topic Re: Nested Models in Statistical Procedures

Nested Models

iuri_leite — Thu, 18 Feb 2021 20:13:34 GMT

Dear All,

I have a simple question that I do not know to define precisely. Suppose I run a logistic regression with a explanatory ordinal variable with for categories, with the first category as refference. Then I agregated the first category with the second (0) and the third with the fouth (1), so that I have now a dummy variable. I run another model. Why is that model a nested one?

If it is nested, how do I define what is being tested. I had B1, B2 and B3 as parameter. Now I have one B measures the effect of the third and fourth category compared to the agregation of the two first categories.

Thank you in advance.

Best regards,

Iuri

Re: Nested Models

StatDave — Thu, 18 Feb 2021 22:04:48 GMT

It is not nested. You've just created a new, dichotomized version of the original variable which I assume you are using in place of the original variable. The new variable tells you the combined effect of two levels compared to the combined effect effect of the other two levels.

Re: Nested Models

iuri_leite — Thu, 18 Feb 2021 22:20:47 GMT

Thanks for the answer. In fact, it is clear to me that it is not nested.
What I do not uderstand is the use of the log-likelihood ratio test
should it onlly be used for nested models?
Thanks again.
Regards?
Iuri

Re: Nested Models

StatDave — Thu, 18 Feb 2021 22:49:16 GMT

Oh, you mean "nested" in that sense. Yes, the likelihood ratio test is only for nested models. You could use a criterion like AICC to compare such models.

Re: Nested Models

iuri_leite — Thu, 18 Feb 2021 22:54:47 GMT

Sorry to bother you again.

My point is that in the Hosmer and Lemeshow book, they use the likelihood
ratio test in a very similar way.
I found it strange. They aggregate the four categories of a variable into
two new categories. And then they compared the two models using the
log-likelihood ratio test.

Regards