measurementInvarianceCat-deprecated: Measurement Invariance Tests for Categorical Items

measurementInvarianceCat-deprecatedR Documentation

Measurement Invariance Tests for Categorical Items


Testing measurement invariance across groups using a typical sequence of model comparison tests.


measurementInvarianceCat(..., = FALSE, strict = FALSE,
                         quiet = FALSE, fit.measures = "default",
                         baseline.model = NULL, method = "default")



The same arguments as for any lavaan model. See cfa for more information.

If TRUE, the fixed-factor method of scale identification is used. If FALSE, the first variable for each factor is used as marker variable.


If TRUE, the sequence requires ‘strict’ invariance. See details for more information.


If FALSE (default), a summary is printed out containing an overview of the different models that are fitted, together with some model comparison tests. If TRUE, no summary is printed.


Fit measures used to calculate the differences between nested models.


custom baseline model passed to fitMeasures


The method used to calculate likelihood ratio test. See lavTestLRT for available options


Theta parameterization is used to represent SEM for categorical items. That is, residual variances are modeled instead of the total variance of underlying normal variate for each item. Five models can be tested based on different constraints across groups.

  1. Model 1: configural invariance. The same factor structure is imposed on all groups.

  2. Model 2: weak invariance. The factor loadings are constrained to be equal across groups.

  3. Model 3: strong invariance. The factor loadings and thresholds are constrained to be equal across groups.

  4. Model 4: strict invariance. The factor loadings, thresholds and residual variances are constrained to be equal across groups. For categorical variables, all residual variances are fixed as 1.

  5. Model 5: The factor loadings, threshoulds, residual variances and means are constrained to be equal across groups.

However, if all items have two items (dichotomous), scalar invariance and weak invariance cannot be separated because thresholds need to be equal across groups for scale identification. Users can specify strict option to include the strict invariance model for the invariance testing. See the further details of scale identification and different parameterization in Millsap and Yun-Tein (2004).


Invisibly, all model fits in the sequence are returned as a list.


Sunthud Pornprasertmanit (

Yves Rosseel (Ghent University;

Terrence D. Jorgensen (University of Amsterdam;


Millsap, R. E., & Yun-Tein, J. (2004). Assessing factorial invariance in ordered-categorical measures. Multivariate Behavioral Research, 39(3), 479–515. doi: 10.1207/S15327906MBR3903_4

See Also



## Not run: 
syntax <- ' f1 =~ u1 + u2 + u3 + u4'

measurementInvarianceCat(model = syntax, data = datCat, group = "g",
                         parameterization = "theta", estimator = "wlsmv",
                         ordered = c("u1", "u2", "u3", "u4"))

## End(Not run)

semTools documentation built on May 10, 2022, 9:05 a.m.