Seemingly Unrelated Poisson Regression with Fixed Effect

[高佳]

Dear All,

As is in the title, I want to conduct a SUR model on Poisson regression with fixed effects.

I've been studying this for a while, but could not find a commonly accepted way to do this.

Any suggestion on whether this is possible at all? If so, where should I start at?

Thanks for your time and knowledge in advance.

[Andrew Musau]

Follow the link in https://www.statalist.org/forums/for...after-ppmlhdfe

[高佳]

Follow the link in https://www.statalist.org/forums/for...after-ppmlhdfe

Hi Andrew, thanks for the reply. I checked the link you posted, but it seems like there is no answer to that question. Also, my question is different from what the OP has.

I'm really new to this stuff, could you please be more specific?

Thank you so much for your time and knowledge.

[Andrew Musau]

Also, my question is different from what the OP has.

Look at the datasets in

help xtpoisson

and then frame your question in terms of a data example.

[高佳]

Look at the datasets in

help xtpoisson

and then frame your question in terms of a data example.

Hi Andrew, thanks for the reply. I checked the dataset in xtpoisson but failed to find a setting (two dependent variables) that can be used to conduct seeminlgy unrelated regression. Any suggestions?

[Andrew Musau]

I checked the dataset in xtpoisson but failed to find a setting (two dependent variables) that can be used to conduct seeminlgy unrelated regression. Any suggestions?

You can generate a second dependent variable using Stata's random number functions. If the wanted dependent variable is a count variable taking values between 1 and 30, e.g.,

set seed 02132023
gen outcome2= runiformint(1, 30)

Then present an example based on this.

[高佳]

webuse ships, clear

set seed 02132023
gen outcome2= runiformint(1, 30)

xtset ship

// poisson regression of the first dependent variable
xtpoisson accident op_75_79 co_65_69 co_70_74 co_75_79, exposure(service) fe

// poisson regression of the second dependent variable
xtpoisson outcome2 op_75_79 co_65_69 co_70_74 co_75_79, exposure(service) fe

Question, how can I estimate an seemingly unrelated regression for the above two xtpoisson regressions?

[Andrew Musau]

Note that ppmlhdfe is from SSC.

webuse ships, clear

set seed 02132023
gen outcome2= runiformint(1, 30)

*poisson regression of the first dependent variable
ppmlhdfe accident op_75_79 co_65_69 co_70_74 co_75_79, absorb(ship) 

*poisson regression of the second dependent variable
ppmlhdfe outcome2 op_75_79 co_65_69 co_70_74 co_75_79, absorb(ship) 

rename (accident outcome2) depvar=
gen long obs=_n
reshape long depvar, i(obs) j(which) string
encode which, gen(Which)
gen ship1= 1.Which#c.ship
gen ship2= 2.Which#c.ship
ppmlhdfe depvar i.Which#(c.op_75_79 c.co_65_69 c.co_70_74 c.co_75_79), absorb(ship1 ship2)

Res.:

.
. ppmlhdfe accident op_75_79 co_65_69 co_70_74 co_75_79, absorb(ship) 
Iteration 1:   deviance = 1.6167e+02  eps = .         iters = 1    tol = 1.0e-04  min(eta) =  -2.14  P  
Iteration 2:   deviance = 1.3971e+02  eps = 1.57e-01  iters = 1    tol = 1.0e-04  min(eta) =  -2.56      
Iteration 3:   deviance = 1.3909e+02  eps = 4.46e-03  iters = 1    tol = 1.0e-04  min(eta) =  -2.69      
Iteration 4:   deviance = 1.3909e+02  eps = 1.15e-05  iters = 1    tol = 1.0e-04  min(eta) =  -2.70      
Iteration 5:   deviance = 1.3909e+02  eps = 2.66e-10  iters = 1    tol = 1.0e-05  min(eta) =  -2.70   S O
------------------------------------------------------------------------------------------------------------
(legend: p: exact partial-out   s: exact solver   h: step-halving   o: epsilon below tolerance)
Converged in 5 iterations and 5 HDFE sub-iterations (tol = 1.0e-08)

HDFE PPML regression                              No. of obs      =         34
Absorbing 1 HDFE group                            Residual df     =         25
                                                  Wald chi2(4)    =       8.14
Deviance             =  139.0852637               Prob > chi2     =     0.0866
Log pseudolikelihood = -118.4758775               Pseudo R2       =     0.6674
------------------------------------------------------------------------------
             |               Robust
    accident |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    op_75_79 |   .2928003   .2736869     1.07   0.285    -.2436162    .8292168
    co_65_69 |   .5824489   .3063304     1.90   0.057    -.0179477    1.182846
    co_70_74 |   .4627844   .3591039     1.29   0.197    -.2410462    1.166615
    co_75_79 |  -.1951267   .3849763    -0.51   0.612    -.9496664     .559413
       _cons |    2.48605   .3500144     7.10   0.000     1.800034    3.172066
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
        ship |         5           0           5     |
-----------------------------------------------------+

.
.
.
. *poisson regression of the second dependent variable

.
. ppmlhdfe outcome2 op_75_79 co_65_69 co_70_74 co_75_79, absorb(ship) 
Iteration 1:   deviance = 1.1280e+02  eps = .         iters = 1    tol = 1.0e-04  min(eta) =   0.23  P  
Iteration 2:   deviance = 1.1229e+02  eps = 4.48e-03  iters = 1    tol = 1.0e-04  min(eta) =   0.19      
Iteration 3:   deviance = 1.1229e+02  eps = 1.12e-06  iters = 1    tol = 1.0e-04  min(eta) =   0.19      
Iteration 4:   deviance = 1.1229e+02  eps = 8.50e-14  iters = 1    tol = 1.0e-05  min(eta) =   0.19      
Iteration 5:   deviance = 1.1229e+02  eps = 1.14e-16  iters = 1    tol = 1.0e-07  min(eta) =   0.19   S O
------------------------------------------------------------------------------------------------------------
(legend: p: exact partial-out   s: exact solver   h: step-halving   o: epsilon below tolerance)
Converged in 5 iterations and 5 HDFE sub-iterations (tol = 1.0e-08)

HDFE PPML regression                              No. of obs      =         40
Absorbing 1 HDFE group                            Residual df     =         31
                                                  Wald chi2(4)    =      10.65
Deviance             =  112.2943475               Prob > chi2     =     0.0308
Log pseudolikelihood = -145.4744978               Pseudo R2       =     0.0997
------------------------------------------------------------------------------
             |               Robust
    outcome2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    op_75_79 |   .0759859    .127497     0.60   0.551    -.1739037    .3258755
    co_65_69 |  -.2307098   .1882286    -1.23   0.220     -.599631    .1382115
    co_70_74 |  -.5483727   .1701134    -3.22   0.001    -.8817889   -.2149565
    co_75_79 |   -.218131   .1553536    -1.40   0.160    -.5226185    .0863565
       _cons |   2.958756   .1406329    21.04   0.000     2.683121    3.234391
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
        ship |         5           0           5     |
-----------------------------------------------------+

.
.


.
. ppmlhdfe depvar i.Which#(c.op_75_79 c.co_65_69 c.co_70_74 c.co_75_79), absorb(ship1 ship2)
Iteration 1:   deviance = 2.7726e+02  eps = .         iters = 2    tol = 1.0e-04  min(eta) =  -1.68  P  
Iteration 2:   deviance = 2.5243e+02  eps = 9.83e-02  iters = 2    tol = 1.0e-04  min(eta) =  -2.22      
Iteration 3:   deviance = 2.5139e+02  eps = 4.17e-03  iters = 2    tol = 1.0e-04  min(eta) =  -2.42      
Iteration 4:   deviance = 2.5138e+02  eps = 2.86e-05  iters = 2    tol = 1.0e-04  min(eta) =  -2.44      
Iteration 5:   deviance = 2.5138e+02  eps = 3.23e-09  iters = 2    tol = 1.0e-05  min(eta) =  -2.44      
Iteration 6:   deviance = 2.5138e+02  eps = 0.00e+00  iters = 1    tol = 1.0e-06  min(eta) =  -2.44   S  
Iteration 7:   deviance = 2.5138e+02  eps = 0.00e+00  iters = 1    tol = 1.0e-09  min(eta) =  -2.44   S O
------------------------------------------------------------------------------------------------------------
(legend: p: exact partial-out   s: exact solver   h: step-halving   o: epsilon below tolerance)
Converged in 7 iterations and 12 HDFE sub-iterations (tol = 1.0e-08)

HDFE PPML regression                              No. of obs      =         74
Absorbing 2 HDFE groups                           Residual df     =         56
                                                  Wald chi2(8)    =      19.04
Deviance             =  251.3796112               Prob > chi2     =     0.0146
Log pseudolikelihood = -263.9503753               Pseudo R2       =     0.5091
----------------------------------------------------------------------------------
                 |               Robust
          depvar |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
Which#c.op_75_79 |
       accident  |   .2928003   .2714732     1.08   0.281    -.2392774     .824878
       outcome2  |   .0759859   .1267526     0.60   0.549    -.1724446    .3244164
                 |
Which#c.co_65_69 |
       accident  |   .5824489   .3038526     1.92   0.055    -.0130912    1.177989
       outcome2  |  -.2307098   .1871295    -1.23   0.218    -.5974769    .1360573
                 |
Which#c.co_70_74 |
       accident  |   .4627844   .3561992     1.30   0.194    -.2353533    1.160922
       outcome2  |  -.5483727   .1691201    -3.24   0.001    -.8798421   -.2169033
                 |
Which#c.co_75_79 |
       accident  |  -.1951267   .3818626    -0.51   0.609    -.9435637    .5533103
       outcome2  |   -.218131   .1544465    -1.41   0.158    -.5208406    .0845786
                 |
           _cons |    2.78843   .1537793    18.13   0.000     2.487028    3.089832
----------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
       ship1 |         6           0           6     |
       ship2 |         6           2           4     |
-----------------------------------------------------+

.

[高佳]

Hi Andrew, thanks so much. Could you please help me to understand how the procedure you presented is a seemingly unrelated regression? I'm new to this material.

[Andrew Musau]

The Stata manual entries of the sureg and suest commands have some good discussions on this topic. See https://www.stata.com/manuals/rsureg.pdf and https://www.stata.com/manuals/rsuest.pdf, respectively.

[高佳]

Thanks. I'll check these and your code above and get back to you soon.

[Matteo Pinna Pintor]

Dear Andrew Musau , do you have moment to recast your example above above to fit the case in which the stacking is requited in order to test for joint significance of one key independent variable across a sequence of models? I'm trying to replicate it but estimates are not the same, so I'm probably making some elementary mistakes there. Many thanks.

[edit]

I'm afraid I might have a collinearity problem. As I need to test the joint significance of not two but six coefficients (from six slightly different discretizations of an underlying continuous treatment variable), I have to stack six models, and while all 6 treatment effects are estimated, some of the interaction terms with the covariates are dropped for collinearity, which I suppose contaminates all other estimates. Any suggestion as how to best proceed in this case? I'm also using ppmlhdfe, with a substantial number of fixed effects to absorb, and not much time to devote to this problem, so that using suest or changing command are not really feasible options.

[Matteo Pinna Pintor]

Ok, perhaps solved as far as the practical purpose of replicating results is concerned - I must have made some fvar notation mistakes. Now reported estimates are identical. However, a strange behavior persists. Somehow the stacked regression fails to exclude base categories for my categorical covariates, and instead proceeds to omit coefficients for the highest-valued categories for collinearity. It also happens if I explicitly specify the base level using

ib0.sex#i.Stack

(where Stack is the stacking variable). I guess it has to do with this issue.

[Andrew Musau]

It is problematic for factor variables to specify a 'base' for interactions without the corresponding main effects. This issue has been discussed here: https://www.statalist.org/forums/for...nuous-variable. A workaround is to use the omission operator to omit the relevant interaction term. Using the example from your linked thread, compare:

use http://www.stata-press.com/data/r15/nlswork, clear
bys idcode: egen any_union = max(union)
replace any_union = 0 if missing(any_union)
* Reduce number of unique idcodes so areg can actually run
keep if idcode <= 100

areg ln_wage i.idcode ib68.year#c.any_union, a(year) noomitted
areg ln_wage i.idcode i.year#c.any_union o68.year#o.any_union , a(year) noomitted

Res.:

. areg ln_wage i.idcode ib68.year#c.any_union, a(year) noomitted
note: 88.year#c.any_union omitted because of collinearity.

Linear regression, absorbing indicators             Number of obs     =    578
Absorbed variable: year                             No. of categories =     15
                                                    F(103, 460)       =   9.63
                                                    Prob > F          = 0.0000
                                                    R-squared         = 0.7160
                                                    Adj R-squared     = 0.6438
                                                    Root MSE          = 0.2677

----------------------------------------------------------------------------------
         ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
          idcode |
              2  |  -.3700416    .109583    -3.38   0.001     -.585387   -.1546961
              3  |  -.5378929   .1338261    -4.02   0.000    -.8008791   -.2749066
              4  |  -.0406853   .1122069    -0.36   0.717    -.2611869    .1798164
              5  |   -.251427   .1433988    -1.75   0.080    -.5332248    .0303708
              6  |  -.2122527   .1041979    -2.04   0.042    -.4170155   -.0074899
              7  |  -.7857883   .1480545    -5.31   0.000    -1.076735   -.4948412
              9  |   .0222342   .1073136     0.21   0.836    -.1886514    .2331197
             10  |  -.7786264   .1485312    -5.24   0.000     -1.07051   -.4867427
             12  |   .6357693   .2162199     2.94   0.003     .2108681    1.060671
             13  |   .1835459   .1121797     1.64   0.102    -.0369022     .403994
             14  |  -.1919685   .2162199    -0.89   0.375    -.6168697    .2329327
             15  |   .3399096   .1233621     2.76   0.006     .0974866    .5823327
             16  |    .007062   .1361566     0.05   0.959    -.2605041    .2746281
             17  |     .03596   .1609364     0.22   0.823    -.2803017    .3522218
             18  |  -.6834794   .1731004    -3.95   0.000    -1.023645   -.3433138
             19  |  -.0525687   .1095709    -0.48   0.632    -.2678902    .1627528
             20  |   .0452353   .1073136     0.42   0.674    -.1656503    .2561208
             21  |  -.2659091   .1691299    -1.57   0.117    -.5982721    .0664538
             22  |   .0130551   .1363353     0.10   0.924    -.2548621    .2809723
             23  |  -.2644427   .1564131    -1.69   0.092    -.5718155    .0429301
             24  |   .0290883   .1041979     0.28   0.780    -.1756745    .2338511
             25  |   .0095992   .1362608     0.07   0.944    -.2581717      .27737
             26  |  -.2298446    .161151    -1.43   0.154     -.546528    .0868389
             27  |  -.0255112   .1811877    -0.14   0.888    -.3815694     .330547
             29  |  -.2578997   .1807832    -1.43   0.154    -.6131629    .0973636
             30  |  -.5022057   .1286937    -3.90   0.000    -.7551061   -.2493054
             33  |  -.4472461   .2998662    -1.49   0.137    -1.036523    .1420312
             35  |  -1.009763   .2988907    -3.38   0.001    -1.597123   -.4224026
             36  |  -.1828299   .1229328    -1.49   0.138    -.4244094    .0587496
             37  |  -.7279486   .1979115    -3.68   0.000    -1.116871   -.3390258
             38  |  -.5092014   .1568003    -3.25   0.001    -.8173351   -.2010677
             39  |   .1209112    .163291     0.74   0.459    -.1999776    .4418001
             40  |     -.4278   .2974751    -1.44   0.151    -1.012379    .1567785
             41  |  -.4659988   .1523977    -3.06   0.002    -.7654807   -.1665169
             43  |  -.3938707   .2271041    -1.73   0.084    -.8401608    .0524194
             44  |   .7924911   .1287705     6.15   0.000     .5394396    1.045543
             45  |   .0768195   .1122114     0.68   0.494    -.1436909    .2973299
             46  |  -1.036681   .2162199    -4.79   0.000    -1.461582   -.6117799
             47  |  -.8106589   .2162199    -3.75   0.000     -1.23556   -.3857577
             48  |   -.683635   .1891362    -3.61   0.000    -1.055313    -.311957
             49  |  -.4115353   .1620469    -2.54   0.011    -.7299793   -.0930913
             50  |   .3465596    .189952     1.82   0.069    -.0267216    .7198408
             51  |  -.7558032   .1524402    -4.96   0.000    -1.055369   -.4562377
             53  |  -.7471401   .1618003    -4.62   0.000    -1.065099   -.4291807
             54  |  -.7229533   .2846661    -2.54   0.011    -1.282361   -.1635461
             55  |  -.4989077   .1525549    -3.27   0.001    -.7986985   -.1991169
             56  |   .1871993   .1806712     1.04   0.301    -.1678439    .5422425
             57  |  -.7015344    .139742    -5.02   0.000    -.9761462   -.4269227
             58  |  -.1638478    .176584    -0.93   0.354    -.5108591    .1831635
             59  |  -.7608437   .1616794    -4.71   0.000    -1.078565   -.4431219
             60  |  -.5382108   .1696545    -3.17   0.002    -.8716047   -.2048168
             61  |  -.7623903   .1696949    -4.49   0.000    -1.095864    -.428917
             62  |  -.7835276   .1442491    -5.43   0.000    -1.066997   -.5000587
             63  |   .5175648   .1128684     4.59   0.000     .2957632    .7393664
             64  |  -.4680247   .1359682    -3.44   0.001    -.7352205   -.2008288
             65  |   .2934283   .1298615     2.26   0.024      .038233    .5486235
             66  |  -.6485326   .1161549    -5.58   0.000    -.8767927   -.4202725
             67  |    .024605   .1515661     0.16   0.871    -.2732428    .3224527
             68  |  -.0674516   .1812773    -0.37   0.710    -.4236858    .2887826
             69  |  -.5045478   .1566088    -3.22   0.001    -.8123051   -.1967905
             70  |   .4834114   .2162199     2.24   0.026     .0585101    .9083126
             71  |   -.624879   .1440632    -4.34   0.000    -.9079826   -.3417754
             72  |  -.4698405   .1229463    -3.82   0.000    -.7114465   -.2282344
             73  |   -.309495   .1394909    -2.22   0.027    -.5836134   -.0353766
             75  |  -.0388518   .1060218    -0.37   0.714    -.2471988    .1694953
             76  |  -.3555371   .2998957    -1.19   0.236    -.9448725    .2337983
             77  |  -.7232812   .1806165    -4.00   0.000    -1.078217   -.3683454
             78  |   .2397953   .1099522     2.18   0.030     .0237244    .4558662
             79  |  -.5189018   .2998662    -1.73   0.084    -1.108179    .0703755
             80  |   .0633665   .1887347     0.34   0.737    -.3075225    .4342556
             81  |   -.780879   .2090741    -3.73   0.000    -1.191738   -.3700203
             82  |   .2654059   .1453692     1.83   0.069    -.0202642    .5510759
             83  |  -.4322357   .1551492    -2.79   0.006    -.7371247   -.1273468
             84  |  -.0311991   .2998662    -0.10   0.917    -.6204764    .5580783
             85  |   -.173676   .1729535    -1.00   0.316    -.5135528    .1662009
             86  |   .1510527   .1080122     1.40   0.163    -.0612057    .3633111
             87  |   .1865182    .226173     0.82   0.410    -.2579422    .6309785
             88  |   -.269514   .2283172    -1.18   0.238    -.7181881      .17916
             89  |    .202736    .226173     0.90   0.371    -.2417244    .6471963
             91  |   .1610576   .2283172     0.71   0.481    -.2876164    .6097317
             92  |  -.1645888   .2850205    -0.58   0.564    -.7246925    .3955148
             93  |  -.1890283   .2983347    -0.63   0.527     -.775296    .3972395
             94  |  -.6225067   .1229725    -5.06   0.000    -.8641643   -.3808492
             95  |  -.8092458    .169853    -4.76   0.000     -1.14303   -.4754618
             96  |  -.3884847   .2271702    -1.71   0.088    -.8349047    .0579353
             97  |  -.3313162   .1776281    -1.87   0.063    -.6803794    .0177469
             98  |  -.0827248   .1242979    -0.67   0.506    -.3269868    .1615373
             99  |  -.2651777    .169946    -1.56   0.119    -.5991444    .0687891
            100  |   .0715955   .1981293     0.36   0.718    -.3177552    .4609462
                 |
year#c.any_union |
             68  |  -.3262181    .143902    -2.27   0.024    -.6090049   -.0434312
             69  |  -.2765695    .141243    -1.96   0.051    -.5541309    .0009919
             70  |  -.2521625   .1226235    -2.06   0.040    -.4931342   -.0111907
             71  |  -.3653427   .1229402    -2.97   0.003    -.6069367   -.1237487
             72  |  -.3290641   .1246493    -2.64   0.009    -.5740166   -.0841115
             73  |  -.2549638   .1242343    -2.05   0.041    -.4991009   -.0108267
             75  |  -.0469036    .124001    -0.38   0.705    -.2905822     .196775
             77  |  -.0034648   .1246678    -0.03   0.978    -.2484537    .2415241
             78  |  -.0916416   .1355933    -0.68   0.499    -.3581006    .1748173
             80  |  -.0130233   .1354706    -0.10   0.923    -.2792413    .2531946
             82  |   -.088694   .1278745    -0.69   0.488    -.3399845    .1625966
             83  |   .0944071   .1285028     0.73   0.463    -.1581181    .3469324
             85  |   .1516057   .1273315     1.19   0.234    -.0986178    .4018292
             87  |  -.0011315   .1154813    -0.01   0.992    -.2280677    .2258047
                 |
           _cons |   2.129733   .1141763    18.65   0.000     1.905362    2.354105
----------------------------------------------------------------------------------
F test of absorbed indicators: F(14, 460) = 1.537             Prob > F = 0.094

.
. areg ln_wage i.idcode i.year#c.any_union o68.year#o.any_union , a(year) noomitted

Linear regression, absorbing indicators             Number of obs     =    578
Absorbed variable: year                             No. of categories =     15
                                                    F(103, 460)       =   9.63
                                                    Prob > F          = 0.0000
                                                    R-squared         = 0.7160
                                                    Adj R-squared     = 0.6438
                                                    Root MSE          = 0.2677

----------------------------------------------------------------------------------
         ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
          idcode |
              2  |  -.3700416    .109583    -3.38   0.001     -.585387   -.1546961
              3  |  -.2116748   .1521673    -1.39   0.165     -.510704    .0873544
              4  |  -.0406853   .1122069    -0.36   0.717    -.2611869    .1798164
              5  |   .0747911   .1571062     0.48   0.634    -.2339438    .3835259
              6  |  -.2122527   .1041979    -2.04   0.042    -.4170155   -.0074899
              7  |  -.4595702    .164011    -2.80   0.005     -.781874   -.1372665
              9  |   .0222342   .1073136     0.21   0.836    -.1886514    .2331197
             10  |  -.4524084   .1642162    -2.75   0.006    -.7751154   -.1297014
             12  |   .9619874   .2393679     4.02   0.000     .4915973    1.432377
             13  |   .1835459   .1121797     1.64   0.102    -.0369022     .403994
             14  |   .1342495   .2393679     0.56   0.575    -.3361405    .6046396
             15  |   .3399096   .1233621     2.76   0.006     .0974866    .5823327
             16  |   .3332801   .1569116     2.12   0.034     .0249277    .6416325
             17  |   .3621781   .1766203     2.05   0.041     .0150954    .7092608
             18  |  -.3572614   .1954827    -1.83   0.068    -.7414112    .0268884
             19  |  -.0525687   .1095709    -0.48   0.632    -.2678902    .1627528
             20  |   .0452353   .1073136     0.42   0.674    -.1656503    .2561208
             21  |   .0603089    .183961     0.33   0.743    -.3011992    .4218171
             22  |   .3392731   .1565301     2.17   0.031     .0316705    .6468757
             23  |   .0617753   .1776744     0.35   0.728    -.2873788    .4109294
             24  |   .0290883   .1041979     0.28   0.780    -.1756745    .2338511
             25  |   .3358172   .1544281     2.17   0.030     .0323453    .6392892
             26  |   .0963735   .1720149     0.56   0.576     -.241659    .4344059
             27  |   .3007068   .1871037     1.61   0.109    -.0669771    .6683907
             29  |   .0683184   .1925569     0.35   0.723    -.3100817    .4467185
             30  |  -.5022057   .1286937    -3.90   0.000    -.7551061   -.2493054
             33  |  -.1210281   .2932195    -0.41   0.680    -.6972438    .4551877
             35  |  -.6835449   .3079363    -2.22   0.027    -1.288681   -.0784087
             36  |  -.1828299   .1229328    -1.49   0.138    -.4244094    .0587496
             37  |  -.4017305   .2014887    -1.99   0.047    -.7976829   -.0057782
             38  |  -.1829833   .1673512    -1.09   0.275    -.5118509    .1458843
             39  |   .4471293   .1855695     2.41   0.016     .0824603    .8117983
             40  |  -.1015819   .3048287    -0.33   0.739    -.7006113    .4974474
             41  |  -.1397807   .1638767    -0.85   0.394    -.4618205    .1822591
             43  |  -.0676527   .2402415    -0.28   0.778    -.5397595    .4044542
             44  |   .7924911   .1287705     6.15   0.000     .5394396    1.045543
             45  |   .0768195   .1122114     0.68   0.494    -.1436909    .2973299
             46  |   -.710463   .2393679    -2.97   0.003    -1.180853   -.2400729
             47  |  -.4844409   .2393679    -2.02   0.044    -.9548309   -.0140508
             48  |  -.3574169   .2114911    -1.69   0.092    -.7730254    .0581915
             49  |  -.0853172   .1719967    -0.50   0.620    -.4233139    .2526794
             50  |   .6727777   .2116227     3.18   0.002     .2569106    1.088645
             51  |  -.4295851   .1715977    -2.50   0.013    -.7667976   -.0923726
             53  |   -.420922   .1775024    -2.37   0.018    -.7697381   -.0721059
             54  |  -.3967353   .3079977    -1.29   0.198    -1.001992    .2085217
             55  |  -.1726896   .1638842    -1.05   0.293     -.494744    .1493648
             56  |   .5134173   .1887339     2.72   0.007     .1425299    .8843048
             57  |  -.3753163   .1576438    -2.38   0.018    -.6851077    -.065525
             58  |  -.1638478    .176584    -0.93   0.354    -.5108591    .1831635
             59  |  -.4346256   .1733103    -2.51   0.012    -.7752036   -.0940476
             60  |  -.2119927   .1834786    -1.16   0.249    -.5725528    .1485675
             61  |  -.4361722   .1837062    -2.37   0.018    -.7971797   -.0751648
             62  |  -.4573096   .1615363    -2.83   0.005    -.7747502   -.1398689
             63  |   .5175648   .1128684     4.59   0.000     .2957632    .7393664
             64  |  -.4680247   .1359682    -3.44   0.001    -.7352205   -.2008288
             65  |   .2934283   .1298615     2.26   0.024      .038233    .5486235
             66  |  -.6485326   .1161549    -5.58   0.000    -.8767927   -.4202725
             67  |    .350823   .1717137     2.04   0.042     .0133826    .6882635
             68  |   .2587665   .1873553     1.38   0.168    -.1094118    .6269448
             69  |  -.1783297   .1709931    -1.04   0.298    -.5143541    .1576947
             70  |   .8096294   .2393679     3.38   0.001     .3392394    1.280019
             71  |  -.2986609   .1656061    -1.80   0.072    -.6240991    .0267773
             72  |  -.4698405   .1229463    -3.82   0.000    -.7114465   -.2282344
             73  |    .016723   .1606808     0.10   0.917    -.2990364    .3324825
             75  |  -.0388518   .1060218    -0.37   0.714    -.2471988    .1694953
             76  |  -.0293191   .3106111    -0.09   0.925    -.6397117    .5810736
             77  |  -.3970632   .1945726    -2.04   0.042    -.7794245   -.0147018
             78  |   .2397953   .1099522     2.18   0.030     .0237244    .4558662
             79  |  -.1926837   .2932195    -0.66   0.511    -.7688995    .3835321
             80  |   .3895846   .2117357     1.84   0.066    -.0265045    .8056737
             81  |   -.780879   .2090741    -3.73   0.000    -1.191738   -.3700203
             82  |   .2654059   .1453692     1.83   0.069    -.0202642    .5510759
             83  |  -.1060177   .1724445    -0.61   0.539    -.4448943    .2328589
             84  |    .295019   .2932195     1.01   0.315    -.2811967    .8712348
             85  |   .1525421   .1949125     0.78   0.434    -.2304871    .5355713
             86  |   .1510527   .1080122     1.40   0.163    -.0612057    .3633111
             87  |   .5127362   .2360251     2.17   0.030     .0489151    .9765573
             88  |    .056704   .2278876     0.25   0.804    -.3911257    .5045338
             89  |    .528954   .2360251     2.24   0.025      .065133    .9927751
             91  |   .4872757   .2278876     2.14   0.033     .0394459    .9351055
             92  |  -.1645888   .2850205    -0.58   0.564    -.7246925    .3955148
             93  |   .1371898   .3071951     0.45   0.655    -.4664898    .7408694
             94  |  -.6225067   .1229725    -5.06   0.000    -.8641643   -.3808492
             95  |  -.4830277     .17858    -2.70   0.007    -.8339615    -.132094
             96  |  -.0622666   .2363236    -0.26   0.792    -.5266742    .4021409
             97  |  -.3313162   .1776281    -1.87   0.063    -.6803794    .0177469
             98  |  -.0827248   .1242979    -0.67   0.506    -.3269868    .1615373
             99  |   .0610404   .1830848     0.33   0.739    -.2987458    .4208266
            100  |   .3978135   .2014967     1.97   0.049     .0018455    .7937816
                 |
year#c.any_union |
             69  |   .0496486   .1487627     0.33   0.739    -.2426902    .3419873
             70  |   .0740556   .1368997     0.54   0.589    -.1949707    .3430819
             71  |  -.0391246   .1367974    -0.29   0.775    -.3079498    .2297006
             72  |   -.002846   .1406131    -0.02   0.984    -.2791696    .2734776
             73  |   .0712543   .1403962     0.51   0.612    -.2046432    .3471518
             75  |   .2793145   .1391808     2.01   0.045     .0058056    .5528233
             77  |   .3227533   .1423174     2.27   0.024     .0430804    .6024261
             78  |   .2345764   .1521309     1.54   0.124    -.0643813    .5335342
             80  |   .3131947   .1541035     2.03   0.043     .0103605    .6160289
             82  |   .2375241   .1465622     1.62   0.106    -.0504903    .5255385
             83  |   .4206252   .1480166     2.84   0.005     .1297526    .7114978
             85  |   .4778237   .1486281     3.21   0.001     .1857496    .7698978
             87  |   .3250866   .1423488     2.28   0.023     .0453522     .604821
             88  |   .3262181    .143902     2.27   0.024     .0434312    .6090049
                 |
           _cons |   1.803515   .1358473    13.28   0.000     1.536557    2.070473
----------------------------------------------------------------------------------
F test of absorbed indicators: F(14, 460) = 1.537             Prob > F = 0.094

[Matteo Pinna Pintor]

Yes Andrew Musau, I did try that shortly after. I have to exclude many categories because most of my covariates are discrete, and I couldn't find a compact way of doing e.g. it using parentheses. For the model id variable stack, continuous age (and treatment variable, omitted here) and categorical covariates sex education ghs and METclass, the code that works for me is the longish

i.stack#c.age##c.age i.stack#i.sex o1.stack#o0.sex o2.stack#o0.sex o3.stack#o0.sex o4.stack#o0.sex o5.stack#o0.sex o6.stack#o0.sex i.stack#i.education o1.stack#o0.education o2.stack#o0.education o3.stack#o0.education o4.stack#o0.education o5.stack#o0.education o6.stack#o0.education i.stack#i.ghs o1.stack#o1.ghs o2.stack#o1.ghs o3.stack#o1.ghs o4.stack#o1.ghs o5.stack#o1.ghs o6.stack#o1.ghs i.stack#i.METclass o1.stack#o1.METclass o2.stack#o1.METclass o3.stack#o1.METclass o4.stack#o1.METclass o5.stack#o1.METclass o6.stack#o1.METclass

I tried to find something better, but fvexpand always showed me it didn't work. Any suggestion as how to further summarize this?

Moreover, alas, now that I enforce these base levels the model runs into sparsity problems ("warning: variance matrix is nonsymmetric or highly singular."). Given that I'm actually interested in testing hypotheses concerning the treatment variable only, which is continuous and correctly estimated irrespectively of the base levels of the covariates, I'm tempted to give up on this problem.