Intercept and slope dummies for regions in a negative binomial regression

[Imran Khan]

Dear all,

I am including intercept and slope dummies for 5 regions in a negative binomial model as follows:

nbreg DV IV Controls Region1 Region1*IV  Region2 Region2*IV Region3 Region3*IV Region4 Region4*IV i.country i.year, vce (cluster country)

where DV= dependent variable, IV= key explanatory variable, Controls= control variables, Region1 and Region1*IV are intercept and slope dummies of the first region until fourth. i.country and i.year are included as country and year fixed effects.

Given this background, I have two questions:

First, Is it okay to include all the intercept and slope dummies for regions in one model or should I include one region at a time?

Second, how should I interpret and the sign and significance on the coefficient on IV? Will it remain the same as the model where regional dummies were not included?

Best regards,
Imran Khan.

[Clyde Schechter]

First,

nbreg DV IV Controls Region1 Region1*IV Region2 Region2*IV Region3 Region3*IV Region4 Region4*IV i.country i.year, vce (cluster country)

is not legal Stata code for any such model because you can't use the * character here.

Second, instead of calculating separate indicators ("dummies") for each region, just have a single variable Region taking on values 1 through 5 and use factor variable notation. Thus:

nbreg DV i.Region##IV Controls i.country i.year, vce(cluster country)

Note: If IV is a continuous variable, then specify it as c.IV in the -nbreg- command.

Second, how should I interpret and the sign and significance on the coefficient on IV? Will it remain the same as the model where regional dummies were not included?

No, it will not be the same as in a model where there are no region indicators. It is interpreted as the slope of the (log) DV:IV relationship in the region that Stata omits as the reference level of the Region variable only.

Interaction models are best interpreted using the -margins- command. Learning -margins- is complicated, but, fortunately, the excellent Richard Williams has written an extremely lucid presentation of it in
https://www3.nd.edu/~rwilliam/stats/Margins01.pdf, which also includes several worked examples. Your time invested in reading it will be amply repaid. He does not, if I recall, include any examples with -nbreg-, but the principles and approach are exactly the same.

[Imran Khan]

Dear Clyde,

Many thanks for your detailed reply.

I have understood it now and I have identified the mistake in my command.

I run the command suggested by you and have got the desired results. However, when I am calculating the marginal effects, dy/dx turned out to be missing and Std.Err. are "non-estimable” for regions.

I used the following codes:

nbreg DV i.Region##IV Controls i.country i.year, vce(cluster country)
eststo margin1: margins, dydx (*) atmeans post
estimates store m1, title (Model 1)

Best regards,
Imran Khan.

[Clyde Schechter]

Add the -noestimchk- option to your -margins- command. But I would also suggest you post the -nbreg- output as well (as it comes directly from -nbreg-). It isn't clear to me why these margins should turn up as "not estimable." Also, after your -nbreg- command you should run -tab Region IV if e(sample)- and verify that all of the possible combinations occur in the estimation sample.

[Imran Khan]

Dear Clyde,

Many thanks for your reply.

Firstly, I am adding -noestimchk- with the margin command but it says the noestimchk option not allowed. How to add this option correctly?
Secondly, I am posting my output below. This is for the first time I am posting an output here. I am not sure how to post it properly.

. nbreg AvPA i.Regions##c.ChinaComm $vars i.recid i.Year, vce(cluster recid)
note: 93.recid omitted because of collinearity
note: 108.recid omitted because of collinearity
note: 129.recid omitted because of collinearity
note: 131.recid omitted because of collinearity

Fitting Poisson model:

Iteration 0:   log pseudolikelihood = -1112.1254  
Iteration 1:   log pseudolikelihood =  -1014.123  
Iteration 2:   log pseudolikelihood = -1013.3503  
Iteration 3:   log pseudolikelihood = -1013.3499  
Iteration 4:   log pseudolikelihood = -1013.3499  

Fitting constant-only model:

Iteration 0:   log pseudolikelihood = -1405.3531  
Iteration 1:   log pseudolikelihood = -1265.9125  
Iteration 2:   log pseudolikelihood = -1258.6133  
Iteration 3:   log pseudolikelihood = -1258.5668  
Iteration 4:   log pseudolikelihood = -1258.5668  

Fitting full model:

Iteration 0:   log pseudolikelihood = -1125.3866  
Iteration 1:   log pseudolikelihood = -1072.4611  
Iteration 2:   log pseudolikelihood = -1023.4222  (not concave)
Iteration 3:   log pseudolikelihood = -1022.4619  
Iteration 4:   log pseudolikelihood = -1015.7561  (not concave)
Iteration 5:   log pseudolikelihood =  -1014.728  
Iteration 6:   log pseudolikelihood = -1013.0476  
Iteration 7:   log pseudolikelihood = -1012.9251  
Iteration 8:   log pseudolikelihood = -1012.9191  
Iteration 9:   log pseudolikelihood = -1012.9191  

Negative binomial regression                    Number of obs     =        400
Wald chi2(28)     =          .
Dispersion           = mean                     Prob > chi2       =          .
Log pseudolikelihood = -1012.9191               Pseudo R2         =     0.1952

(Std. Err. adjusted for 67 clusters    in recid)
    
Robust
AvPA       Coef.   Std. Err.      z    P>z     [95% Conf.    Interval]
    
Regions 
East Asia & Pacific     .3993421   .2078436     1.92   0.055    -.0080238    .8067079
Europe & Central Asia    -.2341186   .1893718    -1.24   0.216    -.6052806    .1370433
Latin America & Caribbean    -.4042735   .1454963    -2.78   0.005    -.6894409    -.1191061
Middle East & South Asia    -1.051309    .160349    -6.56   0.000    -1.365587    -.7370304

ChinaComm   -.0054719   .0032969    -1.66   0.097    -.0119337    .0009899

Regions#c.ChinaComm 
East Asia & Pacific     .0170412   .0066665     2.56   0.011      .003975    .0301073
Europe & Central Asia    -.0045519   .0051887    -0.88   0.380    -.0147216    .0056178
Latin America & Caribbean     .0146773   .0097825     1.50   0.134     -.004496    .0338506
Middle East & South Asia     .0054603   .0079187     0.69   0.490    -.0100601    .0209807

AvFields    .0809264   .0142258     5.69   0.000     .0530442    .1088085
WBComm    .0006814   .0040377     0.17   0.866    -.0072324    .0085952
GDPGrowth    .0070837   .0036676     1.93   0.053    -.0001047    .0142721
CPIGrowth     .117302   .5200761     0.23   0.822    -.9020285    1.136633
GovExpenditures    .0002096   .0115351     0.02   0.986    -.0223987    .0228179
HerReserves    .0368476   .0697293     0.53   0.597    -.0998194    .1735146
Investments   -.0009753   .0046232    -0.21   0.833    -.0100367    .008086
ExternDebt   -.0011231   .0011635    -0.97   0.334    -.0034035    .0011572
UNVotingAffUS   -.0042187   .5562733    -0.01   0.994    -1.094494    1.086057
DemocracyIndex    .0332686   .0126209     2.64   0.008     .0085321    .0580052

recid 
Angola      .490998   .2351235     2.09   0.037     .0301645    .9518315
Argentina     .9375469   .1453702     6.45   0.000     .6526266    1.222467
Armenia     .0364845   .1491634     0.24   0.807    -.2558704    .3288394
Azerbaijan     .5664941   .2481418     2.28   0.022     .0801451    1.052843
Bangladesh     1.002633    .109951     9.12   0.000     .7871327    1.218133
Belarus     .2759178   .3499281     0.79   0.430    -.4099287    .9617643
Bolivia     .2721115     .09128     2.98   0.003      .093206    .4510169
Brazil     .4307272   .1040604     4.14   0.000     .2267725    .6346818
Bulgaria    -.3642696   .1451656    -2.51   0.012     -.648789    -.0797502
Burundi    -.1268907   .1693691    -0.75   0.454     -.458848    .2050666
Cambodia    -.7001023   .1936162    -3.62   0.000    -1.079583    -.3206215
Cameroon     1.015748   .1796122     5.66   0.000      .663715    1.367782
Cape Verde     .0601052   .1329917     0.45   0.651    -.2005537    .3207641
Central African Republic     .4654829   .1481664     3.14   0.002     .1750821    .7558837
Chad     .1026964   .1949731     0.53   0.598    -.2794437    .4848366
Colombia     .0050375   .0987148     0.05   0.959      -.18844    .198515
Comoros    -.2188509   .1356493    -1.61   0.107    -.4847186    .0470169
Congo, Democratic Republic of     .0839117   .2350036     0.36   0.721    -.3766868    .5445102
Congo, Republic of     1.310998   .2022937     6.48   0.000     .9145098    1.707487
Costa Rica    -.0198591   .0957695    -0.21   0.836    -.2075639    .1678457
Djibouti    -.8349859   .2244143    -3.72   0.000     -1.27483    -.395142
Ecuador     .1113069   .1611306     0.69   0.490    -.2045033    .4271171
Egypt, Arab Republic of     .4670416   .1576827     2.96   0.003     .1579891    .776094
Gabon     1.027173   .1820485     5.64   0.000     .6703644    1.383982
Georgia     .2695822   .1367753     1.97   0.049     .0015075    .5376569
Ghana    -.3233007   .0596287    -5.42   0.000    -.4401708    -.2064307
Guyana    -.0273767    .223715    -0.12   0.903    -.4658501    .4110968
Haiti     .5388891   .1320568     4.08   0.000     .2800626    .7977157
India     .6802035     .14217     4.78   0.000     .4015555    .9588515
Indonesia    -.7036069   .2118258    -3.32   0.001    -1.118778    -.2884361
Jamaica     .4474359   .0809339     5.53   0.000     .2888083    .6060635
Jordan     1.409902   .2255477     6.25   0.000     .9678364    1.851967
Kazakhstan     .3707881   .2907324     1.28   0.202    -.1990368    .9406131
Kenya    -.0206182   .1959006    -0.11   0.916    -.4045764    .36334
Lao PDR    -.2750362   .1227011    -2.24   0.025    -.5155259    -.0345464
Lesotho    -.4056063   .3207989    -1.26   0.206    -1.034361    .223148
Liberia    -.0417803   .1554385    -0.27   0.788    -.3464341    .2628736
Macedonia      .017181   .1283764     0.13   0.894    -.2344321    .2687941
Madagascar     .0657541   .0687441     0.96   0.339    -.0689819    .2004901
Malawi    -.3599446   .1394491    -2.58   0.010    -.6332598    -.0866295
Mauritius    -.3196621   .1245528    -2.57   0.010    -.5637811    -.0755431
Mexico     .1328705   .0936951     1.42   0.156    -.0507685    .3165095
Moldova     .0829188    .136873     0.61   0.545    -.1853473    .351185
Mongolia    -.9384252   .2399559    -3.91   0.000     -1.40873    -.4681202
Montenegro     .1565579   .1914724     0.82   0.414    -.2187211    .5318368
Morocco     .4747735   .1945905     2.44   0.015     .0933832    .8561639
Mozambique    -.1367388   .1259846    -1.09   0.278    -.3836642    .1101866
Nepal     1.054296   .1028167    10.25   0.000     .8527791    1.255813
Nicaragua     .0284319   .1395119     0.20   0.839    -.2450063    .3018701
Nigeria      .188949   .1328163     1.42   0.155    -.0713661    .4492641
Pakistan     1.037444   .1141552     9.09   0.000     .8137035    1.261184
Peru            0  (omitted)
Philippines    -.6779857   .2144096    -3.16   0.002    -1.098221    -.2577506
Romania     .1734572   .1040406     1.67   0.095    -.0304586    .377373
Rwanda     .1296724   .1706222     0.76   0.447    -.2047411    .4640858
Sierra Leone    -.1324622   .0721873    -1.83   0.067    -.2739468    .0090224
Sri Lanka            0  (omitted)
Tajikistan     .5127007   .3186581     1.61   0.108    -.1118577    1.137259
Tanzania     .1232803   .1231361     1.00   0.317    -.1180621    .3646227
Thailand    -.8103539    .242525    -3.34   0.001    -1.285694    -.3350136
Tunisia      .266742    .152079     1.75   0.079    -.0313273    .5648113
Turkey     .1916266   .1246915     1.54   0.124    -.0527643    .4360174
Uganda     .0519416   .1344253     0.39   0.699    -.2115271    .3154104
Ukraine    -.0577544   .1416549    -0.41   0.683    -.3353929    .2198841
Vietnam            0  (omitted)
Zambia            0  (omitted)

Year 
2002     -.262433   .1235177    -2.12   0.034    -.5045233    -.0203427
2003    -.4358952   .1377407    -3.16   0.002    -.7058621    -.1659284
2004     -.501171   .1078946    -4.65   0.000    -.7126405    -.2897014
2005    -.7422219   .1252622    -5.93   0.000    -.9877313    -.4967126
2006    -.7914895   .1449701    -5.46   0.000    -1.075626    -.5073533
2007    -.8019043   .1475003    -5.44   0.000       -1.091    -.512809
2008    -.9512423   .1560952    -6.09   0.000    -1.257183    -.6453014
2009    -.9180771   .1581013    -5.81   0.000     -1.22795    -.6082042
2010    -.8823936   .1548212    -5.70   0.000    -1.185838    -.5789496
2011    -.8834462   .1451501    -6.09   0.000    -1.167935    -.5989572
2012    -1.027585   .1480604    -6.94   0.000    -1.317778    -.737392
2013    -1.050608   .1483953    -7.08   0.000    -1.341457    -.7597585
2014    -1.053725   .1382543    -7.62   0.000    -1.324698    -.782751
2015    -.9934422   .1961987    -5.06   0.000    -1.377985    -.6088998

_cons    2.654007      .3512     7.56   0.000     1.965667    3.342346
    
/lnalpha   -5.453549   1.092395                     -7.594605    -3.312493
    
alpha    .0042811   .0046766                      .0005032    .0364252

Regards,
Imran Khan.

[Clyde Schechter]

Firstly, I am adding -noestimchk- with the margin command but it says the noestimchk option not allowed. How to add this option correctly?

Sorry, that was a typo on my part. It's -noestimcheck-.

Your -nbreg- output came out just fine here. Thanks. And I don't see anything troubling in it.

Now, having also seen your regression, I suggest that instead of using dydx(*) in the -margins- command, you use dydx(list_of_variables_whose_marginal_effects_I'm_actua lly_interested_in). You will just waste a lot of time and pixels calculating the marginal effects of your year and recid indicators ("dummies,") unless calculating those marginal effects really contributes to your research goals. It's unusual for anybody to care about the marginal effects of those things. I'm not even sure you want the marginal effects of the region variables or even the ChinaComm variable. If you do, fine. But only ask Stata to calculate the ones you really want. The -margins- calculations are also pretty slow, so the time spent calculating them for variables you don't care about will be appreciable.

[Imran Khan]

Dear Clyde,

Many thanks for your reply.

The suggested option worked fine.

I am also able to save much more time by using dydx for the selected variables.

Best regards,
Imran Khan.