# How to find degree of freedom in SEM-CFA model? [Inquiring Clarification]

I found a link that explains it.

http://reifman-sem.blogspot.com/2007/04/some-of-students-wanted-review-of.html

It is

$$Degree \;of\;Freedom (DF) = Total \;Elements - Total \;Free \;Parameters$$ [correct me if I'm wrong]

Here is a model under my project:

A latent model; 3 Latent Variables, 3 Indicators for each of two Latent Variables and the last Latent Variable with 4 indicators.

Hence, Total of 3 Latent and 10 Measured Variables.

Nature of Variable Relationships

Two latent variables are correlated with each other, while the same last latent variable is negatively correlated both of the other two.

All indicator / measured variables are expected to positively estimate unto their respective latent variables

By my own calculations

Free Parameters :

3 = Covariance of all latent variables

3 = Variance of all latent variables

10 = Covariances between latent and Manifest / Indicator Variables

10 = Residual Indicator variance

3 = Construct Variance

7 = freely estimated factor loadings (one loading per factor being fixed at 1)

[ Out of 3 manifest variables, there are 2 factor loadings not fixed each for 2 latent variables

Out of 4 manifest variables there are 3 factor loadings not fixed for the last latent variable ]

Now for Total Elements

Using the advised formula (from the link above):

$$\frac{(I^2) + I}{2}$$

where $$I = Manifest \;Variables$$

$$\frac{(10^2) + 10}{2} = 55$$

Hence,

\begin{align} Degree \;of\;Freedom (DF) & = 55 - (3 + 3 + 10 + 10 + 3 + 3 + 7)\\ &= (55-36)\\ &= 19 \end{align}

Was my identifications of the elements and free parameters correct? Was my calculation correct?

I'll be needing this for further calculation to determine sample size for validation project.

• Can this be of some help? stats.stackexchange.com/q/279360/3277 Sep 24, 2020 at 9:10
• Hi. @ttnphns. Unfortunately, the information is quite above my current level of my understanding. Guess I have to hope more replies coming in soon. But I appreciate you reaching out to provide some help. Cheers. Sep 24, 2020 at 19:08
• Get to read some book on FA (which include chapters on CFA). They explain it. Sep 24, 2020 at 19:35
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