test 2

[Sebastian Witteler]

I examine the number of co-publications of the last 31 years by six countries that are member of a regional organization. I'm particularly interested in similarities and differences of the countries' co-authorship patterns, especially in those variables that reflect the relation to co-authors' countries such as the trade volume or the geographical distance. For this purpose, I've decided to apply a population-averaged negative binomial model

xtnbreg, pa difficult vce(robust)

following the field-specific literature's recommendation for the case of overdispersed data.

I'm currently, however, at an impasse because including any of these "pair variables" (or virtual proximity variables) results in

no convergence

.

Now this issue is certainly not new and I have found helpful explanations and advice in previous forum threads [1,2,3,4,5] - but I'm not sure if I understand all of it properly and I'm a bit uncertain about which of them apply to my specific case. I have summarized potential issues, their recommended remedies and what I've tried so far to give you a better overview on my current understanding. Please indicate if you see something that I got wrong.

1. It may be the case that there is high collinearity between independent variables [5]. Some year dummies at the end of the time period are dropped due to collinearity but checking correlations with

pwcorr

shows relatively weak correlations between pair variables (<0.4) while they are higher between those variables that reflect the domestic dimension (where convergence is achieved).

no convergence

is also an issue if I exclude the year dummies so I don't think this should be an issue.

2. There is the possibility that the maximum likelihood estimator for my model "does not exist" for my data [1]. This seems to be a possible option as my data has indeed a large number of 0 values in the dependent variable and the "pair" independent variables. A potential remedy would be to start with a poisson regression and plugin the estimates into the negative binomial regression [2]. I wasn't sure what model I should use so I've just run a population-averaged poisson regression

xtpoisson, pa

but it results in

no convergence

as well. I assume using these estimates probably won't help neither, right?

3. In case of using an interaction, the model including the interaction may not be identified by the data [4]. I'm not using interactions so that specific issue should not apply here.

4. My model is insufficient and I should try something different.

I've tried to use -difficult- option to change the steps during the iteration [4], however, to no avail. I have tried to use

xtpoisson, r fe

as a fall back option [3] but with the same result. What I haven't thoroughly tried so far is to use another maximization technique as I lack proper understanding of the particularities of the different techniques.

I should mention that I have isues with an empty Wald chi² statistic that I attribute to a scaling problem as I was able to fix it by re-scaling the problematic pair variables.

Do you have some recommendations on possible next steps?

I've attached an example of the regression and copied the output below for better

. xtnbreg collab_weight rtot_trade gdp_pc tertenrol_epol trade_percgdp mobcell100 colotrad langcom i.year, pa difficult vce(robust)
note: 2015.year omitted because of collinearity
note: 2016.year omitted because of collinearity
note: 2017.year omitted because of collinearity
note: 2018.year omitted because of collinearity

Iteration 1: tolerance = .31055186
Iteration 2: tolerance = .07928357
Iteration 3: tolerance = .08383659
Iteration 4: tolerance = .04340788
Iteration 5: tolerance = .22333106
Iteration 6: tolerance = .20362621
Iteration 7: tolerance = .52943928
Iteration 8: tolerance = .75065012
Iteration 9: tolerance = .08511348
Iteration 10: tolerance = .10210511
Iteration 11: tolerance = .06861638
Iteration 12: tolerance = .04175124
Iteration 13: tolerance = .57174736
Iteration 14: tolerance = .83240469
Iteration 15: tolerance = .13318422
Iteration 16: tolerance = .07155872
Iteration 17: tolerance = .07823117
Iteration 18: tolerance = .07148965
Iteration 19: tolerance = .03836049
Iteration 20: tolerance = .5207436
Iteration 21: tolerance = .77286907
Iteration 22: tolerance = .08953199
Iteration 23: tolerance = .09903163
Iteration 24: tolerance = .07404575
Iteration 25: tolerance = .03569057
Iteration 26: tolerance = .37159328
Iteration 27: tolerance = .54720453
Iteration 28: tolerance = .14373912
Iteration 29: tolerance = .03682585
Iteration 30: tolerance = .38592322
Iteration 31: tolerance = .57121807
Iteration 32: tolerance = .14028013
Iteration 33: tolerance = .04100945
Iteration 34: tolerance = .22680789
Iteration 35: tolerance = .25970474
Iteration 36: tolerance = .09572691
Iteration 37: tolerance = .11652831
Iteration 38: tolerance = .66254531
Iteration 39: tolerance = .77250927
Iteration 40: tolerance = .25295589
Iteration 41: tolerance = .05215284
Iteration 42: tolerance = .04514844
Iteration 43: tolerance = .0596035
Iteration 44: tolerance = .07818158
Iteration 45: tolerance = .07041597
Iteration 46: tolerance = .03923707
Iteration 47: tolerance = .55936823
Iteration 48: tolerance = .81969253
Iteration 49: tolerance = .12112588
Iteration 50: tolerance = .07921637
Iteration 51: tolerance = .08010801
Iteration 52: tolerance = .06113941
Iteration 53: tolerance = .08624978
Iteration 54: tolerance = .63494462
Iteration 55: tolerance = .85733655
Iteration 56: tolerance = .21802994
Iteration 57: tolerance = .04431795
Iteration 58: tolerance = .05111883
Iteration 59: tolerance = .07124833
Iteration 60: tolerance = .07989025
Iteration 61: tolerance = .04704872
Iteration 62: tolerance = .2078943
Iteration 63: tolerance = .13467526
Iteration 64: tolerance = .82616843
Iteration 65: tolerance = .57358112
Iteration 66: tolerance = .31724385
Iteration 67: tolerance = .39922756
Iteration 68: tolerance = .18022887
Iteration 69: tolerance = .10210485
Iteration 70: tolerance = .07338091
Iteration 71: tolerance = .06084837
Iteration 72: tolerance = .05441135
Iteration 73: tolerance = .05120285
Iteration 74: tolerance = .07191157
Iteration 75: tolerance = .07959718
Iteration 76: tolerance = .0462729
Iteration 77: tolerance = .21305515
Iteration 78: tolerance = .15071179
Iteration 79: tolerance = .89146622
Iteration 80: tolerance = .6153406
Iteration 81: tolerance = .19964479
Iteration 82: tolerance = .05179655
Iteration 83: tolerance = .32744225
Iteration 84: tolerance = .55548529
Iteration 85: tolerance = .30313567
Iteration 86: tolerance = .12112433
Iteration 87: tolerance = .07585909
Iteration 88: tolerance = .06068375
Iteration 89: tolerance = .05399522
Iteration 90: tolerance = .05320866
Iteration 91: tolerance = .07358059
Iteration 92: tolerance = .07842722
Iteration 93: tolerance = .04223677
Iteration 94: tolerance = .22502611
Iteration 95: tolerance = .23854644
Iteration 96: tolerance = .19215449
Iteration 97: tolerance = .23957639
Iteration 98: tolerance = .20948912
Iteration 99: tolerance = .26024878
Iteration 100: tolerance = .10269846

GEE population-averaged model                                                       Number of obs        =       3,161
Group variable:                                            target                             Number of groups  =          109

Link:                                                                 log                                  Obs per group:

Family:                              negative binomial(k=1)                                   min =         29
Correlation:                                     exchangeable                                  avg =       29.0
                                                                                                               max =          29

                                                                                       Wald chi2(31)      =   10794.89
Scale parameter:                         1                                 Prob > chi2         =     0.0000

                                   (Std. Err. adjusted for clustering on target)
----------------------------------------------------------------------------------------------------------------------------------------------------------------
               |                                 Semirobust
 collab_weight   |      Coef.          Std. Err.            z    P>|z|                [95% Conf. Interval]
---------------+------------------------------------------------------------------------------------------------------------------------------------------------
rtot_trade          |    2.60e-09       6.37e-09        0.41    0.683           -9.88e-09      1.51e-08
gdp_pc              |     .0000971       .0000247      3.94   0.000             .0000487      .0001454
tertenrol_epol    |   2.22e-06       4.01e-07         5.53   0.000           1.43e-06        3.01e-06
trade_percgdp   |   -.0183561       .0116593      -1.57   0.115           -.0412079      .0044958
mobcell100        |   .0073132        .0011522       6.35   0.000            .0050549      .0095715
colotrad              | 1.594459         .5851681       2.72   0.006            .4475504    2.741367
langcom             | 1.509419         .6002954       2.51   0.012            .3328614    2.685976
----------------------------------------------------------------------------------------------------------------------------------------------------------------
          year |
         1991  |   .2856466   .3194495     0.89   0.371    -.3404629    .9117561
         1992  |  -.0231025   .2237049    -0.10   0.918     -.461556     .415351
         1993  |   .4922213   .1874601     2.63   0.009     .1248063    .8596362
         1994  |   .4741249   .2524005     1.88   0.060     -.020571    .9688208
         1995  |   .4691006   .2529398     1.85   0.064    -.0266523    .9648535
         1996  |   .4894541   .1945354     2.52   0.012     .1081717    .8707365
         1997  |    .927893   .2780302     3.34   0.001     .3829638    1.472822
         1998  |   1.250811   .2103598     5.95   0.000     .8385137    1.663109
         1999  |   1.082485   .2243396     4.83   0.000     .6427869    1.522182
         2000  |     .96179   .2667751     3.61   0.000     .4389204     1.48466
         2001  |   .9312558   .1905119     4.89   0.000     .5578593    1.304652
         2002  |   .8492289   .1903188     4.46   0.000     .4762109    1.222247
         2003  |   .9112329   .2544881     3.58   0.000     .4124454     1.41002
         2004  |   .6635822   .2677673     2.48   0.013      .138768    1.188396
         2005  |   .2132622   .2759962     0.77   0.440    -.3276804    .7542048
         2006  |   .2055204   .3177095     0.65   0.518    -.4171788    .8282196
         2007  |   .0070632   .3180742     0.02   0.982    -.6163507    .6304771
         2008  |  -.4258888   .2031861    -2.10   0.036    -.8241263   -.0276514
         2009  |  -.1525135   .2025328    -0.75   0.451    -.5494704    .2444435
         2010  |  -.2249248    .181555    -1.24   0.215     -.580766    .1309164
         2011  |  -.2851735   .1338686    -2.13   0.033    -.5475511   -.0227958
         2012  |    -.54935   .0686513    -8.00   0.000    -.6839041   -.4147959
         2013  |  -.6197236   .0624535    -9.92   0.000    -.7421302    -.497317
         2014  |  -.4995681   .0395978   -12.62   0.000    -.5771784   -.4219578
         2015  |          0  (omitted)
         2016  |          0  (omitted)
         2017  |          0  (omitted)
         2018  |          0  (omitted)
               |
         _cons |  -.7398958   .8294814    -0.89   0.372    -2.365649    .8858579
--------------------------------------------------------------------------------
convergence not achieved
r(430);

[1] https://www.statalist.org/forums/for...binomial-model
[2] https://www.statalist.org/forums/for...sson-estimates
[3] https://www.statalist.org/forums/for...-fixed-effects
[4] https://www.statalist.org/forums/for...ial-regression
[5] https://www.stata.com/statalist/arch.../msg00288.html