semTools (version 0.5-0)

measurementInvariance: Measurement Invariance Tests

Description

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

Usage

measurementInvariance(..., std.lv = FALSE, strict = FALSE, quiet = FALSE,
  fit.measures = "default", baseline.model = NULL,
  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 FALSE (default), a summary is printed out containing an overview of the different models that are fitted, together with some model comparison tests. If TRUE, no summary is printed.

fit.measures

Fit measures used to calculate the differences between nested models.

baseline.model

custom baseline model passed to fitMeasures

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

If strict = FALSE, the following four models are tested in order:

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 intercepts are constrained to be equal across groups.

4. Model 4: The factor loadings, intercepts and means are constrained to be equal across groups.

Each time a more restricted model is fitted, a \(\Delta\chi^2\) 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 (\(\Delta\)CFI).

If strict = TRUE, the following five models are tested in order:

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 intercepts are constrained to be equal across groups.

4. Model 4: strict invariance. The factor loadings, intercepts and residual variances are constrained to be equal across groups.

5. Model 5: The factor loadings, intercepts, residual variances and means are constrained to be equal across groups.

Note that if the \(\chi^2\) test statistic is scaled (e.g., a Satorra-Bentler or Yuan-Bentler test statistic), a special version of the \(\Delta\chi^2\) test is used as described in http://www.statmodel.com/chidiff.shtml

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.

See Also

longInvariance for the measurement invariance test within person; partialInvariance for the automated function for finding partial invariance models

Examples

# NOT RUN {
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"))

# }