Fixed effects vs Random effects

[lulube]

Hello,

I have a panel dataset and I did two binomial negative regressions, one with random effects and one with fixed effects. I want to test if I choose the random or the fixed effects on my regression. I know that the Hausman test exists but I couldn't find how to do it with a negative binomial regression on sas.

Thank you for your help,

Lulube.

[SteveDenham]

What procedure did you use to run the fixed effect and random effect scenarios?  My inclination would be to look at the various information criteria (AIC, AICC, etc.) to choose between the models.

SteveDenham

[lulube]

I used proc genmod for my regressions

[SteveDenham]

How do you include random effects in GENMOD?  I don't see how you could do this, unless you are referring to the REPEATED statement used to create GEE models.

To implement my idea of looking at the information criteria, I think you will have to switch to GLIMMIX where you can specify random effects in a RANDOM statement.  At this point, greater detail on the design used to collect the data, models considered, and the questions that the data are supposed to address would be in order to provide additional help.

SteveDenham

[PaigeMiller]

It is my understanding that a variable in a model is either fixed, or random, because of the design of the study and the nature of the variable — it is not determined by the data. It can't be both. So I don't understand how you can test to see if one is better than the other.

[SteveDenham]

Sometimes you have to treat a random effect as a fixed effect.  The most common reason is that you lack sufficient number of clusters/levels of the effect to get an accurate estimate of the variance component.  This is much more common in observational studies than in designed experiments.  In a designed experiment, you know what the nature of the factors are, and may be stuck with results where the G matrix is not positive definite.  In observational studies, the number of levels can determine whether a factor is best handled as fixed or random.  Not much use in considering a factor as random if you can't get a good estimate, while if you consider it fixed, at least you can remove its effect by considering it a nuisance or control variable.  This is the situation where looking at information criteria can help, as well as looking at convergence issues and matrix issues, to make a decision on the best way to handle that particular variable.  The idea is that it is probably better to underestimate the variability associated with the study (fixed effect) than to end up in an  area of the likelihood space where the estimate is either undefined or poorly estimated.  The ecological literature is pretty rich in this area.

SteveDenham