GEE: results significant only with independent and exchangeable correlation structure

Hello there!

I am trying to fit a GEE Poisson model on a panel dataset consisting of T=360 and N=304 for a total of >108,000 observations in Stata. My response variable measures a count of people imprisoned, and I am interested in the effect of three dummy variables compared to a baseline scenario (which are originally a factor variable called "intervention2". I am new to this class of models so pardon me if the questions sounds dumb. To exemplify, the syntax used is the following:

Code:

  
 xtgee o1 o5a o6a i.intervention2 i.decade, family(poisson) link(log) corr(exchangeable)

where o5a and o6a are two control variables measuring a continuous value and i.decade is a factor variable controlling for potential temporal effects. My question is the following: I am achieving significant results only when using an exchangeable or independent correlation structure, while when choosing other (as stationary or AR(k)), results for my variables of interest suddenly became largely non significant. Even when I use robust standard errors through the vce(robust) option either results for i.policy are non significant or the model does not achieve convergence. Is there anyone that can help me in understanding why this is happening? Should I assume that the fact the results are significant in the exchangeable scenario mean that the models is correctly estimated and non-biased? Thank you very much in advance for your help!

I attach below some output examples

# EXAMPLE 1: EXCHANGEABLE STRUCTURE

Code:

. xtgee o1 o5a o6a i.intervention2 i.decade, family(poisson) link(log) corr(exchangeable)

Iteration 1: tolerance = .84106964
Iteration 2: tolerance = .48496633
Iteration 3: tolerance = .20312782
Iteration 4: tolerance = .10553827
Iteration 5: tolerance = .03057151
Iteration 6: tolerance = .00465901
Iteration 7: tolerance = .00267481
Iteration 8: tolerance = .00115663
Iteration 9: tolerance = .00024735
Iteration 10: tolerance = .00007535
Iteration 11: tolerance = .00005332
Iteration 12: tolerance = .00001348
Iteration 13: tolerance = 3.161e-06
Iteration 14: tolerance = 2.087e-06
Iteration 15: tolerance = 7.841e-07

GEE population-averaged model                   Number of obs     =    108,000
Group variable:                     run_id      Number of groups  =        300
Link:                                  log      Obs per group:
Family:                            Poisson                    min =        360
Correlation:                  exchangeable                    avg =      360.0
                                                              max =        360
                                                Wald chi2(8)      =   17508.34
Scale parameter:                         1      Prob > chi2       =     0.0000

-------------------------------------------------------------------------------
           o1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
          o5a |   2.334807   .0620962    37.60   0.000       2.2131    2.456513
          o6a |   1.631073    .014881   109.61   0.000     1.601907    1.660239
              |
intervention2 |
  disruptive  |  -1.785197   .0360908   -49.46   0.000    -1.855933    -1.71446
facilitators  |   .0015218    .021609     0.07   0.944     -.040831    .0438746
  preventive  |  -.5608344   .0251605   -22.29   0.000     -.610148   -.5115207
    students  |   .4755749   .0203458    23.37   0.000     .4356979    .5154519
              |
       decade |
           2  |  -.0094256   .0009321   -10.11   0.000    -.0112525   -.0075987
           3  |  -.1130466    .001251   -90.36   0.000    -.1154986   -.1105946
              |
        _cons |   2.324379   .0234435    99.15   0.000      2.27843    2.370327
-------------------------------------------------------------------------------

# EXAMPLE 2: INDEPENDENT STRUCTURE

Code:

 xtgee o1 o5a o6a i.intervention2 i.decade, family(poisson) link(log) corr(independent)

Iteration 1: tolerance = 1.627e-11

GEE population-averaged model                   Number of obs     =    108,000
Group variable:                     run_id      Number of groups  =        300
Link:                                  log      Obs per group:
Family:                            Poisson                    min =        360
Correlation:                   independent                    avg =      360.0
                                                              max =        360
                                                Wald chi2(8)      =    4733.11
Scale parameter:                         1      Prob > chi2       =     0.0000

Pearson chi2(108000):            183882.66      Deviance          =  173787.77
Dispersion (Pearson):             1.702617      Dispersion        =   1.609146

-------------------------------------------------------------------------------
           o1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
          o5a |   4.589151   .1899733    24.16   0.000      4.21681    4.961491
          o6a |   .5389832    .018326    29.41   0.000     .5030649    .5749016
              |
intervention2 |
  disruptive  |  -.0873664    .003151   -27.73   0.000    -.0935423   -.0811906
facilitators  |  -.0306047   .0031123    -9.83   0.000    -.0367047   -.0245047
  preventive  |  -.0515957   .0031221   -16.53   0.000    -.0577149   -.0454766
    students  |  -.0169098   .0031137    -5.43   0.000    -.0230125   -.0108072
              |
       decade |
           2  |  -.0044688   .0030841    -1.45   0.147    -.0105135     .001576
           3  |  -.1194673   .0030201   -39.56   0.000    -.1253864   -.1135481
              |
        _cons |   1.747254   .0201088    86.89   0.000     1.707842    1.786667
-------------------------------------------------------------------------------

# EXAMPLE 3: AR(1) STRUCTURE

Code:

xtgee o1 o5a o6a i.intervention2 i.decade, family(poisson) link(log) corr(ar1)

Iteration 1: tolerance = .59377955
Iteration 2: tolerance = .02410303
Iteration 3: tolerance = .00982333
Iteration 4: tolerance = .00135473
Iteration 5: tolerance = .00015177
Iteration 6: tolerance = .00001665
Iteration 7: tolerance = 1.781e-06
Iteration 8: tolerance = 1.900e-07

GEE population-averaged model Number of obs = 108,300
Group and time vars: run_id step Number of groups = 300
Link: log Obs per group:
Family: Poisson min = 361
Correlation: AR(1) avg = 361.0
max = 361
Wald chi2(8) = 420.30
Scale parameter: 1 Prob > chi2 = 0.0000

-------------------------------------------------------------------------------
o1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
o5a | 1.318071 .1008281 13.07 0.000 1.120452 1.51569
o6a | .2987947 .0203005 14.72 0.000 .2590064 .338583
|
intervention2 |
disruptive | -.1787983 .046164 -3.87 0.000 -.2692781 -.0883185
facilitators | -.0823756 .0451025 -1.83 0.068 -.1707749 .0060236
preventive | -.0417277 .0445182 -0.94 0.349 -.1289818 .0455264
students | -.0016382 .0441991 -0.04 0.970 -.0882669 .0849905
|
decade |
2 | -.0014564 .0017892 -0.81 0.416 -.0049632 .0020504
3 | -.0035202 .0025268 -1.39 0.164 -.0084726 .0014323
|
_cons | 2.077726 .0336093 61.82 0.000 2.011853 2.143599
-------------------------------------------------------------------------------