Description Usage Arguments Details Value Author(s) References See Also Examples
Testing measurement invariance across timepoints (longitudinal) or any context involving the use of the same scale in one case (e.g., a dyad case with husband and wife answering the same scale). The measurement invariance uses a typical sequence of model comparison tests. This function currently works with only one scale, and only with continuous indicators.
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model 
lavaan syntax or parameter table 
varList 
A list containing indicator names of factors used in the invariance testing, such as the list that the first element is the vector of indicator names in the first timepoint and the second element is the vector of indicator names in the second timepoint. The order of indicator names should be the same (but measured in different times or different units). 
auto 
The order of autocorrelation on the measurement errors on the
similar items across factor (e.g., Item 1 in Time 1 and Time 2). If 0 is
specified, the autocorrelation will be not imposed. If 1 is specified,
the autocorrelation will imposed for the adjacent factor listed in

constrainAuto 
If 
fixed.x 
See 
std.lv 
See 
group 
See 
group.equal 
See 
group.partial 
See 
strict 
If 
warn 
See 
debug 
See 
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

... 
Additional arguments in the 
If strict = FALSE
, the following four models are tested in order:
Model 1: configural invariance. The same factor structure is imposed on all units.
Model 2: weak invariance. The factor loadings are constrained to be equal across units.
Model 3: strong invariance. The factor loadings and intercepts are constrained to be equal across units.
Model 4: The factor loadings, intercepts and means are constrained to be equal across units.
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 CFA 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 units.
Model 2: weak invariance. The factor loadings are constrained to be equal across units.
Model 3: strong invariance. The factor loadings and intercepts are constrained to be equal across units.
Model 4: strict invariance. The factor loadings, intercepts and residual variances are constrained to be equal across units.
Model 5: The factor loadings, intercepts, residual variances and means are constrained to be equal across units.
Note that if the χ^2 test statistic is scaled (eg. 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.
Sunthud Pornprasertmanit (psunthud@gmail.com)
Yves Rosseel (Ghent University; Yves.Rosseel@UGent.be)
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(1), 4–70. doi: 10.1177/109442810031002
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  model < ' f1t1 =~ y1t1 + y2t1 + y3t1
f1t2 =~ y1t2 + y2t2 + y3t2
f1t3 =~ y1t3 + y2t3 + y3t3 '
## Create list of variables
var1 < c("y1t1", "y2t1", "y3t1")
var2 < c("y1t2", "y2t2", "y3t2")
var3 < c("y1t3", "y2t3", "y3t3")
constrainedVar < list(var1, var2, var3)
## Invariance of the same factor across timepoints
longInvariance(model, auto = 1, constrainAuto = TRUE,
varList = constrainedVar, data = exLong)
## Invariance of the same factor across timepoints and groups
longInvariance(model, auto = 1, constrainAuto = TRUE,
varList = constrainedVar, data = exLong, group = "sex",
group.equal = c("loadings", "intercepts"))

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