Log likelihoods for path analyses
Message/Author
 Andy Cohen posted on Wednesday, July 18, 2007 - 1:28 pm
I am trying to compare a model of partial mediation to one of no mediation and am having difficulty interpreting the model fit stats (log likelihood, AIC, etc.) that I am getting.

My base model, which is a count dependent variable, models y on x1-x9 and has a log likelihood of -559. I've then tried to model a path model where x1 is modelled on x2, thus testing whether x1 mediates the path between x2 and y. When I add this statement to the model statement, I get log likelihood of -1492, on the surface suggesting a much poorer fitting model. But I don't think so. Any variant of the mediation test (i.e. different relationships between x1 and the other 8 variables) yield similar fit statistics (to the -1492) and the directions are intuitive and align other preliminary exploratory analyses. So, can you help me understand how to reconcile the larger (in absolute value) fit statistics with the more complex model?

Thanks.
 Bengt O. Muthen posted on Wednesday, July 18, 2007 - 7:01 pm
I think you are running into the following. The likelihood is computed conditional on the covariates. In the first model you have 9 and in the second you have 8. This means that the likelihood metrics are not comparable. I think you can get around this by letting x1 be taken off the covariate list also in the first model. This is done by referring to an x1 parameter, such as its mean - it then turn into a "y variable" in Mplus parlance, and is no longer conditioned on in the likelihood.
 Andy Cohen posted on Thursday, July 19, 2007 - 5:00 am
Thanks for the response. I'm not sure I understand, but let me try. My first, base, model, is

y on x1 x2...x9;

My second model is

y on x1 x2...x9;
x1 on x2;

Are you suggesting that I make my first model look like this?:

y on x1 x2...x9;
x1;

Or did I misunderstand?

Thanks.
 Linda K. Muthen posted on Thursday, July 19, 2007 - 9:32 am
Yes.