Ayfer, this output tells you that your number of df is zero, which means that you have a saturated model. Your empirical information (such as the number of nun-redundant - unique - variances and covariances) are the same as the number of free parameters in the model. In your model, there are no constraints that could be tested, and there is no way to test the model fit. Therefore, this does not mean that your model fit the data perfectly, but that this test is not available.

Does this help?

Kind regards, Karin

Thank you very much Karin. Now, I understand what it actually means. What kind of mistakes may cause such a result? Are there any steps I should take to fix this or should I just stop testing the model?

Regards,

Ayfer

In addition to Dr Karin,

Three different types of  models available in structural equation modeling framework. Overidentified, underidentified, and just identified models. If models is overidentified your number of parameters were higher than the number of parameters you used, just identified models have the same number of parameteres with your model, underidentified models have less parameteres than your estimated models.

Just identified models generally occur when you used regression analysis.

In order to clarify, Let I have five items and want to test a one factor model.

I have  p. (p+1)/ 2 free parameteres. ın other words   (5 x 6)/2 = 15 free parameters. If ı test one factor model I have to use (using this formula= b = (p * m) + [(m * (m + 1)] / 2) + p –m^2,    where p is the number of observed variables and m is the estimated factor))=  (5*1)+(1*2)/2)+ 5- 1= 5+ 1+4 = 10 parameters

thus ıf I test this model I will have 15-10 = 5 degrees of freedom. model overidentified.

ıf ı test for above example for two factor model I will have 17 degrees of freedom and model underidentified.

Hello Ayfer,

A saturated model isn't a mistake; while parameter estimates are generated, one simply cannot test model-data fit, as Karin Schermelleh-Engel points out.  That is, the estimated parameters perfectly reproduce the observed relationships among the variables.

However, you can ask questions such as whether individual parameter estimates are significantly different from zero. From that perspective, such a model can still be informative.  If you're determined to be able to test a model, you'll generally have to: (a) add more variates; (b) fix the values of one or more parameters; or (c) eliminate links among variates (e.g., presume that some parameters are zero).

David Kenny has a nice explanation of the possible conditions that arise in measurement (e.g., factor) and structural models: http://davidakenny.net/cm/identify.htm

Good luck with your work!

Dear Ertuğrul and Şahin,

Many thanks for your answer. It is more clear now.

Regards,

Ayfer