Reasonable results in ZINB, but bizarre results after margins, dydx(*) (data attached)

[Zhongying Gan]

Hello,

I try to use margins, dydx(*) after zinb, but it yields crazy results.

. zinb sum_l2 mud_sqft_per_capita office_sqft_per_capita retail_sqft_per_capita,inflate(mud_sqft_per_capita owned) vce(robust)

Fitting constant-only model:

Iteration 0:   log pseudolikelihood = -1935.8032  (not concave)
Iteration 1:   log pseudolikelihood = -1398.7715  
Iteration 2:   log pseudolikelihood = -1339.4624  
Iteration 3:   log pseudolikelihood = -1327.9422  
Iteration 4:   log pseudolikelihood = -1326.7051  
Iteration 5:   log pseudolikelihood = -1326.6635  
Iteration 6:   log pseudolikelihood = -1326.6634  

Fitting full model:

Iteration 0:   log pseudolikelihood = -1326.6634  
Iteration 1:   log pseudolikelihood = -1310.2141  
Iteration 2:   log pseudolikelihood = -1301.1221  
Iteration 3:   log pseudolikelihood = -1291.9257  
Iteration 4:   log pseudolikelihood =  -1290.279  
Iteration 5:   log pseudolikelihood = -1290.2517  
Iteration 6:   log pseudolikelihood = -1290.2517  

Zero-inflated negative binomial regression      Number of obs     =      1,594
                                                Nonzero obs       =        258
                                                Zero obs          =      1,336

Inflation model      = logit                    Wald chi2(3)      =      19.52
Log pseudolikelihood = -1290.252                Prob > chi2       =     0.0002

----------------------------------------------------------------------------------------
                       |               Robust
                sum_l2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
sum_l2                 |
   mud_sqft_per_capita |  -.0350013    .674072    -0.05   0.959    -1.356158    1.286155
office_sqft_per_capita |   3.080568   1.015168     3.03   0.002     1.090875    5.070261
retail_sqft_per_capita |   1.813879   .5685284     3.19   0.001     .6995834    2.928174
                 _cons |   .3769259   .2642011     1.43   0.154    -.1408988    .8947507
-----------------------+----------------------------------------------------------------
inflate                |
   mud_sqft_per_capita |  -11.19935   1.662089    -6.74   0.000    -14.45699    -7.94172
                 owned |  -.5364868   .5588103    -0.96   0.337    -1.631735    .5587612
                 _cons |   1.413014   .4707848     3.00   0.003     .4902923    2.335735
-----------------------+----------------------------------------------------------------
              /lnalpha |   1.650809   .1652354     9.99   0.000     1.326953    1.974664
-----------------------+----------------------------------------------------------------
                 alpha |   5.211192   .8610735                       3.76954    7.204199
----------------------------------------------------------------------------------------

. margins, dydx(*)

Average marginal effects                        Number of obs     =      1,594
Model VCE    : Robust

Expression   : Predicted number of events, predict()
dy/dx w.r.t. : mud_sqft_per_capita office_sqft_per_capita retail_sqft_per_capita owned

----------------------------------------------------------------------------------------
                       |            Delta-method
                       |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
   mud_sqft_per_capita |   2.16e+08   1.85e+09     0.12   0.907    -3.41e+09    3.84e+09
office_sqft_per_capita |   7.35e+09   6.57e+10     0.11   0.911    -1.21e+11    1.36e+11
retail_sqft_per_capita |   4.33e+09   3.74e+10     0.12   0.908    -6.91e+10    7.77e+10
                 owned |   1.44e+07   1.23e+08     0.12   0.907    -2.27e+08    2.56e+08
----------------------------------------------------------------------------------------

You can see that the coefficients of variables after margins, dydx(*) are eight figures. However, if I reduce the number of variables, it works fine.

. zinb sum_l2 mud_sqft_per_capita,inflate(mud_sqft_per_capita owned) vce(robust)

Fitting constant-only model:

Iteration 0:   log pseudolikelihood = -1935.8032  (not concave)
Iteration 1:   log pseudolikelihood = -1398.7715  
Iteration 2:   log pseudolikelihood = -1339.4624  
Iteration 3:   log pseudolikelihood = -1327.9422  
Iteration 4:   log pseudolikelihood = -1326.7051  
Iteration 5:   log pseudolikelihood = -1326.6635  
Iteration 6:   log pseudolikelihood = -1326.6634  

Fitting full model:

Iteration 0:   log pseudolikelihood = -1326.6634  
Iteration 1:   log pseudolikelihood = -1318.5842  
Iteration 2:   log pseudolikelihood = -1317.6977  
Iteration 3:   log pseudolikelihood = -1317.6921  
Iteration 4:   log pseudolikelihood = -1317.6921  

Zero-inflated negative binomial regression      Number of obs     =      1,594
                                                Nonzero obs       =        258
                                                Zero obs          =      1,336

Inflation model      = logit                    Wald chi2(1)      =       6.17
Log pseudolikelihood = -1317.692                Prob > chi2       =     0.0130

-------------------------------------------------------------------------------------
                    |               Robust
             sum_l2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
sum_l2              |
mud_sqft_per_capita |   2.266131   .9126316     2.48   0.013     .4774059    4.054856
              _cons |   .5442042   .2637812     2.06   0.039     .0272026    1.061206
--------------------+----------------------------------------------------------------
inflate             |
mud_sqft_per_capita |  -9.984647   1.612426    -6.19   0.000    -13.14494   -6.824349
              owned |  -.6016932   .5475992    -1.10   0.272    -1.674968    .4715815
              _cons |   1.391733   .4705785     2.96   0.003      .469416     2.31405
--------------------+----------------------------------------------------------------
           /lnalpha |   1.802471    .169724    10.62   0.000     1.469818    2.135123
--------------------+----------------------------------------------------------------
              alpha |   6.064612    1.02931                      4.348442     8.45809
-------------------------------------------------------------------------------------

. margins, dydx(*)

Average marginal effects                        Number of obs     =      1,594
Model VCE    : Robust

Expression   : Predicted number of events, predict()
dy/dx w.r.t. : mud_sqft_per_capita owned

-------------------------------------------------------------------------------------
                    |            Delta-method
                    |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
mud_sqft_per_capita |   6.844191   1.356783     5.04   0.000     4.184946    9.503436
              owned |   .2546788   .2433755     1.05   0.295    -.2223285     .731686
-------------------------------------------------------------------------------------

You can see now the coefficients of variables after margins, dydx(*) are of reasonable magnitude.


I really wanted to share my data using dataex, but since the dataset is large I surpassed the maximum number of characters. The complete dataset is here:https://drive.google.com/file/d/1cRK...ew?usp=sharing
The following is a list of the data:

. list in 1/100

     +-----------------------------------------------------+
     | sum_l2   mud_sq~a   office~a   retail~a       owned |
     |-----------------------------------------------------|
  1. |      0   .0898069          0          0   .57094592 |
  2. |      0   .0035725          0          0   .80785125 |
  3. |      1   .0953043   .0008397          0   .34204793 |
  4. |      1          0          0   .0742383   .76895308 |
  5. |      0    .093042          0          0   .66618496 |
     |-----------------------------------------------------|
  6. |      0    .068348          0          0   .40298507 |
  7. |      0          0          0          0   .81931466 |
  8. |      1   .0758335   .0026269          0   .56521738 |
  9. |      0   .1456166   .0043934          0   .30172414 |
 10. |      0          0          0          0    .4860681 |
     |-----------------------------------------------------|
 11. |      0          0          0          0   .80697054 |
 12. |      0   .0292876          0          0   .44064388 |
 13. |      0          0          0          0   .89447236 |
 14. |      0   .0066272          0          0   .73400676 |
 15. |      0          0          0          0   .85809314 |
     |-----------------------------------------------------|
 16. |      0   .0046185   .0025944   .0053238   .62865949 |
 17. |      0   .0038844   .0026464          0    .6130268 |
 18. |      0   .0124808   .0001208          0   .66139239 |
 19. |      1   .0056831   .0072896          0   .55831265 |
 20. |      0    .013271          0          0   .45341614 |
     |-----------------------------------------------------|
 21. |      0   .0128877   .0007828          0   .63519311 |
 22. |      0          0          0          0   .71408248 |
 23. |      2    .026289          0          0   .76016682 |
 24. |      0          0          0          0   .89873415 |
 25. |      0          0          0          0   .91246682 |
     |-----------------------------------------------------|
 26. |      0          0          0          0   .71515149 |
 27. |      0   .1051657    .000997          0   .24758843 |
 28. |      0   .0929398          0          0   .21495327 |
 29. |      0   .0373987          0   .0087623   .75645757 |
 30. |      1          0          0   .0029182   .65680474 |
     |-----------------------------------------------------|
 31. |      0          0          0          0   .87826085 |
 32. |      0          0          0          0   .90302265 |
 33. |      0          0          0          0   .90434784 |
 34. |      0          0          0          0   .93874425 |
 35. |      0   .2111307          0          0   .05439331 |
     |-----------------------------------------------------|
 36. |      4   .0051789          0          0   .72692305 |
 37. |      0          0          0          0   .92931032 |
 38. |      1          0   .0105478    .173447   .84762865 |
 39. |      0          0          0          0    .9598214 |
 40. |      0          0          0          0   .78552973 |
     |-----------------------------------------------------|
 41. |      0   .0086437          0          0   .62358278 |
 42. |      0          0          0          0    .9366197 |
 43. |      0   .0283563          0          0   .81930691 |
 44. |      0          0          0   .1779139   .95726496 |
 45. |      0          0   .0013528          0   .97846156 |
     |-----------------------------------------------------|
 46. |      0   .0162672   .0212537          0   .79591835 |
 47. |      0          0          0   .0839658   .84812623 |
 48. |      0    .070872   .0101204          0    .6792717 |
 49. |      0          0          0   .1069245   .69617707 |
 50. |      0          0          0          0   .85393256 |
     |-----------------------------------------------------|
 51. |      0   .0505848   .0426975    .022869   .45894736 |
 52. |      0          0   .0099472   .0426096   .68670309 |
 53. |      1   .2311722          0    .002651   .06952965 |
 54. |      1          0          0   .0411989   .93725491 |
 55. |      0   .0880984   .0184813   .0271888   .42549923 |
     |-----------------------------------------------------|
 56. |      0          0   1.496133          0   .85321099 |
 57. |      2    .282277          0   .0589427   .14414415 |
 58. |      0          0   .0006414          0    .6652602 |
 59. |     13   .2656941   .1226111   .5887356   .35841957 |
 60. |      2   .0916511   .0135128          0   .31596452 |
     |-----------------------------------------------------|
 61. |      0          0          0          0   .85137618 |
 62. |      2   .2368419   .0040762          0   .05069124 |
 63. |      0          0          0   .0500728   .82165605 |
 64. |     24          0          0          0           0 |
 65. |      1   .2184411   .0055871          0   .30309987 |
     |-----------------------------------------------------|
 66. |      0   .1965653   .0323297   .0081131   .19964664 |
 67. |      0   .1154042          0          0   .37626776 |
 68. |      0   .1270162    .027308   .0632858   .54897958 |
 69. |      1   .0138945          0          0   .63136458 |
 70. |      0          0          0          0   .88686132 |
     |-----------------------------------------------------|
 71. |      0          0          0          0   .84666669 |
 72. |      5          0          0   .0035174   .83356071 |
 73. |      0   .0378089   .0081194   .0117317   .63396782 |
 74. |      1   .1965736    .007549          0   .14772727 |
 75. |      0          0          0          0   .82617587 |
     |-----------------------------------------------------|
 76. |      0          0          0          0   .78370786 |
 77. |      0          0          0          0   .77880186 |
 78. |      0          0          0          0           1 |
 79. |      0   .0094124          0          0   .67676765 |
 80. |      0   .1000855   .0007475          0   .47757256 |
     |-----------------------------------------------------|
 81. |      0          0          0   .0061988   .77049178 |
 82. |      0          0          0          0   .88834953 |
 83. |      0          0          0          0   .81171548 |
 84. |      0          0          0          0   .77253217 |
 85. |      2   .3587315   .1451557   .0146335   .10459184 |
     |-----------------------------------------------------|
 86. |      0   .0802478   .0154736   .0465494    .2591241 |
 87. |      0   .1259107          0          0    .2429022 |
 88. |      0          0   .0146921   .4493715   .82840234 |
 89. |      0          0          0   .0142334    .9254902 |
 90. |      0   .0522075          0          0   .37804878 |
     |-----------------------------------------------------|
 91. |      0   .0767034          0          0   .64864862 |
 92. |      0          0   .0177341          0   .84394902 |
 93. |      0          0          0          0   .73134327 |
 94. |      0          0   .0004407          0   .70403588 |
 95. |      0    .050782          0          0   .48205128 |
     |-----------------------------------------------------|
 96. |      0   .0881407          0          0   .41935483 |
 97. |      0   .0318145   .0050043   .0561125   .57430339 |
 98. |      3   .1423303   .0013297          0   .29166666 |
 99. |      0   .0023224   .0111253   .1082391   .60655737 |
100. |      1   .2379044          0   .0040009   .12743823 |
     +-----------------------------------------------------+

.

I also notice that if I make the number of observations smaller, margins, dydx(*) also generates coefficients with reasonable magnitude

. drop if !mod(_n,2)
(797 observations deleted)

.
. zinb sum_l2 mud_sqft_per_capita office_sqft_per_capita retail_sqft_per_capita,inflate(mud_sqft_per_capita owned) vce(robust)

Fitting constant-only model:

Iteration 0:   log pseudolikelihood = -961.15273  (not concave)
Iteration 1:   log pseudolikelihood = -687.27718  
Iteration 2:   log pseudolikelihood = -656.77257  
Iteration 3:   log pseudolikelihood = -650.22461  
Iteration 4:   log pseudolikelihood = -649.32756  
Iteration 5:   log pseudolikelihood = -649.28166  
Iteration 6:   log pseudolikelihood = -649.28131  
Iteration 7:   log pseudolikelihood = -649.28131  

Fitting full model:

Iteration 0:   log pseudolikelihood = -649.28131  
Iteration 1:   log pseudolikelihood = -640.25357  
Iteration 2:   log pseudolikelihood = -638.13366  
Iteration 3:   log pseudolikelihood = -638.08243  
Iteration 4:   log pseudolikelihood = -638.08236  
Iteration 5:   log pseudolikelihood = -638.08236  

Zero-inflated negative binomial regression      Number of obs     =        797
                                                Nonzero obs       =        125
                                                Zero obs          =        672

Inflation model      = logit                    Wald chi2(3)      =      24.62
Log pseudolikelihood = -638.0824                Prob > chi2       =     0.0000

----------------------------------------------------------------------------------------
                       |               Robust
                sum_l2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
sum_l2                 |
   mud_sqft_per_capita |  -.8490054     .70847    -1.20   0.231    -2.237581    .5395703
office_sqft_per_capita |   3.356185   1.067579     3.14   0.002     1.263769    5.448601
retail_sqft_per_capita |   2.473402   .8377714     2.95   0.003     .8313999    4.115403
                 _cons |   .8226928   .3300019     2.49   0.013     .1759011    1.469485
-----------------------+----------------------------------------------------------------
inflate                |
   mud_sqft_per_capita |   -10.9113   2.320612    -4.70   0.000    -15.45962   -6.362985
                 owned |   -.312362    .694893    -0.45   0.653    -1.674327    1.049603
                 _cons |    1.66365   .5588054     2.98   0.003     .5684117    2.758889
-----------------------+----------------------------------------------------------------
              /lnalpha |   1.539509   .2407484     6.39   0.000     1.067651    2.011367
-----------------------+----------------------------------------------------------------
                 alpha |     4.6623   1.122442                      2.908538    7.473528
----------------------------------------------------------------------------------------

. margins, dydx(*)

Average marginal effects                        Number of obs     =        797
Model VCE    : Robust

Expression   : Predicted number of events, predict()
dy/dx w.r.t. : mud_sqft_per_capita office_sqft_per_capita retail_sqft_per_capita owned

----------------------------------------------------------------------------------------
                       |            Delta-method
                       |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
   mud_sqft_per_capita |    4.90122   1.353754     3.62   0.000      2.24791     7.55453
office_sqft_per_capita |   4.170577   2.461296     1.69   0.090    -.6534743    8.994629
retail_sqft_per_capita |   3.073583   1.065935     2.88   0.004     .9843888    5.162777
                 owned |   .1705116   .3809638     0.45   0.654    -.5761638     .917187
----------------------------------------------------------------------------------------

The thing is here I just used a subsample of my data and an easier regression to showcase the issues. In my real regression, I have more than 6000 observations, and I have about 30 variables in the ZINB model with two variables in the "inflate" part. I really need to use margins, dydx(*) to see the effects of the variables on the predicted number of events. It would be really helpful if you could let me know why the coefficients after margins, dydx(*) would be of such an unreasonably large magnitude and how I could deal with this issue. Thank you.

[Weiwen Ng]

First, you may already know this, but just so everyone is clear: the coefficients that margins reports are in raw units. That is, you'd interpret them like the predicted count of whatever sum_12 is (i.e. like a risk difference). In contrast, the raw coefficients from the ZINB model are interpreted like log incidence rate ratios (from the main model) or log odds (from the logit model, aka the zero inflated part of the model).

To answer your main question, my instinct is that it's a scaling issue. When you request margins, dydx(), you're asking Stata to compute the marginal effects of a one-unit change in whatever explanatory variable. From your data sample (thanks for providing one!), it looks like for the most part, the explanatory variables usually take on values from 0 to 0.01something, although some are higher. So, a one unit change in one of those variables is a big change. The names imply that they are the number of square feet of something per capita. Maybe think about multiplying them by 100 or 1000, so that they're the number of square feet per 100 or per 1,000 persons.

[Zhongying Gan]

First, you may already know this, but just so everyone is clear: the coefficients that margins reports are in raw units. That is, you'd interpret them like the predicted count of whatever sum_12 is (i.e. like a risk difference). In contrast, the raw coefficients from the ZINB model are interpreted like log incidence rate ratios (from the main model) or log odds (from the logit model, aka the zero inflated part of the model).

To answer your main question, my instinct is that it's a scaling issue. When you request margins, dydx(), you're asking Stata to compute the marginal effects of a one-unit change in whatever explanatory variable. From your data sample (thanks for providing one!), it looks like for the most part, the explanatory variables usually take on values from 0 to 0.01something, although some are higher. So, a one unit change in one of those variables is a big change. The names imply that they are the number of square feet of something per capita. Maybe think about multiplying them by 100 or 1000, so that they're the number of square feet per 100 or per 1,000 persons.

Hello Weiwen,

Thank you for your reply. The regressors are in the unit of 1000 sqft per capita, so the margins result means that an increase of 1000 sqft per capita of the regressor is associated with an eight-figure increase in y. This is still ridiculous. I expect that an increase of 1000 sqft per capita of the regressor to be associated with a one-figure increase in y, maybe about 2-8 units of increase in y. Also scaling issues cannot explain why the margins results are reasonable when I reduce the number of regressors and when I reduce the sample size. I was wondering whether you may have other explanations as to why the margins results are so ridiculous. Thank you.