R: Measurement Invariance Tests

measurementInvariance-deprecated {semTools} | R Documentation

## 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

### 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 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:

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 χ^2 test statistic is scaled (e.g., a Satorra-Bentler or Yuan-Bentler test statistic), a special version of the Δχ^2 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.

### Author(s)

Yves Rosseel (Ghent University; Yves.Rosseel@UGent.be)

Sunthud Pornprasertmanit (psunthud@gmail.com)

Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)

### 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

`semTools-deprecated`

### Examples

    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"))

[Package semTools version 0.5-1 Index]