AIC for linear vs. logistic regressi... PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Hadas Hawlena posted on Thursday, December 06, 2012 - 1:58 am
Dear Drs. Muthen,
I am running path analyses and comparing the AIC values of competing models. Since some of my variables are categorical and some continuous, sometimes a change in only the direction of one of the direct effects may change the model from linear regression to logistic regression. I got the impression that in all these cases, the AIC value significantly increases, independent on the specific variables and the relationships among them. Am I correct? If so, what is the right way to compare between these models?
Thanks in advance, Hadas
 Bengt O. Muthen posted on Thursday, December 06, 2012 - 8:52 am
I don't understand your question - perhaps you reformulate it.
 Hadas Hawlena posted on Thursday, December 13, 2012 - 11:26 am
I am sorry that I was not clear.
I will give you an example.
I wish to compare the AIC values of two alternative models, with parameters A-D, where A is a continuous variable and B is a categorical variable. The models are identical except for the last line:
A on C;
A on D ;
B on A;
AIC= 301.750

A on C;
A on D ;
A on B;
AIC= 241.887

As you see, I received a lower AIC value for the second model and I was wondering whether the reason for the lower AIC value in model 2 could be that in this model the last line represents a linear regression whereas in model 1 it represents a logistic regression (since B is categorical).
Thanks in advance, Hadas
 Bengt O. Muthen posted on Friday, December 14, 2012 - 4:05 pm
The two AIC values are in different metric. You have to have the same DV's for two models to have the same logL and therefore AIC metric. Your two models have different sets of DVs due to variable B.
 Hadas Hawlena posted on Wednesday, January 16, 2013 - 5:39 am
Thanks for your answer. Does that mean that I have to have also the same mediators in two models if I wish to compare between them, using AIC?
e.g., I cannot compare between the models:

Model 1:
A on C;
D on A;

Model 2:
D on B;
B on G;

Thanks, Hadas
 Linda K. Muthen posted on Wednesday, January 16, 2013 - 7:29 am
Yes, mediators are dependent variables. To compare, the variables on the left-hand side of ON must be the same.
 Hadas Hawlena posted on Wednesday, January 16, 2013 - 10:41 am
Thank you very much for the helpful answer. Is there any way to compare between competing models that have different mediators? For example, if I wish to know whether the indirect relations between A and B are mediated by C or D?

 Linda K. Muthen posted on Wednesday, January 16, 2013 - 4:02 pm
Not that I know of when the dependent variables are not the same.
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