eqMI.projection {equaltestMI}

Projection-based method for testing latent means equality

Description

Perform projection method for testing the equality of latent means without requiring the equality of cross-group intercepts to hold.

Usage

eqMI.projection(...)

Arguments

...

The same arguments as for any lavaan model. See lavaan::sem for more information. All models fitted by Lavaan are estimated by fixing the variances of latent factors to 1.

Users must explicitly specify the name of the input elements for this function to catch. For example, specify 'data = HolzingerSwineford' instead just 'HolzingerSwineford'.

Details

Perform projection method for testing the equality of two latent means without requiring the cross-group intercepts to be the same. A validity index is provided as the proportion of the differences in manifest variables intercepts explained by latent mean differences as a gauge of the quality of measurements.

Value

A list is returned with:

fit.metric

test of metric invariance (factor loadings). This is a prerequisite for testing equality of latent means.

mvdif.test

t tests of the cross-group sample means for each variable.

chi.stat

Three chi-square tests for intercepts, common factors, and specific factors. chi.stat will be needed for equivalence testing.

common.test

t tests of common factors for each variable.

specific.test

t tests of specific factors for each variable.

latent.test

t tests of latent means

V.index

validity index

Pmat

projection matrix of intercepts into the space of common factors

Qmat

projection matrix of intercepts into the space of specific factors

References

Yuan, K. H., & Chan, W. (2016). Measurement invariance via multigroup SEM: Issues and solutions with chi-square-difference tests. Psychological methods, 21(3), 405-426.

Examples

data(HolzingerSwineford)
semmodel<-'
L1 =~ V1 + V2 + V3
L2 =~ V4 + V5 + V6
L3 =~ V7 + V8
L4 =~ V9 + V10 + V11
'
run.proj <- eqMI.projection(model = semmodel, data = HolzingerSwineford,
          group = "school", meanstructure = TRUE)