Re: Multinomial Logistic Regression - Category Size

Posted by Bruce Weaver on Dec 02, 2010; 3:07am
URL: http://spssx-discussion.165.s1.nabble.com/Multinomial-Logistic-Regression-Category-Size-tp3286013p3288831.html

I responded to Ryan off-list to ask if he meant to say that the parameter estimates are interpreted as the change in the log(odds) relative to a reference category.  He responded that he did indeed mean log(risk), not log(odds); and we have been having a vigorous back and forth discussion since, exchanging examples and links.  Here is one link I sent to Ryan:

   http://faculty.chass.ncsu.edu/garson/PA765/logistic.htm#estimates

And here's one he just sent to me (which I've not read yet--it's bed time here).

   http://www.columbia.edu/~so33/SusDev/Lecture_10.pdf

Just thought I'd post this, in case anyone else was interested.  I may have some more to say after reading that last document.

Cheers,
Bruce

R B wrote

Stefan,

What do you mean by the following statement?: "...if the overall model
is significant, I can conclude that there is a significant
relationship between the dependent and independent variable for all
categories of the dependent variable?"

In the typical multinomial logistic regression assuming a single
continuous predictor, X, the parameter estimates are interpreted as
the change in the log(risk relative to the reference category), given
a one-point increase in X. The parameter estimates do NOT reflect a
change in the log(risk) of observing each category, given a one-point
increase in X. Moreover, it's certainly possible to observe a
non-significant log(relative risk) in the presence an overall
significant model effect.

Ryan

On Tue, Nov 30, 2010 at 7:49 AM, s-volk <[e-mail]> wrote:
> Dear all,
>
> I ran a multinomial logistic regression analysis with one continuous
> independent variable. I have a sample size of 68 subjects (psychological
> experiment) which end up split into 5 categories ranging in size from 5 to
> 24 (dependent variable). The MLR-model has a Nagelkerke R2 of 0.27 and Model
> Fit χ2=19.71, p<0.01.
>
> Now here is the problem: A reviewer complains that my results may be sample
> specific because one of the 5 categories of the dependent variable consists
> of only 5 observations (subjects), i.e. sh/e argues that very few
> participants (five) are responsible for the observed effects. Is this valid
> argument? I thought that if the overall model is significant, I can conclude
> that there is a significant relationship between the dependent and
> independent variable for all categories of the dependent variable? That is,
> the calculations for the overall model are based on all observations (68)
> and not only on the observations in specific categories (e.g., 5)?
>
> I was wondering if someone could provide me with or point me to some
> arguments for reviewers (ideally including some references)?
>
> Many thanks in advance,
> Stefan
>
>
>
>
> --
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