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/10.1027/10155759/a000500
A. Number of indicators
C. Number of crossloadings
E. Number of resid. covar.
B. Number of factors
D. Number of ortho. factors
F. Number of groups
MI testing
constraints
df
comparison
delta(df)
config.
(item:factor)
0


metric
(loadings)
2
metricconfig
2
scalar
(loadings+intercepts)
4
scalarmetric
2
residual
(loadings+residuals)
5
residualmetric
3
strict
(loadings+intercepts+residuals)
7
strictscalar
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 crossloadings. 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. & OliveraAguilar, M. (2012). Investigating measurement invariance using confirmatory factor analysis. In R. H. Hoyle (Ed.), Handbook of Structural Equation Modeling (pp. 380392). New York: Guilford Press.
Kline, R. B. (2011). Principles and practice of structural equation modeling. New York: Guilford Press.