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
A. Number of indicators
C. Number of cross-loadings
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
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.
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