interpret logit vs fixed effects logit (conditional logit) estimates

[Emil Holst]

I'm running two logit models on passing or failing an exam - one random effects logit, and one fixed effects logit (conditional logit) where I use "community" as my group variable. I've set my estimates to be log-odds ratios in both models. My question is, is it sensible to compare estimates from these two models or am I comparing apples and oranges?

For example, I get a log-odds ratio for the effect of "age" on passing the exam of 1.06 in the std. logit and 1.08 in the community fixed effects logit.

thanks in advance :-)

[Clyde Schechter]

It depends.

In principle, you are comparing two different varieties of apple. The most important difference is that the conditional logistic regression is estimating within-community effects only. By contrast, the random effects logit estimates both within- and between-community effects and combines them in a single summary statistic. If the things your variables represent in the real world are such that within- and between- community effects do not differ, then the results of the two models should be similar and are readily comparable. But if the effect of "being age 50" is potentially different from the effect of "turning age 50," then the results can be quite different (even opposite in sign) and a comparison of the two serves only to emphasize and quantify the difference bewteen within- and between-community effects.

If you are not clear on the distinction between within- and between- group (community) effects, here's a simple example. It is based on linear regression (-xtreg-) rather than logit, but the same reasoning would apply.

clear
set obs 5
gen panel_id = _n
expand 2

set seed 1234
by panel_id , sort: gen y = 4*panel_id - _n + 3 + rnormal(0, 0.5)
by panel_id: gen x = panel_id + _n

xtset panel_id 

xtreg y x, fe
regress y x

//    GRAPH THE DATA TO SHOW WHAT'S HAPPENING
separate y, by(panel_id)

graph twoway connect y? x || lfit y x

[Emil Holst]

Thank you very. much, that was what I suspected :-)