For example, when we test a CFA measurement invariance and compare a model assuming configural (no constraints except these necessary for model identification) against a model assuming week invariance (add equal loadings), the week MI model has more degrees of freedom than the model assuming configural MI.
I know how to determine the df, but I want to understand it conceptually, why adding contraints increases the df, even though the freedom of the loadings is restricted.
Many thanks in advance!
Hi Manuel
Degrees of freedom in SEM is defined as the number of observations in your model minus the number of parameters you are estimating. If you constrain a parameter in a model then you are no longer estimating that parameter, thus reducing the number of estimated parameters and thus increasing df.
On a conceptual level think of df as a quality not of your model itself but also of your observations. Each time you estimate a parameter your model consumes a degree of freedom from your pool of observations. That is why you should have at least a few observations per parameter, so you will have enough observations for your model to estimate those parameters while still giving you plenty of leftover df.
Dear Robert,
thank you for your response. Probably i get your explanation wrong (please corerct me if I do so), but i think the degrees of freedom are calculated as:
df = number of observed parameters (not observations!) - number of free parameters.
If I add contrains, i reduce the number of free parameters, and therefore gain degrees of freedom, however, i actually force the the parameters into a special directions by my contrains, and therefore actually reduce their freedom to fit the varaince-covariance-matrix optimal - so where is the freedom?
Sorry, if I don't get you point, I am happy about every comment.
Best wihes, Manuel
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