Ordinal Dependent Variable (Panel Data)

[Andreas Baltin]

Hello fellow statisticians!

I have got a quick question that (hopefully) a more experienced statistician is able to answer.

I have a balanced panel data set where I am looking at several dependent variables. Some of them are continuous (%) and some of them are ordinal (categories 1-4, ordered from highest to lowest).

The continuous variables, I want to analyse with a standard Fixed Effects (within) estimator. However, as far is I know, I cannot just do this for the ordinal variables right, because they are not linear? Is there any way to justify that the ordinal variables can be treated as continuous? I do know this works if the ordinal variable is an independent variable, I normally follow this methodology when encountering this problem: https://www3.nd.edu/~rwilliam/xsoc73...ndependent.pdf


So to sum up my question: Is it possible to 'argue' that my ordinal dependent variables can be treated as continuous and I can therefore use FE for them as well? If yes - could you point me towards the appropriate literature/methodology? Or is this not possible and I need to use logit/probit for the ordinal dependent variables?

Many thanks in advance folks!!
Andreas

[Richard Williams]

Thanks Eric. So I wonder why there is no implementation in Stata yet? As far as I can tell there isn’t even a user-written routine, unless I am missing it.

[Eric de Souza]

Richard Williams : I see that the slides below provide some code; I just got interested in FE ordered logit models, which led me to hunt for code. I haven't had a look at the code or the method used as yet:
http://repec.org/usug2011/UK11_Hole.pdf

[Joseph Coveney]

Do you mean:

1. Treat them as continuous and estimate in fixed effects
2. Estimate using logit

And then compare the results and go from there?

I meant just 1, and see how badly the test size is affected by the model misspecification. Maybe something along the lines of the following.

version 15.1

clear *

set seed `=strreverse("1493732")'

program define simem, rclass
    version 15.1
    syntax

    drop _all
    set obs 200
    generate int pid = _n
    generate double pid_u = rnormal()

    expand 3
    bysort pid: generate byte tim = _n
    generate double stg = runiform() - 0.5
    generate double xb = pid_u + rnormal()
    generate byte sco = 0
    forvalues cut = 1/3 {
        replace sco = sco + 1 if xb > invnormal(`cut'/4) * sqrt(2)
    }

    xtreg sco c.stg, i(pid) fe
    test stg
    return scalar p = r(p)
end

simulate p = r(p), reps(3000) nodots: simem
generate byte pos = p < 0.05
summarize pos

exit

If you have an idea of the data-generating mechanism, then you'd want to emulate that. If not, you'd probably at least want to try to get close to the marginal distribution of the categories. You could also look into what kind of hit power takes, too.

[Richard Williams]

In the wishlist for Stata 16, I just added the wish that support for FE ordinal models be added. At least if the procedures others have used are legitimate. It may be that there are terrible problems with them that I am not aware of.

[Richard Williams]

I don't know of any ideal model, at least one that has been implemented in Stata. Some things you might try:

Use a hybrid model (I think maybe the user-written xthybrid can do it easily) Allison discusses the pros and cons of that approach at https://statisticalhorizons.com/prob...-hybrid-method

Treat the DV as continuous or collapse it into a dichotomy. Yes, that is less than ideal, but there are tradeoffs no matter what you do. The logit approach may be especially defensible -- it would be the same as if you had just offered fewer options in the first place.

This paper claims that "The fixed effects ordered logit model is widely used in empirical research in economics." Well, maybe so, but I don't know how they do it. But if you read the article carefully maybe you can figure it out. https://www.cemmap.ac.uk/uploads/cem...is%20Muris.pdf If the methods used are valid I would like to see them implemented in Stata.

[Andreas Baltin]

I recall this kind of question arising on the list before, on a couple of occasions. You might want to scan through the archives for discussion and for any literature cited in the posts.

It would probably be unwise to dismiss the incidental variables problem as unimportant.

If your primary interest lies in testing, how about using simulation to see just how badly you'd be led astray by treating the four ordered categories as continuous in the fixed-effect model that you're contemplating?

Hi Jospeh,

Many thanks for your input! I have digged through a lot of pages on the search and find a lot of 'similar' threads but havent found the ONE definitive answer yet. I will have another look though.

I do not fully understand what your last sentence means. Do you mean:

1. Treat them as continuous and estimate in fixed effects
2. Estimate using logit

And then compare the results and go from there?

Many thanks for your help so far!!

[Joseph Coveney]

I recall this kind of question arising on the list before, on a couple of occasions. You might want to scan through the archives for discussion and for any literature cited in the posts.

It would probably be unwise to dismiss the incidental variables problem as unimportant.

If your primary interest lies in testing, how about using simulation to see just how badly you'd be led astray by treating the four ordered categories as continuous in the fixed-effect model that you're contemplating?