Regression across sub-samples vs by using interaction term

[Abdan Syakura]

Dear all,

I want to do regression across three sub-samples. However the result of regressing them separately vs. using interaction term is different. Could you please help? What did I do wrong? Thank you for your help.


Result by using separate regression for each sub-samples, if sector=1:

xtprobit over2 l.over2 c.l.lnGSCITOTSD##c.l.GSCITOTMG l.wgdp l.hgdp l.infl l.geopol if sector==1, re vce(robust)  


Random-effects probit regression                Number of obs     =      3,103
Group variable: firm                            Number of groups  =        107

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         29
                                                              avg =       29.0
                                                              max =         29

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(8)      =     392.93
Log pseudolikelihood  = -1087.6732              Prob > chi2       =     0.0000

                                                (Std. Err. adjusted for 107 clusters in firm)
---------------------------------------------------------------------------------------------
                            |               Robust
                      over2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
                      over2 |
                        L1. |   1.268935   .1114277    11.39   0.000     1.050541    1.487329
                            |
                lnGSCITOTSD |
                        L1. |  -.2170595   .0465004    -4.67   0.000    -.3081985   -.1259205
                            |
                  GSCITOTMG |
                        L1. |   .0275061   .0199155     1.38   0.167    -.0115275    .0665398
                            |
cL.lnGSCITOTSD#cL.GSCITOTMG |  -.0032262   .0033667    -0.96   0.338    -.0098247    .0033724
                            |
                       wgdp |
                        L1. |  -.0863806   .0282783    -3.05   0.002    -.1418052   -.0309561
                            |
                       hgdp |
                        L1. |   .2159382   .0230128     9.38   0.000      .170834    .2610424
                            |
                       infl |
                        L1. |   .0931856   .0088384    10.54   0.000     .0758627    .1105085
                            |
                     geopol |
                        L1. |   .0061763   .0016261     3.80   0.000     .0029892    .0093633
                            |
                      _cons |  -.8966739   .3538679    -2.53   0.011    -1.590242   -.2031056
----------------------------+----------------------------------------------------------------
                   /lnsig2u |  -.8778675   .2561907                     -1.379992    -.375743
----------------------------+----------------------------------------------------------------
                    sigma_u |   .6447235   .0825861                      .5015781    .8287212
                        rho |   .2936199   .0531358                      .2010103     .407154
---------------------------------------------------------------------------------------------

Result by using interaction term:

xtprobit over2 i.sector#(c.l.over2 c.l.lnGSCITOTSD##c.l.GSCITOTMG c.l.wgdp c.l.hgdp c.l.infl c.l.geopol), re vce(robust) 



Random-effects probit regression                Number of obs     =     14,732
Group variable: firm                            Number of groups  =        508

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         29
                                                              avg =       29.0
                                                              max =         29

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(24)     =    1278.97
Log pseudolikelihood  = -4527.8125              Prob > chi2       =     0.0000

                                                       (Std. Err. adjusted for 508 clusters in firm)
----------------------------------------------------------------------------------------------------
                                   |               Robust
                             over2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------------------+----------------------------------------------------------------
                   sector#cL.over2 |
                                1  |   1.233693   .0995269    12.40   0.000     1.038624    1.428762
                                2  |   1.116174   .0856663    13.03   0.000     .9482715    1.284077
                                3  |   1.587107   .0876541    18.11   0.000     1.415308    1.758906
                                   |
             sector#cL.lnGSCITOTSD |
                                1  |   -.199594    .043342    -4.61   0.000    -.2845426   -.1146453
                                2  |  -.1114354   .0398321    -2.80   0.005    -.1895049   -.0333658
                                3  |  -.2216074    .043049    -5.15   0.000    -.3059818    -.137233
                                   |
               sector#cL.GSCITOTMG |
                                1  |   .0319543   .0200931     1.59   0.112    -.0074275    .0713361
                                2  |   .0587539   .0139361     4.22   0.000     .0314396    .0860682
                                3  |     .03742   .0156501     2.39   0.017     .0067464    .0680936
                                   |
sector#cL.lnGSCITOTSD#cL.GSCITOTMG |
                                1  |  -.0040029    .003388    -1.18   0.237    -.0106433    .0026376
                                2  |  -.0094008   .0023272    -4.04   0.000     -.013962   -.0048396
                                3  |  -.0052052   .0026101    -1.99   0.046     -.010321   -.0000894
                                   |
                    sector#cL.wgdp |
                                1  |  -.0853107   .0278813    -3.06   0.002    -.1399571   -.0306643
                                2  |  -.0565951   .0211258    -2.68   0.007    -.0980009   -.0151892
                                3  |  -.0896959   .0247988    -3.62   0.000    -.1383006   -.0410912
                                   |
                    sector#cL.hgdp |
                                1  |   .2314884   .0191855    12.07   0.000     .1938855    .2690913
                                2  |   .1925916   .0168027    11.46   0.000     .1596588    .2255243
                                3  |   .2353004   .0173111    13.59   0.000     .2013714    .2692295
                                   |
                    sector#cL.infl |
                                1  |   .0986052   .0077632    12.70   0.000     .0833896    .1138208
                                2  |   .0789797    .006462    12.22   0.000     .0663145    .0916449
                                3  |   .0970083   .0061669    15.73   0.000     .0849215    .1090951
                                   |
                  sector#cL.geopol |
                                1  |   .0064281   .0016887     3.81   0.000     .0031183    .0097378
                                2  |   .0054656   .0011434     4.78   0.000     .0032247    .0077066
                                3  |   .0091764    .001425     6.44   0.000     .0063835    .0119694
                                   |
                             _cons |  -1.090354   .1779324    -6.13   0.000    -1.439095    -.741613
-----------------------------------+----------------------------------------------------------------
                          /lnsig2u |  -.5038364   .0954541                     -.6909231   -.3167497
-----------------------------------+----------------------------------------------------------------
                           sigma_u |   .7773083   .0370987                      .7078936    .8535298
                               rho |   .3766395   .0224109                      .3338278    .4214681
----------------------------------------------------------------------------------------------------

Best regards,

[Carlo Lazzaro]

Abdan:
no wonder that different codes give back different results.
That said, I would go with your second code that hosts -sector- as a predictor.

[Abdan Syakura]

Dear Carlo,

Thank you for your reply. I was following the method is post #2 by @Andrew Musau in this thread: https://www.statalist.org/forums/for...for-panel-data. In that thread, doing regression separately across group & using interaction term result in the same coefficeint estimates. So I am not sure why it is not the case with mine, is it because the model is binary/non-linear? Thank you.

Best regards,

[Joseph Coveney]

is it because the model is binary/non-linear?

I think that a bigger source of the difference is that you have a different estimate of the variance component (σ_u) between the subset and the whole set. When you allow for the subset's variance component to be estimated on its own while fitting the interaction model to the whole dataset, you can get much closer estimates of the fixed effects parameters.

For example, compare 1 versus 2 below (analogous to what you're doing) and then 1 versus 3 (allowing separate variance component estimates).

The same phenomenon is observed even in linear mixed models, albeit less dramatically: compare 6 versus 7 and then 6 versus 8.

(For ease of comparison, I've collected the pertinent regression coefficients into a matrix and then listed them together after fitting the last model of each series of three.)

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1634262")'

.ÿ
.ÿquietlyÿsetÿobsÿ500

.ÿ
.ÿgenerateÿintÿpidÿ=ÿ_n

.ÿgenerateÿdoubleÿpid_uÿ=ÿrnormal()

.ÿ
.ÿgenerateÿbyteÿgrpÿ=ÿmod(_n,ÿ2)

.ÿgenerateÿdoubleÿpr1ÿ=ÿruniform(-0.5,ÿ0.5)

.ÿ
.ÿquietlyÿexpandÿ10

.ÿgenerateÿdoubleÿpr2ÿ=ÿruniform(-0.5,ÿ0.5)

.ÿ
.ÿgenerateÿdoubleÿxbuÿ=ÿpr1ÿ+ÿpr2ÿ+ÿpid_u

.ÿgenerateÿbyteÿoutÿ=ÿrbinomial(1,ÿnormal(xbu))

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿtempnameÿB

.ÿ//ÿ1
.ÿmeprobitÿoutÿc.pr?ÿifÿ!grpÿ||ÿpid:ÿ,ÿnolog

Mixed-effectsÿprobitÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ2,500
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿ250

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ10.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ10

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(2)ÿÿÿÿÿÿ=ÿÿÿÿÿ111.91
Logÿlikelihoodÿ=ÿ-1427.8888ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000
------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿpr1ÿ|ÿÿÿ.8699703ÿÿÿ.2369952ÿÿÿÿÿ3.67ÿÿÿ0.000ÿÿÿÿÿ.4054682ÿÿÿÿ1.334472
ÿÿÿÿÿÿÿÿÿpr2ÿ|ÿÿÿ1.073432ÿÿÿÿ.107106ÿÿÿÿ10.02ÿÿÿ0.000ÿÿÿÿÿ.8635078ÿÿÿÿ1.283355
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ.0260819ÿÿÿÿ.067657ÿÿÿÿÿ0.39ÿÿÿ0.700ÿÿÿÿ-.1065233ÿÿÿÿ.1586871
-------------+----------------------------------------------------------------
pidÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿvar(_cons)|ÿÿÿ.9060531ÿÿÿ.1223909ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.6952998ÿÿÿÿ1.180688
------------------------------------------------------------------------------
LRÿtestÿvs.ÿprobitÿmodel:ÿchibar2(01)ÿ=ÿ462.92ÿÿÿÿÿÿÿÿProbÿ>=ÿchibar2ÿ=ÿ0.0000

.ÿmatrixÿdefineÿ`B'ÿ=ÿ(_b[_cons],ÿ_b[pr1],ÿ_b[pr2])

.ÿ//ÿ2
.ÿmeprobitÿoutÿibn.grpÿi.grp#c.pr1ÿi.grp#c.pr2,ÿnoconstantÿ||ÿpid:ÿ,ÿnolog

Mixed-effectsÿprobitÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ5,000
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿ500

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ10.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ10

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(6)ÿÿÿÿÿÿ=ÿÿÿÿÿ225.75
Logÿlikelihoodÿ=ÿ-2787.4286ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000
ÿ(ÿ1)ÿÿ[out]_consÿ=ÿ0
------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿgrpÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.0281212ÿÿÿ.0727523ÿÿÿÿÿ0.39ÿÿÿ0.699ÿÿÿÿ-.1144707ÿÿÿÿ.1707131
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ.0474851ÿÿÿ.0733542ÿÿÿÿÿ0.65ÿÿÿ0.517ÿÿÿÿ-.0962864ÿÿÿÿ.1912566
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿgrp#c.pr1ÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.8857161ÿÿÿ.2546667ÿÿÿÿÿ3.48ÿÿÿ0.001ÿÿÿÿÿ.3865786ÿÿÿÿ1.384854
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ.8324888ÿÿÿ.2610894ÿÿÿÿÿ3.19ÿÿÿ0.001ÿÿÿÿÿ.3207629ÿÿÿÿ1.344215
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿgrp#c.pr2ÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿÿ1.08886ÿÿÿ.1076909ÿÿÿÿ10.11ÿÿÿ0.000ÿÿÿÿÿ.8777891ÿÿÿÿÿ1.29993
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ1.116619ÿÿÿ.1087964ÿÿÿÿ10.26ÿÿÿ0.000ÿÿÿÿÿ.9033822ÿÿÿÿ1.329856
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿÿÿÿÿÿÿÿ0ÿÿ(omitted)
-------------+----------------------------------------------------------------
pidÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿvar(_cons)|ÿÿÿÿ1.07713ÿÿÿ.1022494ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.8942636ÿÿÿÿÿ1.29739
------------------------------------------------------------------------------
LRÿtestÿvs.ÿprobitÿmodel:ÿchibar2(01)ÿ=ÿ1080.19ÿÿÿÿÿÿÿProbÿ>=ÿchibar2ÿ=ÿ0.0000

.ÿmatrixÿdefineÿ`B'ÿ=ÿ`B'ÿ\ÿ(_b[0.grp],ÿ_b[0.grp#c.pr1],ÿ_b[0.grp#c.pr2])

.ÿ//ÿ3
.ÿquietlyÿtabulateÿgrp,ÿgenerate(grp)

.ÿmeprobitÿoutÿibn.grpÿi.grp#c.pr1ÿi.grp#c.pr2,ÿnoconstantÿ||ÿpid:ÿgrp1ÿgrp2,ÿ///
>ÿÿÿÿÿÿÿÿÿnoconstantÿcovariance(independent)ÿnolog

Mixed-effectsÿprobitÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ5,000
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿ500

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ10.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ10

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(6)ÿÿÿÿÿÿ=ÿÿÿÿÿ226.55
Logÿlikelihoodÿ=ÿ-2785.8573ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000
ÿ(ÿ1)ÿÿ[out]_consÿ=ÿ0
------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿgrpÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.0260818ÿÿÿ.0676571ÿÿÿÿÿ0.39ÿÿÿ0.700ÿÿÿÿ-.1065238ÿÿÿÿ.1586873
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ.0486297ÿÿÿ.0786676ÿÿÿÿÿ0.62ÿÿÿ0.536ÿÿÿÿÿ-.105556ÿÿÿÿ.2028154
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿgrp#c.pr1ÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.8699673ÿÿÿ.2369958ÿÿÿÿÿ3.67ÿÿÿ0.000ÿÿÿÿÿ.4054641ÿÿÿÿ1.334471
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿÿ.853779ÿÿÿ.2802631ÿÿÿÿÿ3.05ÿÿÿ0.002ÿÿÿÿÿ.3044735ÿÿÿÿ1.403085
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿgrp#c.pr2ÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ1.073432ÿÿÿÿ.107106ÿÿÿÿ10.02ÿÿÿ0.000ÿÿÿÿÿ.8635081ÿÿÿÿ1.283356
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ1.134964ÿÿÿ.1102606ÿÿÿÿ10.29ÿÿÿ0.000ÿÿÿÿÿ.9188567ÿÿÿÿÿ1.35107
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿÿÿÿÿÿÿÿ0ÿÿ(omitted)
-------------+----------------------------------------------------------------
pidÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿvar(grp1)|ÿÿÿ.9060588ÿÿÿ.1223921ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.6953035ÿÿÿÿ1.180697
ÿÿÿÿvar(grp2)|ÿÿÿ1.269235ÿÿÿ.1701886ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.9759024ÿÿÿÿ1.650736
------------------------------------------------------------------------------
LRÿtestÿvs.ÿprobitÿmodel:ÿchi2(2)ÿ=ÿ1083.34ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0000

Note:ÿLRÿtestÿisÿconservativeÿandÿprovidedÿonlyÿforÿreference.

.ÿmatrixÿdefineÿ`B'ÿ=ÿ`B'ÿ\ÿ(_b[0.grp],ÿ_b[0.grp#c.pr1],ÿ_b[0.grp#c.pr2])

.ÿmatrixÿlistÿ`B',ÿformat(%08.6f)ÿnoheader

ÿÿÿÿÿÿÿÿÿÿc1ÿÿÿÿÿÿÿÿc2ÿÿÿÿÿÿÿÿc3
r1ÿÿ0.026082ÿÿ0.869970ÿÿ1.073432
r2ÿÿ0.028121ÿÿ0.885716ÿÿ1.088860
r3ÿÿ0.026082ÿÿ0.869967ÿÿ1.073432

.ÿ
.ÿgenerateÿdoubleÿxbueÿ=ÿxbuÿ+ÿrnormal()

.ÿ/*ÿ//ÿ4
>ÿregressÿxbueÿc.pr?ÿifÿ!grp
>ÿ//ÿ5
>ÿregressÿxbueÿibn.grpÿi.grp#c.pr1ÿi.grp#c.pr2,ÿnoconstantÿ*/
.ÿ
.ÿ//ÿ6
.ÿmixedÿxbueÿc.pr?ÿifÿ!grpÿ||ÿpid:ÿ,ÿnolrtestÿnolog

Mixed-effectsÿMLÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ2,500
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿ250
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ10.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(2)ÿÿÿÿÿÿ=ÿÿÿÿÿ172.48
Logÿlikelihoodÿ=ÿ-3835.2935ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿxbueÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿpr1ÿ|ÿÿÿ.8136101ÿÿÿ.2243124ÿÿÿÿÿ3.63ÿÿÿ0.000ÿÿÿÿÿ.3739658ÿÿÿÿ1.253254
ÿÿÿÿÿÿÿÿÿpr2ÿ|ÿÿÿ.9106619ÿÿÿ.0720843ÿÿÿÿ12.63ÿÿÿ0.000ÿÿÿÿÿ.7693793ÿÿÿÿ1.051945
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ.0318109ÿÿÿ.0641209ÿÿÿÿÿ0.50ÿÿÿ0.620ÿÿÿÿ-.0938638ÿÿÿÿ.1574857
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿparametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿerr.ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-----------------------------+------------------------------------------------
pid:ÿIdentityÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(_cons)ÿ|ÿÿÿ.9276529ÿÿÿ.0919464ÿÿÿÿÿÿ.7638652ÿÿÿÿÿ1.12656
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(Residual)ÿ|ÿÿÿ.9971148ÿÿÿ.0297285ÿÿÿÿÿÿ.9405177ÿÿÿÿ1.057118
------------------------------------------------------------------------------

.ÿmatrixÿdefineÿ`B'ÿ=ÿ(_b[_cons],ÿ_b[pr1],ÿ_b[pr2])

.ÿ//ÿ7
.ÿmixedÿxbueÿibn.grpÿi.grp#c.pr1ÿi.grp#c.pr2,ÿnoconstantÿ||ÿpid:ÿ,ÿnolrtestÿnolog

Mixed-effectsÿMLÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ5,000
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿ500
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ10.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(6)ÿÿÿÿÿÿ=ÿÿÿÿÿ408.78
Logÿlikelihoodÿ=ÿ-7749.7942ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿxbueÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿgrpÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.0318186ÿÿÿ.0695243ÿÿÿÿÿ0.46ÿÿÿ0.647ÿÿÿÿ-.1044465ÿÿÿÿ.1680836
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ.0587324ÿÿÿ.0696837ÿÿÿÿÿ0.84ÿÿÿ0.399ÿÿÿÿ-.0778451ÿÿÿÿ.1953099
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿgrp#c.pr1ÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.8135965ÿÿÿ.2432151ÿÿÿÿÿ3.35ÿÿÿ0.001ÿÿÿÿÿ.3369036ÿÿÿÿ1.290289
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ.9162256ÿÿÿ.2477042ÿÿÿÿÿ3.70ÿÿÿ0.000ÿÿÿÿÿ.4307343ÿÿÿÿ1.401717
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿgrp#c.pr2ÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿÿ.909239ÿÿÿ.0727646ÿÿÿÿ12.50ÿÿÿ0.000ÿÿÿÿÿ.7666231ÿÿÿÿ1.051855
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿÿÿ1.0763ÿÿÿ.0715522ÿÿÿÿ15.04ÿÿÿ0.000ÿÿÿÿÿ.9360597ÿÿÿÿ1.216539
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿparametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿerr.ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-----------------------------+------------------------------------------------
pid:ÿIdentityÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(_cons)ÿ|ÿÿÿ1.106369ÿÿÿ.0764218ÿÿÿÿÿÿ.9662814ÿÿÿÿ1.266765
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(Residual)ÿ|ÿÿÿ1.014438ÿÿÿ.0213863ÿÿÿÿÿÿ.9733755ÿÿÿÿ1.057232
------------------------------------------------------------------------------

.ÿmatrixÿdefineÿ`B'ÿ=ÿ`B'ÿ\ÿ(_b[0.grp],ÿ_b[0.grp#c.pr1],ÿ_b[0.grp#c.pr2])

.ÿ//ÿ8
.ÿmixedÿxbueÿibn.grpÿi.grp#c.pr1ÿi.grp#c.pr2,ÿnoconstantÿ||ÿpid:ÿgrp1ÿgrp2,ÿ///
>ÿÿÿÿÿÿÿÿÿnoconstantÿcovariance(independent)ÿresiduals(independent,ÿby(grp))ÿ///
>ÿÿÿÿÿÿÿÿÿnolrtestÿnolog

Mixed-effectsÿMLÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ5,000
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿ500
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ10.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(6)ÿÿÿÿÿÿ=ÿÿÿÿÿ408.06
Logÿlikelihoodÿ=ÿ-7746.6449ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿxbueÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿgrpÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.0318109ÿÿÿ.0641209ÿÿÿÿÿ0.50ÿÿÿ0.620ÿÿÿÿ-.0938638ÿÿÿÿ.1574857
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ.0587277ÿÿÿÿ.074707ÿÿÿÿÿ0.79ÿÿÿ0.432ÿÿÿÿ-.0876953ÿÿÿÿ.2051508
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿgrp#c.pr1ÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.8136101ÿÿÿ.2243125ÿÿÿÿÿ3.63ÿÿÿ0.000ÿÿÿÿÿ.3739658ÿÿÿÿ1.253254
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ.9162326ÿÿÿ.2655618ÿÿÿÿÿ3.45ÿÿÿ0.001ÿÿÿÿÿÿ.395741ÿÿÿÿ1.436724
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿgrp#c.pr2ÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ.9106619ÿÿÿ.0720843ÿÿÿÿ12.63ÿÿÿ0.000ÿÿÿÿÿ.7693793ÿÿÿÿ1.051945
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ1.075803ÿÿÿ.0721943ÿÿÿÿ14.90ÿÿÿ0.000ÿÿÿÿÿ.9343043ÿÿÿÿ1.217301
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿparametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿerr.ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-----------------------------+------------------------------------------------
pid:ÿIndependentÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(grp1)ÿ|ÿÿÿÿ.927653ÿÿÿ.0919464ÿÿÿÿÿÿ.7638653ÿÿÿÿÿ1.12656
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(grp2)ÿ|ÿÿÿ1.285065ÿÿÿ.1242076ÿÿÿÿÿÿ1.063291ÿÿÿÿ1.553094
-----------------------------+------------------------------------------------
Residual:ÿIndependent,ÿÿÿÿÿÿÿ|
ÿÿÿÿbyÿgrpÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ0:ÿvar(e)ÿ|ÿÿÿ.9971146ÿÿÿ.0297285ÿÿÿÿÿÿ.9405176ÿÿÿÿ1.057118
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1:ÿvar(e)ÿ|ÿÿÿ1.031763ÿÿÿ.0307613ÿÿÿÿÿÿ.9731996ÿÿÿÿÿ1.09385
------------------------------------------------------------------------------

.ÿmatrixÿdefineÿ`B'ÿ=ÿ`B'ÿ\ÿ(_b[0.grp],ÿ_b[0.grp#c.pr1],ÿ_b[0.grp#c.pr2])

.ÿmatrixÿlistÿ`B',ÿformat(%08.6f)ÿnoheader

ÿÿÿÿÿÿÿÿÿÿc1ÿÿÿÿÿÿÿÿc2ÿÿÿÿÿÿÿÿc3
r1ÿÿ0.031811ÿÿ0.813610ÿÿ0.910662
r2ÿÿ0.031819ÿÿ0.813597ÿÿ0.909239
r3ÿÿ0.031811ÿÿ0.813610ÿÿ0.910662

.ÿ
.ÿexit

endÿofÿdo-file


.

[Øyvind Snilsberg]

Thank you for your reply. I was following the method is post #2 by @Andrew Musau in this thread: https://www.statalist.org/forums/for...for-panel-data. In that thread, doing regression separately across group & using interaction term result in the same coefficeint estimates. So I am not sure why it is not the case with mine, is it because the model is binary/non-linear? Thank you.

If you want to replicate Andrew's method you need to include sector in the regression.
If sector is binary,

xtprobit over2 l.over2 c.l.lnGSCITOTSD##c.l.GSCITOTMG   l.wgdp   l.hgdp   l.infl   l.geopol i.sector if sector==1, re vce(robust) 
xtprobit over2 l.over2 c.l.lnGSCITOTSD##c.l.GSCITOTMG   l.wgdp   l.hgdp   l.infl   l.geopol i.sector if sector==0, re vce(robust) 
xtprobit over2 i.sector#(c.l.over2 c.l.lnGSCITOTSD##c.l.GSCITOTMG c.l.wgdp c.l.hgdp c.l.infl c.l.geopol i.sector), re vce(robust)

If sector is categorical ranging from, say, 1-3,

gen newvar = sector < 3
xtprobit over2 l.over2 c.l.lnGSCITOTSD##c.l.GSCITOTMG   l.wgdp   l.hgdp   l.infl   l.geopol i.sector if newvar==1, re vce(robust) 
xtprobit over2 l.over2 c.l.lnGSCITOTSD##c.l.GSCITOTMG   l.wgdp   l.hgdp   l.infl   l.geopol i.sector if newvar==0, re vce(robust) 
xtprobit over2 i.newvar#(c.l.over2 c.l.lnGSCITOTSD##c.l.GSCITOTMG c.l.wgdp c.l.hgdp c.l.infl c.l.geopol i.sector), re vce(robust)

[Abdan Syakura]

Hi Joseph and Oyvind,

Thank you for your time and suggestion. I am now able to obtain the same estimates between sub-samples and interaction model by using Joseph's method above.


Best regards,