Plase cite as follows:
Schroeders, U., & Gnambs, T. (2020). Degrees of freedom in multigroup confirmatory factor analyses: Are models of measurement invariance testing correctly specified? European Journal of Psychological Assessment, 36(1), 105–113. https://doi.org/10.1027/1015-5759/a000500
| MI testing |
constraints |
df |
comparison |
delta(df) |
| config. |
(item:factor) |
0 |
- |
- |
| metric |
(loadings) |
2 |
metric-config |
2 |
| scalar |
(loadings+intercepts) |
4 |
scalar-metric |
2 |
| residual |
(loadings+residuals) |
5 |
residual-metric |
3 |
| strict |
(loadings+intercepts+residuals) |
7 |
strict-scalar |
3 |
Additional information
| A |
Indicates the number of indicators or items. |
| B |
Indicates the number of latent variables or factors. |
| C |
Indicates the number of cross-loadings. For example, in case of a bifactor model the number equals twice the number of indicators (A). |
| D |
Indicates the number of orthogonal factors. For example, in case of a nested factor model with six indicators loading on a common factor
and three items additionally loading on a nested factors, you have to specify 2 factors (B) and 1 orthogonal factor (D). |
| E |
Indicates the number of residual covariances. |
| F |
Indicates the number of groups. |
Further reading
- Beaujean, A. A. (2014). Latent variable modeling using R: a step by step guide. New York: Routledge/Taylor & Francis Group.
- Millsap, R. E. & Olivera-Aguilar, M. (2012). Investigating measurement invariance using confirmatory factor analysis. In R. H. Hoyle (Ed.), Handbook of Structural Equation Modeling (pp. 380-392). New York: Guilford Press.
- Kline, R. B. (2011). Principles and practice of structural equation modeling. New York: Guilford Press.