R: Measurement Invariance Tests

measurementInvariance {lavaan}

R Documentation

Measurement Invariance Tests

Description

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

Usage

measurementInvariance(..., strict = FALSE, quiet = FALSE)

Arguments

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

Details

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 chi-square difference 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 (delta.cfi).

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 chi-square test statistic is scaled (eg. a Satorra-Bentler or Yuan-Bentler test statistic), a special version of the chi-square difference test is used as described in http://www.statmodel.com/chidiff.shtml

Value

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

References

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.

Examples

HW.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

measurementInvariance(HW.model, data=HolzingerSwineford1939, group="school")

[Package lavaan version 0.4-12 Index]