measurementInvariancedeprecated  R Documentation 
Testing measurement invariance across groups using a typical sequence of model comparison tests.
measurementInvariance(..., std.lv = FALSE, strict = FALSE, quiet = FALSE, fit.measures = "default", baseline.model = NULL, method = "satorra.bentler.2001")
... 
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

If strict = FALSE
, the following four models are tested in order:
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 intercepts are constrained to be equal across groups.
Model 4: The factor loadings, intercepts and means are constrained to be equal across groups.
Each time a more restricted model is fitted, a Δχ^2 test is reported, comparing the current model with the previous one, and comparing the current model to the baseline model (Model 1). In addition, the difference in CFI is also reported (ΔCFI).
If strict = TRUE
, the following five models are tested in order:
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 intercepts are constrained to be equal across groups.
Model 4: strict invariance. The factor loadings, intercepts and residual variances are constrained to be equal across groups.
Model 5: The factor loadings, intercepts, residual variances and means are constrained to be equal across groups.
Note that if the χ^2 test statistic is scaled (e.g., a SatorraBentler or YuanBentler test statistic), a special version of the Δχ^2 test is used as described in http://www.statmodel.com/chidiff.shtml
Invisibly, all model fits in the sequence are returned as a list.
Yves Rosseel (Ghent University; Yves.Rosseel@UGent.be)
Sunthud Pornprasertmanit (psunthud@gmail.com)
Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)
Vandenberg, R. J., and Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3, 4–70.
semToolsdeprecated
HW.model < ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' measurementInvariance(model = HW.model, data = HolzingerSwineford1939, group = "school", fit.measures = c("cfi","aic"))
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