whole set of results tables. It is interesting to check the Info Table.

First, notice that the note informs us that items 1 to 6 type has been changed into ordered type, which is another way to say ordinal. Thus, the module knows that the variables are not to be considered continuous measures, and thus the appropriate estimation method is used. Indeed, we can see in the Estimation Method row of the table that lavaan used the DWLS method, meaning Diagonally weighted least squares. The method is appropriated for ordinal observed variables, implying that the estimates are based upon polychoric correlations. Furthermore, a scaled chi-square test is used as the omnibus test. Which scaled test is used is indicated in the Scaled test row. By default, it is the Mean adjusted scaled and shift test here details from lavaan. Finally, we can see that the standard errors are computed as robust standard errors.

This is the automatic setup one obtains when the model involves ordered variables. Possible changes in the combination of estimation method, scaled omnibus test and standard errors can be done by changing the estimation method and standard errors method in the input panel (see SEMLj computation details for more details).

For instance, selecting Robust Weighted Least Squared (WLSM) implies robust standard errors and the Satorra-Bentler mean adjusted omnibus test. The adjusted test is always referred to as “Scaled test” in the Model Tests table, but the Info table signals which test is used depending on the estimation method selected.

If an estimation method is selected and it is not appropriate, like ML for ordered variables, an error is issued.

In order to let lavaan choose the appropriate combination of estimator, standard errors method and scaled test, it is recommended to leave the standard errors method equal to automatic. Obviously, if you know what you’re doing, you are free to set the options as you like.

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