Description Usage Arguments Details Value Author(s) References See Also Examples
Testing measurement invariance across groups using a typical sequence of model comparison tests.
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The same arguments as for any lavaan model. See

std.lv 
If 
strict 
If 
quiet 
If 
fit.measures 
Fit measures used to calculate the differences between nested models. 
baseline.model 
custom baseline model passed to

method 
The method used to calculate likelihood ratio test. See

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.
Model 1: configural invariance. The same factor structure is imposed on all groups.
Model 2: weak invariance. The factor loadings are constrained to be equal across groups.
Model 3: strong invariance. The factor loadings and thresholds are constrained to be equal across groups.
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.
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 YunTein (2004).
Invisibly, all model fits in the sequence are returned as a list.
Sunthud Pornprasertmanit (psunthud@gmail.com)
Yves Rosseel (Ghent University; Yves.Rosseel@UGent.be)
Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)
Millsap, R. E., & YunTein, J. (2004). Assessing factorial invariance in orderedcategorical measures. Multivariate Behavioral Research, 39(3), 479–515. doi: 10.1207/S15327906MBR3903_4
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