semTools (version 0.4-13)

measurementInvarianceCat: Measurement Invariance Tests for Categorical Items

Description

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

Usage

measurementInvarianceCat(..., std.lv = FALSE, strict = FALSE, quiet = FALSE,
fit.measures = "default", method = "satorra.bentler.2001")

Arguments

...

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

std.lv

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

strict

If TRUE, the sequence requires `strict' invariance. See details for more information.

quiet

If TRUE, a summary is printed out containing an overview of the different models that are fitted, together with some model comparison tests.

fit.measures

Fit measures used to calculate the differences between nested models.

method

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

Value

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

Details

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).

References

Millsap, R. E., & Yun-Tein, J. (2004). Assessing factorial invariance in ordered-categorical measures. Multivariate Behavioral Research, 39, 479-515.

See Also

measurementInvariance for measurement invariance for continuous variables; longInvariance For the measurement invariance test within person with continuous variables; partialInvariance for the automated function for finding partial invariance models

Examples

## Not run: 
# model <- ' f1 =~ u1 + u2 + u3 + u4'
# 
# measurementInvarianceCat(model, data = datCat, group = "g", parameterization="theta", 
#     estimator="wlsmv", ordered = c("u1", "u2", "u3", "u4"))
# ## End(Not run)