Probit with fixed effects

[Elin Vimefall]

Hi

I'm analyzing the determinants of chil labor and schooling using a bivariate probit model.
I'm especially interested in the charactersitics of siblings and to control for unobserved factors who might influence the results I would like to use fixed effects at the household level.
Is there anyway to do this with a probit (or even better bivariate probit)?

Best regards /Elin Vimefall

[Carlo Lazzaro]

Elin:
as per -xtprobit- entry in Stata 13.1 .pdf manual, fixed-effect specification in -xtprobit- leads to biased results.
Things would be probably easier switching to -xtlogit-.

[Elin Vimefall]

Thanks a lot Carlo. So if I understand it correctly; I should not use FE in a probit setting, but it works fine with a logit?

Does anyone know about meprobit, (mixed effects probit) if I understand it correctly this model should be able to deal with both random and fixed effects, or?

Tanks //Elin

[Maarten Buis]

There is no such thing as a fixed effects probit, so meprobit only estimates a random effects model.

[Elin Vimefall]

Thanks (again) Martin Just out of curiosity; why is it called a mixed effect probit (and not random effect probit) if it only estimates random effects?

[Maarten Buis]

Mixed models as Stata uses the term are models where the constant and the effects of variables can be random.

[Marcos Almeida]

[...] to control for unobserved factors who might influence the results.

I gather the unobserved time-invariant component cannot be eschewed or even dutifully curbed under probit models.

Best,

Marcos

[Stephen Jenkins]

On this topic, see for example: http://people.stern.nyu.edu/wgreene/...xedeffects.pdf. Or Greene's published article, "The behaviour of the maximum likelihood estimator of limited dependent variable models in the presence of fixed effects", Econometrics Journal (2004), volume 7, pp. 98–119.

[daniel klein]

To add to Maarten's comment, the term "fixed-effects" seems to be used to describe very different things in the literature.

The way I see it - and this might well apply to social sciences only - people either come from the multilevel-literature, where the classical example of the data structure is pupils nested in schools. For them the term "fixed-effects" means that a variables' effect is fixed in the sense, that the effect does not vary between units (pupils or schools). These effects are estimated in so called mixed-models. This has nothing to do with the ability to control for (unobserved) heterogeneity that is constant within the higher level observations (here: schools).

The second group comes form the panel-literature, where the classical example is individuals observed at different points in time, or in other words, occasions nested in individuals. Here "fixed-effects" usually means (time) demeaned or within-variance estimator (in non-linear models it is a conditional likelihood estimator). These effects are not estimated (aside for the LSDV estimator). Such models control for (unobserved) heterogeneity that is constant within the higher level observations (here: individuals).

It took me quite a while to figure out that the data structure is the very same in both cases and that the very same methods for analyzing them can be used in both cases. This is actually pretty clear to me now, but in my experience a lot of people do not realize that these two things are actually the same and talk about multilevel or hierarchical models as being something completely different from what they call panel-models.

Best
Daniel

[Marcos Almeida]

I tend to think that panel data (i.e.,longitudinal models) should be taken as a specific case of - the much broader - multilevel (i.e., hierarchical) mixed-effects models, particularly whenever there is only one level for the observations.

If I misunderstood the main concepts or missed the point, please correct me.

Best,

Marcos.

[Stephen Jenkins]

I second Daniel's observations. But my interpretation differs from Marcos's. To me, reference to "multilevel (i.e., hierarchical) mixed-effects models" virtually always refers to what economists refer to as "random effects" models. "Fixed effects" models to economists are those in which there are fixed unit-specific intercepts (though, degrees of freedom permitting, could also refer to unit-specific slope parameters). NB "unit-specific", meaning that the intercepts are not drawn from a distribution, typically normal, and are assumed uncorrelated with observed characteristics of the unit. The FE approach does not rely on uncorrelatedness. Just because data have a nested or hierarchical structure does not necessarily imply that one should use a multilevel (i.e. random effects) model. Which is consistent with what Daniel says.

[Marcos Almeida]

It seems we reached a controversial point under a few aspects. Or not, hopefully.

On theoretical terms, I cannot really give a personal reply: far beyond my skills. But I still don’t understand what is wrong with stating that panel data should be taken as a specific case of the much broader multi-level mixed models, with equivalent results when there is only one level. Actually, and maybe that’s not a unanimous point-of-view, it’s the way I’ve learned, according to referential books and lecturers. For example:

“The variance-components model considered here [ using – xtreg -] is a simple special case of a linear mixed-effects model the xtmixed command” (Rabe-Hesketh and Skrondal. Multilevel and longitudinal modeling using Stata. Third edition. StataPress, 2012, p.85).

“The simplest sort of model of this type is the linear mixed model, a regression model with one or more random effects. A special case of this model is the random effects panel data model implemented by xtreg, re which we have already discussed. If the only random coefficient is a random intercept, that command should be used to estimate the model. For more complex models, the command xtmixed may be used to estimate a multilevel mixed-effects regression.” (Cristopher F Baum: Models for Longitudinal / Panel Data and Mixed Models. Link: http://www.economics.adelaide.edu.au...a_Lecture3.pdf

From Stata’s manual (http://www.stata.com/manuals13/me.pdf) : “Because this [- mixed- ] model is a simple random-intercept model fit by ML, it would be equivalent to using xtreg with its mle option”.

Also, there is a query I made last year to Gustavo Sanchez (StataCorp) during a netcourse on Panel Data, exactly due to my “amazement” by the comparison I did between – mixed – and – xtreg- . In the letter, I commented: “I did a comparison between both models and I got exactly the same results”. How am I supposed to choose the “best” one?
And the reply from StataCorp: “You get the same result with mixed ,ml stddeviations and xtreg ,mle because the latter fits a model that is a particular case for the mixed effects model. In addition, both command line specifications are using the same mle estimator. Notice that with xtreg ,mle you fit a one-way random effects model, which is the same as the mixed effects model with only one level for the random effects component”.

Regarding the relationship between hierarchal and multi-level models:

“It is convenient to specify a liner mixed model (LMM) in terms of an explicitly defined hierarchy of simpler models, which correspond to the levels of a clustered or longitudinal data set. When LMMs are specified in such a way, they are often referred to as hierarchical linear models (HLMs), or multilevel models (MLMs)” (West, Welch, Gatecki. Linear Mixed Models: a practical guide using statistical software. Second edition. CRC Press, 2015, page 22)

All of these authors, coincidentally, seem to go on the same direction we underlined in the last message. Sincerely, I cannot envisage in what point these statements might be wrong.
Therefore, and also sincerely, it seems to me that we are all talking in this thread on the same subject, but no necessarily against or in favour. And I agree, absolutely, that fixed-effects may have different meanings under different specialties, and not only mixed models but also nested models (such as – nestreg – , for example) can cope with hierarchical structures, under certain conditions.

I really apologize for having written such a long message. My fault, undoubtedly. As Pascal once said (and here just paraphrasing the Philosopher-Mathematician), unfortunately I didn’t have the time to make it shorter, as I should.

Best,
Marcos

[Maarten Buis]

I think there are two terminological confusion happening at the same time: the term fixed effects means different things in different traditions and multi-level models and panel models are pretty much the same thing.

The problem Stephen had with your assertion that "that panel data should be taken as a specific case of multilevel mixed-effects models". The problem is that for economists "multi-level" is equal to random effects. This is not true in other disciplines, but that does not make this less of a problem if you are an economist.

So I suspect you are both right, and that the terminology used in this area is a hopeless mess.

[Marcos Almeida]

Thank you so much for your comments, Maarten. I really appreciated that. Indeed, we cannot help but face this: no matter the field, different meanings as well as different perspectives can make any scenario appears more arcane and contradictory than it truly is.

Best,

Marcos

[Elin Vimefall]

Thanks a lot! This discussion was really helpful to me


Best regards //Elin Vimefall