I tested for an interaction effect between two attributes. Each attribute had 3 levels.

Thus 3 levels * 3 levels = 9 effects to test.

What number of degrees of freedom do I have here? Is this 9

I found this information regarding the 2-Log Likelihood Test for interactions but did not understand what my degrees of freedom would be:

1. Using aggregate (pooled) logit, estimate the model using main effects only. Record the log-likelihood for this model.

2. Using aggregate logit, estimate the model using main effects plus a 2-way interaction effect. Record the log-likelihood for this second, larger model.

3. Compute the difference in log-likelihood between the main effects only model and the main effects model that includes a selected interaction effect. That value times 2 is distributed Chi-Square, with degrees of freedom equal to the difference in the number of parameters in the two models. Use the Chi-Square distribution to compute the p-value, which is the likelihood that we would observe a difference this large in fit just by chance. If the p-value is <0.05, then we are at least 95% confident that the interaction effect is significant.