Help with multilevel fixed effects model?

[Catie Bailard]

Hello all,
I need to run a multilevel, fixed effects model with a binary dependent variable. I am having a difficult time figuring out the correct command in Stata (I have access to either Stata 11 or 12). I have tried using xtlogit with the , fe specification, but having a difficult time figuring out how to get it to run especially with clustering at multilevels. Perhaps this is because I should be using the xtmelogit command? Nevertheless, I can't seem to get the command right.

Here is what I have and need to figure out:

Binary dependent variable.
Unit of analysis is at the "group" level, but also need to cluster at the country and region levels. (812 unique groups spread over 123 countries across 6 regions)
Three years of data for 2007, 2008, 2009

So, essentially, I have time-series cross-sectional data, and I would like to run a fixed effects multilevel model clustered at the country and region level.

Any help regarding the best/correct way to write this command would be really, really appreciated.

Thank you!!!

[Stephen Jenkins]

Catie: please give more precise details of the model that you wish to fit. You have data that is hierarchically organised (unit-year obs nested within countries nested within regions). But such data can be modelled in several different ways. E.g. one can treat countries/regions as fixed effects (like a series of binary indicator explantory variables) or as random effects (the approach taken by 'multilevel' or 'hierarchical' models). This is different from running a unit-level regression in which standard errors are clustered e.g. by country/region. Your choice of specification will, I presume, be partly determined by which of the parameter estimates you are most interested in. Are you most interested in the coefficients on the individual unit-level covariates? Or in explicit estimates of 'country/region' effects? Observe, also, that using xtlogit, fe (equivalent to clogit) will not provide estimates of the coefficients on explanatory variables that are constant over time (which in your case would include the country/region in which your units are located, I guess).

[Catie Bailard]

Hi,

Thanks for your response. Those are very good questions, which I am actually still working through.

I am interested in the unit-level coefficients, while controlling for country- and region-specific effects. So, would this mean running xtlogit including country/region as a series of binary indicators?

But, I am also interested in estimating both within-unit effects and between-unit effects, which then makes me wonder if I really need the random effects estimator? My understanding is that fixed-effects models only estimate within-unit effects. So, if I still want to test whether the effects are robust for country-level and region-level "fixed effects" does that actually mean I am running a random effects model that clusters standard errors by country/region?

I have spent a lot of time reading up on the literature of fixed versus random effects and speaking with various colleagues, and I am getting a lot of mixed messages and contradictory advice. Any thoughts you might have would be really appreciated.

Thanks again!

[Maarten Buis]

The advise on this list is not going to be any less mixed than the advise you apperently already received. The best way forward for you is probably not to look for "the true advise" but to understand the argument underlying that advise. Often such advise is phrased too strong (I have been guilty of that too), but the underlying arguments are sound (I leave it to others to decide whether that also applies to my advise). If you understand the arguments, you can make an informed decision on what is best for your project.

In most projects you want to "compare like with like" and in fixed effects models you try to achieve that by comparing someone with hisself or herself at other points in time. This means that you delibaretly throw away information you could have obtained by compering different persons. This is deliberate and there are good arguments for it, but it is an important decision. Also, a fixed effects model only adjust for things that are constant, and people and other social entities rarely are constant. Whether this is a big or small problem depends on the exact project you want to apply it to. A random effects model allows you to also use the information from comparing different persons, but then you run an increased risk of no longer comparing like with like. You could think of this as the risk is no larger than in any cross sectional study, or as you are not making full use of the panel structure of the data. Both views are true, and the valuation of these depends on the exact details of your project. There is also a hybrid form, but, as you can expect, this has its own set of strengths and weaknesses.

[Stephen Jenkins]

I agree with Maarten's remarks about both the mixed (pun intended) advice you're likely to get, and his discussion of the distinction between FE and RE models and the "exchangeability" assumption of the latter. Whether exchangeability is appropriate in your context is your call, depending on topic-specific knowledge, I think. (You have not told us anything about that, but the cases of having relatively few level-1 units relative to the number of level-2 units seems a bit like education data sets in which a small number of students is sampled within each of a relatively large number of schools.) There are additional twists that will arise because you have a binary dependent outcome variable (in particular for the FE logit estimator) -- please read up on this in a standard text (e.g. Wooldridge's wonderful graduate econometrics text -- the 'big black book'). That said, what happens if you fit a random effects logit (or probit) model clustering on country, i.e. xtset unit_id year, then xtlogit unit_outcome unit_covariates , re vce(cluster country_id)? I'm not sure that region is likely to add much.

[Catie Bailard]

Thank you Stephen and Maarten. I will definitely follow up on the suggested reading.

Maarten, I am respectful of the the risk associated with no longer comparing like-with-like with a random effects estimator, which I agree presents some concerns. However, as you suggest, after thinking it through, my "informed decision" is that across group-effects are actually very important to the "story" I am testing.

To provide more context, I am using time-series cross-sectional data to determine whether the level of access to communication technology increases the likelihood a group will organize to engage in violent conflict. (Basically, do reduced communication costs facilitate violent collective action?)

So, another complication with a fixed effects estimator is that it throws out any cases that do not vary (those with all 0's or all 1's: either no conflict at all or conflict every year) during my 3-year time period. (At least the xtlogit ___, fe command in Stata throws them out.) And, collective violence is a relatively rare event in my data set--only 5% of the cases experience violence during this time period. So, obviously, throwing out any cases that do not vary would severely restrict my N.

Moreover, I am actually testing interaction effects (I know, why not add another layer of difficulty) to test which group characteristics condition the effect of communication technology. Essentially, which group-level characteristics magnify/diminish the effect of communication technology on a group's propensity to organize for violence. As such, across-group variation is a key component of the theory I am testing. (Especially since a lot of the group-level characteristics of interest do not vary much at all within a single group, but vary substantially across groups.)

So, it seems to me that I want to use a random effects estimator but cluster at the country-level to test for the "fixed effect" of living in a specific country. Which I believe is the model that Stephen recommended. Does this seem about right?

Thanks again for all the input and advice. It is incredibly helpful.