I am fitting ACE and ADE families of models and comparing them to the fully saturated model. I am getting results like this:

observed statistics: 2965

estimated parameters: 4

degrees of freedom: 2961

-2 log likelihood: 848.4525

saturated -2 log likelihood: 844.858

number of observations: 2266

chi-square: 3.594549

p: 1

I am a bit confused by the interpretation of the chi-squared statistic and its degrees of freedom. Before, I have seen output from classic Mx where the df for the chi-square statistic would be three for an ACE model, because it had six observed statistics (i.e. four variances and two covariances from the MZ and DZ covariance matrices) and three estimated parameters (not estimating means).

Here, the df are given as 2961 and all of the p-values for the different models round to 1, because of the very high df. This makes the chi-squared test virtually useless for assessing model fit. Am I missing something here? Is there anything else I could do?

Thankyou

Karin