Is my panel regression correct?

[Matthew Williams]

Hi all,

I have three countries and each of them was surveyed two times at least (country C) and three times at most (countries A and B). I pool the data together and then examine the determinant of y. In the data, observations are uniquely identified by three variables: id, round, and country.

First, I create a paneled variable and tell Stata that I will use panel regressions as follows:

egen panelid = group(id country)
     xtset panelid round

Second, I use xtpoisson command since my dedepent variable is a count

qui xtpoisson y x1 x2 x3, re vce(cluster panelid)
    margins, dydx(*)

Since I do not have much experience with panel data analysis, I am not sure if my code above is correct. I would appreciate if anyone can take a look at my code and give advice if any. Thanks!

Data example

clear
input float(id round country y x1 x2 x3)
 1 1 1  15 1 1 1
 1 2 1  15 1 0 1
 1 3 1  15 1 0 1
 1 1 2   1 0 1 1
 1 2 2   1 0 0 1
 1 3 2   1 0 1 1
 1 1 3   2 0 0 0
 1 2 3   2 0 0 0
 2 1 1  10 1 1 1
 2 2 1  10 1 0 1
 2 3 1  10 1 0 1
 2 1 2   1 0 1 1
 2 2 2   1 0 0 1
 2 3 2   1 0 1 1
 2 1 3   5 0 0 1
 2 2 3   5 0 0 1
 3 1 1  10 0 1 1
 3 2 1  10 0 0 1
 3 1 2   8 0 1 1
 3 2 2   8 0 0 1
 3 3 2   8 0 1 1
 3 1 3   1 0 0 0
 4 1 1   2 1 0 1
 4 2 1   3 1 1 1
 4 1 2   2 0 0 1
 4 2 2   2 0 0 1
 4 1 3   5 0 1 0
 4 2 3   5 0 0 0
 5 3 1   3 1 1 1
 5 1 2   1 0 0 1
 5 2 2   1 0 1 1
 5 3 2   1 0 0 1
 5 1 3   7 1 0 1
 6 1 1   7 0 1 0
 6 2 1   7 0 0 0
 6 3 1   7 0 0 0
 6 1 2 100 0 1 1
 6 2 2 100 0 0 1
 6 3 2 100 0 0 1
 6 1 3  10 0 1 1
 6 2 3  10 0 0 1
 7 1 1  15 1 0 1
 7 2 1   8 1 1 1
 7 1 2   2 0 0 1
 7 2 2   2 0 1 1
 7 3 2   2 0 0 1
 7 1 3   5 0 0 1
 7 2 3   5 0 1 1
 8 1 1   4 1 0 1
 8 2 1  10 1 0 1
 8 1 2  10 0 1 1
 8 2 2  10 0 0 1
 8 3 2  10 0 0 1
 8 1 3   3 0 1 1
 8 2 3   3 0 0 1
 9 1 1   1 1 0 0
 9 2 1   1 1 1 0
 9 3 1   1 1 0 0
 9 1 2   4 0 1 1
 9 2 2   4 0 1 1
 9 3 2   4 0 0 1
 9 1 3   1 0 1 1
 9 2 3   1 0 0 1
10 1 1  30 1 1 1
10 2 1   5 1 0 1
10 1 2   0 0 0 1
10 2 2   0 0 1 1
10 2 3   5 0 0 1
11 1 1  40 1 1 1
11 2 1  40 1 0 1
11 3 1  40 1 0 1
11 1 2  20 0 1 1
11 2 2  20 0 0 1
11 3 2  20 0 0 1
11 1 3  12 0 1 1
11 2 3  12 0 0 1
12 1 1   8 1 0 0
12 2 1   8 1 1 0
12 3 1   8 1 0 0
12 1 2   1 0 1 1
12 2 2   1 0 0 1
12 3 2   1 0 1 1
12 1 3   3 0 0 1
12 2 3   3 0 0 1
13 1 1 100 0 1 1
13 2 1 100 0 0 1
13 3 1 100 0 0 1
13 1 2   7 0 1 1
13 2 2   7 0 0 1
13 3 2   7 0 0 1
13 1 3   7 0 1 1
13 2 3   7 0 0 1
14 1 1  10 1 0 1
14 2 1  10 1 1 1
14 3 1  10 1 0 1
14 1 3  10 0 0 1
14 2 3  10 0 0 1
15 1 1   0 0 1 0
15 2 1   0 0 0 0
15 3 1   0 0 0 0
15 1 2  20 0 1 1
15 2 2  20 0 0 1
15 3 2  20 0 0 1
15 1 3   4 1 0 1
end
label values country country
label def country 1 "A", modify
label def country 2 "B", modify
label def country 3 "C", modify

[Carlo Lazzaro]

Matthew:
what I'm not clear with your -xtset- code is the -panelid-: -id- or -country-?

[Jared Greathouse]

Yeah I agree with Carlo, why is the country and the id your panel variable?

Your code may be fine, but maybe not. What's your outcome, the number of people kicked to death by horses in each country?

[Matthew Williams]

Dear Carlo Lazzaro and Jared Greathouse,

Thank you for your promote reply. The reason I used panelid and country in my xtset is that I have three variables (id, round, and country) that uniquely identify observations, so I was unable to use id and round in my xtset because of the following errors:

repeated time values within panel

The xtset command above is also the reason that makes me unconfident about my regression. I am not sure if the way I generate panelid and subsequent xtset and xtpoission commands are correct. Any advice is appreciated.

It works fine if I run separate regressions for each country, for example:

preserve
keep if country==1
xtset id round
qui xtpoisson y x1 x2 x3, re vce(cluster id)
margins, dydx(*)
restore

@Jared Greathouse: the outcome is the number of clients of a drug store per week in each country. Since the data I am using is confidential, I have to code all variables in a way that they are not recognized.

[Carlo Lazzaro]

Matthew:
if you do not plan to use time-series related operators (such as lags and leads) yoiu can safely -xtset- your dataset with -id- as -panelid- and even add -i.round- as a predictor in the right hand-side of your -xtpoisson. regression.
In addition,exploiting Jared Greathouse 's assist, as far as the number of the Prussian soldiers kicked to death by their horses (which was one of the first application of the Poisson distribution in the real world - see https://en.wikipedia.org/wiki/Ladislaus_Bortkiewicz and StataPress colophon), you may find the following article interesting: https://www.jstor.org/stable/2348169.

[Matthew Williams]

Dear Carlo Lazzaro,

if you do not plan to use time-series related operators (such as lags and leads) you can safely -xtset- your dataset with -id- as -panelid- and even add -i.round- as a predictor in the right-hand-side of your -xtpoisson. regression.

To make sure that I understand your advice correctly, do you mean the following code?

xtset id
qui xtpoisson y x1 x2 x3 i.round i.country, re vce(cluster id)
margins, dydx(*)

Many thanks for the relevant references.

[Carlo Lazzaro]

Matthew:
yes, I'd go that way.

[Matthew Williams]

Matthew:
yes, I'd go that way.

Thank you so much .

[Joseph Coveney]

. . . the outcome is the number of clients of a drug store per week in each country.

Are you saying that id is the identifier for a drug store? If so, then I think that your model isn't specified correctly, inasmuch as a given drug store cannot simultaneously exist in each of three countries.

On the other hand, if you have a fixed sample of fifteen drug store chains with franchise stores in each of the three countries, and you want to treat the international drug-store-chain chain firms as the exchangeable variable, then you'd probably be OK.

[Matthew Williams]

Are you saying that id is the identifier for a drug store? If so, then I think that your model isn't specified correctly, inasmuch as a given drug store cannot simultaneously exist in each of three countries.

On the other hand, if you have a fixed sample of fifteen drug store chains with franchise stores in each of the three countries, and you want to treat the international drug-store-chain chain firms as the exchangeable variable, then you'd probably be OK.

Dear Prof. Joseph,

Thank you for your comments. Yes, id is the identifier for a drug store.

If so, then I think that your model isn't specified correctly, in as much as a given drug store cannot simultaneously exist in each of three countries.

So, do you have any advice for me regarding the model specification?

Thank you.

[Jared Greathouse]

Given that you've made an ID for each brand and country, i think your intuition is fine. I mean where I live, near Atlanta Georgia, Kroger and Publix are popular grocery stores. If I were studying these stores specifically, I would just xtset them by their ID and (presumably county) that they're in. And that's okay, because we have one identifier per individual store over time.

My only real question is, is Poisson appropriate? I mean I don't know how many people visit my local drug stores, but it has to be.... I don't know, hundreds, per day. I guess my real question is, could you get away with (or at least experiment with) OLS in this scenario? Any regression you'd do, poisson or normal, would just be

xtreg y Xs i.round, fe

But, do see this article on FE estimators. People tend to throw FE at everything, sometimes inappropriately.

[Joseph Coveney]

My only real question is, is Poisson appropriate?

Yeah, he's ostensibly got up to a hundred patrons per week, but if these are counts and given that there are a fair number of zeros, onsies, threesies and other low counts, then it would seem that a count model would be more defensible than a linear model. Specifying a negative binomial distribution family doesn't seem to do much here, and so maybe Poisson is a reasonable first-pass specification for the distribution.

But, do see this article on FE estimators. People tend to throw FE at everything, sometimes inappropriately.

I think that he's not using a fixed-effects specification.

Yes, id is the identifier for a drug store.

So, do you have any advice for me regarding the model specification?

As Jared implies, it seems that you were on the right track originally, with the egen . . . group() data-management step. So, perhaps something like the following (variable names shortened for brevity).

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿquietlyÿinputÿfloat(idÿroundÿcountryÿyÿx1ÿx2ÿx3)

.ÿ
.ÿquietlyÿcompress

.ÿ
.ÿrenameÿcountryÿcid

.ÿrenameÿroundÿtim

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿgenerateÿintÿpidÿ=ÿ100ÿ*ÿcidÿ+ÿid

.ÿisidÿpidÿtim,ÿsort
(dataÿnowÿsortedÿbyÿpidÿtim)

.ÿ
.ÿmeglmÿyÿi.(x?ÿtimÿcid),ÿfamily(poisson)ÿ||ÿpid:ÿ,ÿnolrtestÿnolog

Mixed-effectsÿGLMÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ104
Family:ÿPoisson
Link:ÿÿÿLog
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ44

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿÿ1
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿÿ2.4
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿÿ3

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(7)ÿÿÿÿÿÿ=ÿÿÿÿÿÿ10.67
Logÿlikelihoodÿ=ÿ-278.16066ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.1536
------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿyÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿ1.x1ÿ|ÿÿ-.3233068ÿÿÿ.5579446ÿÿÿÿ-0.58ÿÿÿ0.562ÿÿÿÿ-1.416858ÿÿÿÿ.7702446
ÿÿÿÿÿÿÿÿ1.x2ÿ|ÿÿ-.0112909ÿÿÿ.1009929ÿÿÿÿ-0.11ÿÿÿ0.911ÿÿÿÿ-.2092334ÿÿÿÿ.1866516
ÿÿÿÿÿÿÿÿ1.x3ÿ|ÿÿÿ1.430379ÿÿÿ.5366718ÿÿÿÿÿ2.67ÿÿÿ0.008ÿÿÿÿÿ.3785212ÿÿÿÿ2.482236
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿtimÿ|
ÿÿÿÿÿÿÿÿÿÿ2ÿÿ|ÿÿ-.0607674ÿÿÿÿ.099528ÿÿÿÿ-0.61ÿÿÿ0.541ÿÿÿÿ-.2558386ÿÿÿÿ.1343039
ÿÿÿÿÿÿÿÿÿÿ3ÿÿ|ÿÿ-.0332801ÿÿÿ.1112711ÿÿÿÿ-0.30ÿÿÿ0.765ÿÿÿÿ-.2513674ÿÿÿÿ.1848072
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿcidÿ|
ÿÿÿÿÿÿÿÿÿÿ2ÿÿ|ÿÿÿ-1.23794ÿÿÿ.6318782ÿÿÿÿ-1.96ÿÿÿ0.050ÿÿÿÿ-2.476398ÿÿÿÿ.0005186
ÿÿÿÿÿÿÿÿÿÿ3ÿÿ|ÿÿÿ-.912386ÿÿÿ.5530151ÿÿÿÿ-1.65ÿÿÿ0.099ÿÿÿÿ-1.996276ÿÿÿÿ.1715036
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ1.257814ÿÿÿ.5969795ÿÿÿÿÿ2.11ÿÿÿ0.035ÿÿÿÿÿ.0877558ÿÿÿÿ2.427872
-------------+----------------------------------------------------------------
pidÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿvar(_cons)|ÿÿÿ1.220383ÿÿÿ.3069654ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.7454042ÿÿÿÿ1.998024
------------------------------------------------------------------------------

.ÿ
.ÿ//ÿAlternativeÿ(youÿdon'tÿhaveÿenoughÿdataÿtoÿstructureÿtheÿworkingÿcorrelationÿmatrix)
.ÿxtgeeÿyÿi.(x?ÿtimÿcid),ÿi(pid)ÿ/*ÿt(tim)ÿ*/ÿfamily(poisson)ÿcorr(independent)ÿvce(robust)ÿnolog

GEEÿpopulation-averagedÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿ=ÿÿÿÿÿÿ104
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿ=ÿÿÿÿÿÿÿ44
Family:ÿPoissonÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:ÿÿ
Link:ÿÿÿLogÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿ1
Correlation:ÿindependentÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿ2.4
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿ3
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(7)ÿÿÿÿÿ=ÿÿÿÿ47.97
Scaleÿparameterÿ=ÿ1ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿ=ÿÿÿ0.0000

Pearsonÿchi2(104)ÿÿÿÿ=ÿÿ2475.87ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDevianceÿÿÿÿÿÿÿÿÿ=ÿÿ1617.12
Dispersionÿ(Pearson)ÿ=ÿ23.80649ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDispersionÿÿÿÿÿÿÿ=ÿ15.54923

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(Std.ÿerr.ÿadjustedÿforÿclusteringÿonÿpid)
------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRobust
ÿÿÿÿÿÿÿÿÿÿÿyÿ|ÿCoefficientÿÿstd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿ1.x1ÿ|ÿÿ-1.328568ÿÿÿ.5391672ÿÿÿÿ-2.46ÿÿÿ0.014ÿÿÿÿ-2.385316ÿÿÿ-.2718197
ÿÿÿÿÿÿÿÿ1.x2ÿ|ÿÿ-.2364593ÿÿÿ.1487161ÿÿÿÿ-1.59ÿÿÿ0.112ÿÿÿÿ-.5279374ÿÿÿÿ.0550188
ÿÿÿÿÿÿÿÿ1.x3ÿ|ÿÿÿ2.059836ÿÿÿ.6187065ÿÿÿÿÿ3.33ÿÿÿ0.001ÿÿÿÿÿ.8471932ÿÿÿÿ3.272478
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿtimÿ|
ÿÿÿÿÿÿÿÿÿÿ2ÿÿ|ÿÿ-.1846983ÿÿÿÿ.095755ÿÿÿÿ-1.93ÿÿÿ0.054ÿÿÿÿ-.3723746ÿÿÿÿÿ.002978
ÿÿÿÿÿÿÿÿÿÿ3ÿÿ|ÿÿÿ.0749424ÿÿÿ.1611165ÿÿÿÿÿ0.47ÿÿÿ0.642ÿÿÿÿ-.2408402ÿÿÿÿ.3907249
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿcidÿ|
ÿÿÿÿÿÿÿÿÿÿ2ÿÿ|ÿÿÿ-1.48177ÿÿÿÿÿ.72726ÿÿÿÿ-2.04ÿÿÿ0.042ÿÿÿÿ-2.907174ÿÿÿ-.0563668
ÿÿÿÿÿÿÿÿÿÿ3ÿÿ|ÿÿ-2.082517ÿÿÿ.5170389ÿÿÿÿ-4.03ÿÿÿ0.000ÿÿÿÿ-3.095894ÿÿÿ-1.069139
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ2.141616ÿÿÿ.5156226ÿÿÿÿÿ4.15ÿÿÿ0.000ÿÿÿÿÿ1.131014ÿÿÿÿ3.152217
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

The maginitude of the difference in regression coefficients between the population average (robust standard errors) and individual-specific (random effects) models seems larger than I would have anticipated, and maybe you'd want to look into that.

[Matthew Williams]

Dear Prof. Joseph,

Thank you for your insightful advice. Do I need to compute marginal effects after running meglm or xtgee?