[Carlo Lazzaro]

Mary:
1) if the LR test outcome reaches statistical significance you have evidence of a group- wise effect and you should be better using -xtlogit-;
2) if the LR null is not rejected, you should switch to pooled -logit-. You can add categorical variables (e.g.; -i.round-) in the right-hand side of your regression equation via -fvvarlist- notation.

[Mary Burckhette]

Dear Carlo,

Thank you very much for your time and knowledge! May I ask one last question regarding the LR test outcome? What is an appropriate number at which group-wise effects seem to be present?

Here (https://www.statalist.org/forums/for...lr-test-is-1): LR test of rho=0: chibar2(01) = 0.00 and you suggest switching to the pooled logit model.

In my case

LR test of rho=0: chibar2(01) = 13.36                  Prob >= chibar2 = 0.000

Once again, thank you so much for your insights and help! I very appreciate your recommendations!

[Carlo Lazzaro]

Mary:
your LR outcome reject the null of no difference between -xtlogit- an pooled -logit-. Thus, you have a panel-wise effect and you should stick with -xtlogit-.

[Mary Burckhette]

Thank you Carlo! How does this decision-making work? Do you compare the chibar2(01) =13.36 to 0 and establish that it's greater than 0 and hence group-wise effects exist? Or do you look at Prob >= chibar2 = 0.000? Understanding this would help me greatly in future models.

I very much appreciate your support!

[Carlo Lazzaro]

Mary:
I take a look at Prob chibar2=0.000, that clearly rejects the null of no difference between pooled -logit' and -xtlogit-.

[Jeff Wooldridge]

The issue is more subtle than just testing rho = 0. That test will pick up any kind of serial correlation. There could be no groupwise effect but AR(1) serial correlation and the test will reject. The test is derived under the assumption that there is no serial correlation in the idiosyncratic errors. That's almost always false in the linear case; there's no reason to think it's true in the binary case.

It's important to understand the statistical properties of estimation methods that you're going to use. In a recent paper with two former students of mine, we establish, via simulation, that the fixed effects logit model is biased when there is extra serial correlation. Fortunately, because Mary has a randomized intervention, she doesn't need to use fixed effects. She can use random effects logit or pooled logit. RE logit requires no serial correlation in the idiosyncratic errors for consistency. Pooled logit does not. And this has nothing to do with the size of rho. As I said, one can estimate a large rho simple because the e(i,t) are correlated across t. And then xtlogit, re is inconsistent.

Pooled logit doesn't care about the presence of a panel effect when you have an experiment. For robustness -- that is, using the estimator that is consistent under the weakest set of assumptions -- pooled logit is the winner. You simply cluster your standard errors. And include any variables you want: time constant, time varying. Then, use the margins command if you want effects on the probabilities.

Of course you can use both, but it's tricky to compare the magnitudes of the coefficients. The scale factors are different. You can compare the average marginal effects to see if they are close. If they are, it doesn't matter. If they aren't, one would tend to use pooled logit because of its robustness.

[Mary Burckhette]

Dear Jeff, thank you very much for your detailed and constructive answer! I much appreciate it!