# The 2-Log Likelihood Test for Interaction Effects

I want to test whether my interaction term is significant.

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.
asked Mar 30, 2017

## 1 Answer

0 votes
Two three level attributes have 4 degrees of freedom for their main effects (each has 3-1=2) and you add them.

There will also be 4 d.f. in the interaction (this time there are 2 in each and you multiply them:  2 x 2 = 4).
answered Mar 30, 2017 by Platinum (70,125 points)
But I guess we can not use 2LL measure as these two models are not nested.
I am not sure what models you are talking about or how they are specified, so I cannot respond.  There are other tests you can use for non-nested models (e.g. you can compute BIC or CAIC).