Coefficient Interpretation and marginal effects

[Nikos Tsileponis]

Dear Statalisters,

I am using a Poisson model (no fixed effects) and I have a question that is not directly related to this model. So, I guess that even someone not familiar with count data models might be able to help.

Cameron & Trivedi (Microeconometrics using Stata - Revised edition - page 576) use an example where the dependent variable is the number of doctor visits (0, 1, 2, 3, ...) and one independent variable of interest is the years of education (EDUCYR). They run a Poisson model. The coefficient of EDUCYR is 0.03 and in order to interpret this number they take the exponential and say:
" One more year of education is associated with doctor visits increasing by the multiple exp(0.03)=1.030 ".

In the next paragraph, they calculate the Average Marginal Effect (AME) using the margins, dydx(*) command. The AME is 0.202 and they say that " One more year of education is associated with 0.202 additional doctor visits ".

Therefore, my question is: What is the difference between these two interpretations? What does the expression "increases by the multiple of" mean in practice? The above two interpretations are very different from each other. I encounter a similar problem with my results, and so I really need to know which of the two to use.

Thank you all in advance.

Best,
Nikos

[Nikos Tsileponis]

Dear members,

After a lot of reading I have got the impression that the interpretation " One more year of education is associated with doctor visits increasing by the multiple exp(0.03)=1.030 ". can also be written as " One more year of education is associated with doctor visits increasing by 3% ".

Any other views are highly appreciated. Thank you.

Best,
Nikos

[Jeff Wooldridge]

Nikos: You have hit on the correct interpretations: You can say a year of education increases the average doctor visits by .202 or that a year of education increases average doctor visits by 3%. The other statement about increasing by the multiple exp(.030) = 1.030 is correct but awkward. As you stated, it's another way of saying a 3% increase.

Generally, for exponential models you can estimate the effect on the expected number of counts (.2 above) or the percentage effect (3% above). They're just two ways of measuring the effect. If you start at the mean count and go up by .2, that will be roughly a 3% increase.

[Nikos Tsileponis]

Nikos: You have hit on the correct interpretations: You can say a year of education increases the average doctor visits by .202 or that a year of education increases average doctor visits by 3%. The other statement about increasing by the multiple exp(.030) = 1.030 is correct but awkward. As you stated, it's another way of saying a 3% increase.

Generally, for exponential models you can estimate the effect on the expected number of counts (.2 above) or the percentage effect (3% above). They're just two ways of measuring the effect. If you start at the mean count and go up by .2, that will be roughly a 3% increase.

Dear Prof. Wooldridge thank you so much for your reply. I appreciate it a lot.

I feel a bit confused for the following reason:

In my research, the dependent variable (y) is the number of media articles (media coverage), while the main independent variable of interest (x1) is the number of corporate disclosures.

Therefore, I've decided to use both a Poisson model and a Negative Binomial model. Because of the presence of significant overdispersion I used cluster-robust standard errors in the poisson model (as a matter of fact I did the same for Neg. Binomial model).

For some reason, I get very different results.

A) POISSON MODEL " An additional corporate disclosure is associated with media articles increasing by a factor of 2.864, holding other factors constant ". I get this number from this command (after the regression)

listcoef x1, help

If I use the following command

listcoef x1, percent

then I conclude that: For every additional corporate disclosure, the company's expected media coverage increases by 186.4% ".

In addition, I can use the more preferable command

margins, dydx(x1)

:
Based on the result (AME): " On average, increasing the number of corporate disclosures by 1 is expected to increase the firm's media coverage by 0.15 articles "

B) NEGATIVE BINOMIAL MODEL " An additional corporate disclosure is associated with media articles increasing by a factor of 9.469, holding other factors constant "

OR: " For every additional corporate disclosure, the company's expected media coverage increases by 846.9% ".

Based on the AME: " On average, increasing the number of corporate disclosures by 1 is expected to increase the firm's media coverage by 2.53 articles "



Is it normal that I get so different results (e.g. compare the AMEs between the 2 models)? (please notice that I am using the same variables in the 2 regressions with cluster-robust standard errors.)


PS. A simple pooled OLS model with cluster-robust standard errors gives me a coefficient of 0.761 on x1.

PS2. Some more info about my dependent variable:
Overall, the mean of Media Coverage (y) is 0.143 and the st.dev is 0.82. The mean of Corporate Disclosure (x1) is 0.042 and the st.dev is 0.215. (260,051 observations)

The mean of Media Coverage when Corporate Disclosure > 0 is 0.97 and the st.dev is 2.255. (10,070 observations)
The mean of Media Coverage when Corporate Disclosure = 0 is 0.11 and the st.dev is 0.68. (249,981 observations)







Thank you all in advance.

Best,
Nikos

[Richard Williams]

I suggest showing your exact commands and output. Use code tags (see pt 12 of the FAQ). I suspect something important is getting done differently between your poisson and nbreg commands. As things now stand you are not showing us the actual poisson and nbreg commands nor are you showing us any of the output from them, so that makes it very hard to advise you.

[Carlo Lazzaro]

Nikos.
as far as your post #2 is concerned, you may want to read an excellent explanation on how to interpret exp(coefficient) in terms of change of a logged dependent variable in: Treiman DJ. Quantitative Data Analysis: Doing Social Research to Test Ideas. San Francisco, CA: Jossey-Bass, 2009: 142-144.
Credits go to Maarten Buis for posting the reference of this interesting textbook on Statalist some years ago.

[Nikos Tsileponis]

I suggest showing your exact commands and output. Use code tags (see pt 12 of the FAQ). I suspect something important is getting done differently between your poisson and nbreg commands. As things now stand you are not showing us the actual poisson and nbreg commands nor are you showing us any of the output from them, so that makes it very hard to advise you.

Dear members,

Thank you for taking the time to read this post. I am following Richard's advice and showing you more details (thanks Richard!). Carlo thank you for your suggestion.

/* 
I have got panel data (id is the company identifier)
I have a sample of 37,080 media articles and 10,796 corporate disclosures 
I am examining the time period 2000-2012 and for each trading day during this
time period I have the number of media articles about firm i published during 
the day (t) and also the number of corporate disclosures issued by firm i on
day t. When there is no media article issuance, y takes the value zero, similarly when
there is no corporate disclosure, x1 takes the value 0. Apparently, most observations 
are zero. These are the main variables that I am using:

y is number of media articles on day t
x1 is the number of corporate disclosures on day t
l.x1 is the number of corporate disclosures on day t-1
l2.x1 is the number of corporate disclosures on day t-2
l3.x1 is the number of corporate disclosures on day t-3
l4.x1 is the number of corporate disclosures on day t-4
l5.x1 is the number of corporate disclosures on day t-5
l6.x1 is the number of corporate disclosures on day t-6
l7.x1 is the number of corporate disclosures on day t-7
f.x1 is the number of corporate disclosures on day t+1

I also include some Control Variables in the regressions

Notice that $xlist contains x1, l.x1, l2.x1 ... f.x1 and Controls.
*/

//Regressions
* pooled OLS regression using Industry dummies
reg y $xlist WEEKDAY_Dummies MONTH_dummies YEAR_dummies INDUSTRY_dummies, cluster(id)


* Firm fixed effects
xtreg y $xlist WEEKDAY_Dummies MONTH_dummies YEAR_dummies, robust i(id) fe


* Poisson regression using Industry dummies
poisson y $xlist WEEKDAY_Dummies MONTH_dummies YEAR_dummies INDUSTRY_dummies, cluster(id)


*Negative Binomial regression
nbreg y $xlist WEEKDAY_Dummies MONTH_dummies YEAR_dummies INDUSTRY_dummies, cluster(id)

This is the OUTPUT (Notice that y is denoted as ma_date and x1 is denoted as pr_date. dff* are fama-french industry dummies):

. * pooled OLS regression using Industry dummies
. reg ma_date $xlist dff_* $if, cluster(id)
note: monday_dummy omitted because of collinearity
note: dff_481 omitted because of collinearity

Linear regression                               Number of obs     =    260,051
                                                F(67, 98)         =          .
                                                Prob > F          =          .
                                                R-squared         =     0.1802
                                                Root MSE          =     .73784

                                       (Std. Err. adjusted for 99 clusters in id)
---------------------------------------------------------------------------------
                |               Robust
        ma_date |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        pr_date |   .7605139   .0875883     8.68   0.000     .5866978    .9343299
   lag1_pr_date |   .4825091   .0952037     5.07   0.000     .2935805    .6714377
   lag2_pr_date |   .0861454   .0331071     2.60   0.011     .0204454    .1518454
   lag3_pr_date |   .0246917   .0169088     1.46   0.147    -.0088633    .0582467
   lag4_pr_date |   .0324686   .0159028     2.04   0.044     .0009101    .0640271
   lag5_pr_date |   .0387474   .0189591     2.04   0.044     .0011237    .0763711
   lag6_pr_date |  -7.16e-06   .0091293    -0.00   0.999    -.0181239    .0181096
   lag7_pr_date |   .0228384   .0150706     1.52   0.133    -.0070688    .0527455
  lead1_pr_date |   .0286069   .0229251     1.25   0.215    -.0168873    .0741011
  NANAL_ALLFPIs |   .0043392    .004456     0.97   0.333    -.0045036    .0131821
        lnvolat |   .0072135   .0204724     0.35   0.725    -.0334133    .0478402
            lmc |   .1155514   .0156665     7.38   0.000     .0844617    .1466411
          b2m_w |   .0785913   .0552231     1.42   0.158    -.0309972    .1881798
          lev_w |   .1245543   .0861025     1.45   0.151    -.0463133     .295422
         turn_w |  -.0141478    .031312    -0.45   0.652    -.0762854    .0479898
     car_3day_w |   2.031429   .3970039     5.12   0.000     1.243587     2.81927
            BAD |  -.0076696   .0043173    -1.78   0.079    -.0162371    .0008979
         CARBAD |  -4.573971   .8196057    -5.58   0.000    -6.200451    -2.94749
      jan_dummy |   .0725037   .0250049     2.90   0.005     .0228822    .1221251
      feb_dummy |   .0410373    .012211     3.36   0.001      .016805    .0652696
      mar_dummy |  -.0119421   .0076872    -1.55   0.124     -.027197    .0033128
      apr_dummy |   .1020945   .0253551     4.03   0.000     .0517783    .1524108
      may_dummy |   .0035999    .009451     0.38   0.704    -.0151553     .022355
      jun_dummy |  -.0110158   .0077167    -1.43   0.157    -.0263293    .0042978
      jul_dummy |   .0981752   .0227713     4.31   0.000     .0529863    .1433641
      aug_dummy |   .0141012   .0101757     1.39   0.169    -.0060922    .0342947
      sep_dummy |  -.0104314   .0074128    -1.41   0.163    -.0251418     .004279
      oct_dummy |   .0995491    .022815     4.36   0.000     .0542734    .1448248
      nov_dummy |    .018959   .0117758     1.61   0.111    -.0044096    .0423277
   monday_dummy |          0  (omitted)
  tuesday_dummy |   .0194678   .0120975     1.61   0.111    -.0045393    .0434748
wednesday_dummy |   .0239853   .0129269     1.86   0.067    -.0016678    .0496383
 thursday_dummy |    .040748   .0126396     3.22   0.002     .0156652    .0658308
   friday_dummy |   .0070803    .008154     0.87   0.387    -.0091011    .0232616
          y2001 |  -.0106487   .0091631    -1.16   0.248    -.0288325    .0075351
          y2002 |   .0450249   .0154516     2.91   0.004     .0143617    .0756881
          y2003 |   .0182299   .0195922     0.93   0.354    -.0206503      .05711
          y2004 |   -.003463   .0253076    -0.14   0.891    -.0536851    .0467592
          y2005 |  -.0211891   .0270852    -0.78   0.436    -.0749388    .0325606
          y2006 |  -.0579699   .0266219    -2.18   0.032    -.1108002   -.0051397
          y2007 |  -.0958997   .0283028    -3.39   0.001    -.1520657   -.0397337
          y2008 |  -.1100676   .0211222    -5.21   0.000    -.1519839   -.0681512
          y2009 |  -.0184289   .0300843    -0.61   0.542    -.0781303    .0412725
          y2010 |   .0119355   .0380139     0.31   0.754    -.0635018    .0873729
          y2011 |  -.0330826   .0327648    -1.01   0.315    -.0981033    .0319382
          y2012 |    .002179   .0445933     0.05   0.961     -.086315     .090673
        dff_481 |          0  (omitted)
        dff_482 |   .0540352   .0314067     1.72   0.088    -.0082904    .1163608
        dff_483 |   .1118085   .0417701     2.68   0.009     .0289172    .1946999
        dff_484 |   .0202149   .0235933     0.86   0.394    -.0266052     .067035
        dff_485 |   .0887661   .0305283     2.91   0.005     .0281838    .1493485
        dff_486 |   .0297492   .0513664     0.58   0.564    -.0721856    .1316841
        dff_487 |   .0092118   .0319785     0.29   0.774    -.0542485     .072672
        dff_488 |   .0490415   .0424323     1.16   0.251    -.0351639    .1332469
        dff_489 |   .0862771   .0329118     2.62   0.010     .0209648    .1515894
       dff_4810 |   .0003823   .0458321     0.01   0.993    -.0905699    .0913346
       dff_4811 |   1.614708   .1589417    10.16   0.000     1.299293    1.930123
       dff_4812 |  -.0003293   .0321261    -0.01   0.992    -.0640824    .0634238
       dff_4813 |  -.1377024   .0212722    -6.47   0.000    -.1799164   -.0954884
       dff_4814 |    .008416   .0371932     0.23   0.821    -.0653926    .0822246
       dff_4815 |   -.054558   .0639399    -0.85   0.396    -.1814446    .0723287
       dff_4816 |  -.0166955   .0456584    -0.37   0.715    -.1073032    .0739121
       dff_4817 |   .0034234   .0576897     0.06   0.953      -.11106    .1179068
       dff_4818 |   .1120077   .0638364     1.75   0.082    -.0146735    .2386889
       dff_4819 |   .8376386    .144736     5.79   0.000     .5504146    1.124863
       dff_4820 |   .0956658   .0568609     1.68   0.096    -.0171728    .2085044
       dff_4821 |   .0527137   .0581529     0.91   0.367    -.0626887    .1681162
       dff_4822 |  -.0124361   .0328997    -0.38   0.706    -.0777245    .0528523
       dff_4823 |  -.0292961   .0443813    -0.66   0.511    -.1173693    .0587772
       dff_4824 |   .0794532   .0322286     2.47   0.015     .0154965    .1434099
       dff_4825 |   .0967242   .0568191     1.70   0.092    -.0160314    .2094798
       dff_4826 |   .0154503    .042885     0.36   0.719    -.0696535    .1005541
       dff_4827 |  -.0731509   .0641186    -1.14   0.257    -.2003923    .0540904
       dff_4828 |  -.0683275   .0469822    -1.45   0.149    -.1615621    .0249071
       dff_4829 |  -.0458207   .0398154    -1.15   0.253    -.1248331    .0331917
       dff_4830 |  -.0286193   .0538964    -0.53   0.597    -.1355749    .0783363
          _cons |  -1.255398   .1996281    -6.29   0.000    -1.651553   -.8592425
---------------------------------------------------------------------------------

. estimates store m1, title(Pooled OLS)

. 
. 
. * Firm fixed effects
. xtreg ma_date $xlist $if, robust i(id) fe
note: friday_dummy omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =    260,051
Group variable: id                              Number of groups  =         99

R-sq:                                           Obs per group:
     within  = 0.0849                                         min =         69
     between = 0.2708                                         avg =    2,626.8
     overall = 0.1083                                         max =      3,127

                                                F(45,98)          =       5.81
corr(u_i, Xb)  = 0.0716                         Prob > F          =     0.0000

                                       (Std. Err. adjusted for 99 clusters in id)
---------------------------------------------------------------------------------
                |               Robust
        ma_date |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        pr_date |   .7600781   .0870658     8.73   0.000     .5872988    .9328574
   lag1_pr_date |   .4820599   .0949106     5.08   0.000      .293713    .6704068
   lag2_pr_date |   .0857863   .0331792     2.59   0.011     .0199432    .1516293
   lag3_pr_date |   .0243094   .0171652     1.42   0.160    -.0097543    .0583731
   lag4_pr_date |   .0325906   .0160058     2.04   0.044     .0008276    .0643536
   lag5_pr_date |   .0387894    .019249     2.02   0.047     .0005903    .0769884
   lag6_pr_date |  -.0007854   .0098383    -0.08   0.937    -.0203091    .0187383
   lag7_pr_date |   .0223459   .0151122     1.48   0.142    -.0076437    .0523355
  lead1_pr_date |    .028041   .0219199     1.28   0.204    -.0154583    .0715403
  NANAL_ALLFPIs |   .0088185   .0068122     1.29   0.199       -.0047     .022337
        lnvolat |   .0025622   .0140671     0.18   0.856    -.0253535    .0304779
            lmc |    .066363   .0542046     1.22   0.224    -.0412043    .1739304
          b2m_w |  -.0031526   .0732315    -0.04   0.966    -.1484781    .1421728
          lev_w |   .2006621   .1571932     1.28   0.205    -.1112828     .512607
         turn_w |  -.0205623   .0339269    -0.61   0.546    -.0878891    .0467646
     car_3day_w |   2.017716   .4311864     4.68   0.000      1.16204    2.873391
            BAD |  -.0079802   .0040943    -1.95   0.054    -.0161053    .0001448
         CARBAD |   -4.56862   .8518405    -5.36   0.000     -6.25907    -2.87817
      jan_dummy |   .0696571   .0252854     2.75   0.007     .0194791    .1198351
      feb_dummy |   .0381078   .0115755     3.29   0.001     .0151366     .061079
      mar_dummy |  -.0151987   .0061745    -2.46   0.016    -.0274518   -.0029455
      apr_dummy |   .0985166   .0254578     3.87   0.000     .0479963    .1490368
      may_dummy |   .0000133   .0085069     0.00   0.999    -.0168684     .016895
      jun_dummy |  -.0148966   .0072895    -2.04   0.044    -.0293624   -.0004309
      jul_dummy |   .0962284   .0227745     4.23   0.000     .0510332    .1414237
      aug_dummy |   .0122334   .0099765     1.23   0.223    -.0075647    .0320315
      sep_dummy |  -.0124046   .0072244    -1.72   0.089    -.0267412     .001932
      oct_dummy |   .0995868   .0227366     4.38   0.000     .0544669    .1447068
      nov_dummy |   .0191777   .0118538     1.62   0.109    -.0043458    .0427012
   monday_dummy |  -.0070663   .0080608    -0.88   0.383    -.0230628    .0089301
  tuesday_dummy |   .0124257   .0095892     1.30   0.198    -.0066038    .0314552
wednesday_dummy |   .0169807   .0096943     1.75   0.083    -.0022573    .0362188
 thursday_dummy |     .03372   .0092884     3.63   0.000     .0152874    .0521526
   friday_dummy |          0  (omitted)
          y2001 |  -.0051046   .0078736    -0.65   0.518    -.0207295    .0105203
          y2002 |   .0462954   .0142524     3.25   0.002      .018012    .0745789
          y2003 |   .0173871   .0177403     0.98   0.329    -.0178179    .0525922
          y2004 |   .0020241   .0303957     0.07   0.947    -.0582952    .0623435
          y2005 |  -.0106579   .0361829    -0.29   0.769    -.0824616    .0611459
          y2006 |  -.0402909   .0437395    -0.92   0.359    -.1270904    .0465087
          y2007 |  -.0707804   .0527026    -1.34   0.182    -.1753671    .0338062
          y2008 |  -.0758291   .0440204    -1.72   0.088    -.1631861     .011528
          y2009 |   .0100258   .0336667     0.30   0.766    -.0567845    .0768362
          y2010 |   .0431309   .0473295     0.91   0.364    -.0507928    .1370547
          y2011 |   .0026761    .058858     0.05   0.964    -.1141257    .1194778
          y2012 |   .0558489   .0574474     0.97   0.333    -.0581537    .1698515
          _cons |  -.8539239   .6777539    -1.26   0.211    -2.198905    .4910568
----------------+----------------------------------------------------------------
        sigma_u |  .22479391
        sigma_e |  .73183632
            rho |  .08621543   (fraction of variance due to u_i)
---------------------------------------------------------------------------------

. estimates store m2, title(Firm Fixed Effects)

. 
. 
. * Poisson regression using Industry dummies
. poisson ma_date $xlist dff_* $if, cluster(id)
note: friday_dummy omitted because of collinearity
note: dff_4830 omitted because of collinearity

Iteration 0:   log pseudolikelihood = -614820.73  
... (omitted by me)
Iteration 11:  log pseudolikelihood = -84570.774  

Poisson regression                              Number of obs     =    260,051
                                                Wald chi2(67)     =          .
Log pseudolikelihood = -84570.774               Prob > chi2       =          .

                                       (Std. Err. adjusted for 99 clusters in id)
---------------------------------------------------------------------------------
                |               Robust
        ma_date |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        pr_date |   1.052171   .0937032    11.23   0.000     .8685157    1.235826
   lag1_pr_date |    .831192   .0544695    15.26   0.000     .7244337    .9379503
   lag2_pr_date |   .2219545   .0526119     4.22   0.000      .118837     .325072
   lag3_pr_date |   .1053613   .0565342     1.86   0.062    -.0054438    .2161663
   lag4_pr_date |   .1760903    .068556     2.57   0.010      .041723    .3104576
   lag5_pr_date |   .2145987   .0897551     2.39   0.017     .0386819    .3905156
   lag6_pr_date |  -.0292285   .0555804    -0.53   0.599    -.1381641    .0797072
   lag7_pr_date |   .0400491   .0832442     0.48   0.630    -.1231064    .2032047
  lead1_pr_date |   .0683708   .0757644     0.90   0.367    -.0801246    .2168663
  NANAL_ALLFPIs |   .0104664   .0040809     2.56   0.010      .002468    .0184649
        lnvolat |  -.0104961   .1075254    -0.10   0.922     -.221242    .2002497
            lmc |   .7414319    .039859    18.60   0.000     .6633097     .819554
          b2m_w |   .8289121   .2013191     4.12   0.000     .4343339     1.22349
          lev_w |  -.5888024   .4966844    -1.19   0.236    -1.562286     .384681
         turn_w |   .2845151   .0810917     3.51   0.000     .1255783    .4434518
     car_3day_w |   11.40727   1.508173     7.56   0.000     8.451301    14.36323
            BAD |  -.0178649   .0350596    -0.51   0.610    -.0865804    .0508507
         CARBAD |  -24.98132   3.373921    -7.40   0.000    -31.59409   -18.36856
      jan_dummy |   .7629438   .1042771     7.32   0.000     .5585644    .9673231
      feb_dummy |   .6285196   .1205681     5.21   0.000     .3922104    .8648287
      mar_dummy |  -.0712191   .0644546    -1.10   0.269    -.1975478    .0551095
      apr_dummy |   .8368928   .1277526     6.55   0.000     .5865024    1.087283
      may_dummy |   .2351686     .09122     2.58   0.010     .0563807    .4139565
      jun_dummy |  -.0353584   .0973626    -0.36   0.716    -.2261856    .1554688
      jul_dummy |   .8399003    .112776     7.45   0.000     .6188634    1.060937
      aug_dummy |   .1497484   .1613117     0.93   0.353    -.1664167    .4659135
      sep_dummy |   .0068434   .0984036     0.07   0.945    -.1860242    .1997109
      oct_dummy |    .885785    .117634     7.53   0.000     .6552266    1.116343
      nov_dummy |   .3304572    .128144     2.58   0.010     .0792996    .5816148
   monday_dummy |  -.1641189   .0769339    -2.13   0.033    -.3149065   -.0133313
  tuesday_dummy |   .0692184     .08258     0.84   0.402    -.0926355    .2310723
wednesday_dummy |   .1667098   .0792965     2.10   0.036     .0112915    .3221281
 thursday_dummy |   .2860659    .061211     4.67   0.000     .1660946    .4060373
   friday_dummy |          0  (omitted)
          y2001 |   .1485574   .0918057     1.62   0.106    -.0313785    .3284934
          y2002 |   .5946169   .0814243     7.30   0.000     .4350281    .7542056
          y2003 |   .3750105    .169289     2.22   0.027     .0432102    .7068108
          y2004 |   .4402744   .1291267     3.41   0.001     .1871907    .6933581
          y2005 |   .3752835    .167754     2.24   0.025     .0464918    .7040752
          y2006 |    .131868   .1672273     0.79   0.430    -.1958915    .4596274
          y2007 |  -.1350724   .1633576    -0.83   0.408    -.4552474    .1851027
          y2008 |  -.3510506    .127634    -2.75   0.006    -.6012087   -.1008926
          y2009 |   .2322236   .1552849     1.50   0.135    -.0721293    .5365765
          y2010 |    .466434   .1394796     3.34   0.001      .193059    .7398091
          y2011 |   .1870592   .1260207     1.48   0.138    -.0599368    .4340551
          y2012 |   .4009425   .1627046     2.46   0.014     .0820475    .7198376
        dff_481 |   .6884734   .2087523     3.30   0.001     .2793265     1.09762
        dff_482 |   1.246825   .2423402     5.14   0.000     .7718466    1.721803
        dff_483 |   .8453428   .2155314     3.92   0.000      .422909    1.267777
        dff_484 |   .8194704   .1790813     4.58   0.000     .4684774    1.170463
        dff_485 |   .7856193   .1951966     4.02   0.000     .4030409    1.168198
        dff_486 |   .4175662   .2486582     1.68   0.093    -.0697949    .9049273
        dff_487 |   .4195727    .244095     1.72   0.086    -.0588446    .8979901
        dff_488 |   .6323451   .1634474     3.87   0.000      .311994    .9526961
        dff_489 |  -.6701857   .1986414    -3.37   0.001    -1.059516   -.2808556
       dff_4810 |  -.3087553   .3851635    -0.80   0.423    -1.063662    .4461513
       dff_4811 |   2.969264   .2131779    13.93   0.000     2.551443    3.387085
       dff_4812 |    .431152   .3880328     1.11   0.267    -.3293783    1.191682
       dff_4813 |  -.9811808   .2808127    -3.49   0.000    -1.531564    -.430798
       dff_4814 |  -.8521513   .3707946    -2.30   0.022    -1.578895   -.1254072
       dff_4815 |  -.1199974   .2673118    -0.45   0.654     -.643919    .4039241
       dff_4816 |   .1511852   .2457659     0.62   0.538     -.330507    .6328774
       dff_4817 |   .4677143   .1917512     2.44   0.015      .091889    .8435397
       dff_4818 |   .8502777   .2266748     3.75   0.000     .4060032    1.294552
       dff_4819 |   1.168738   .3709716     3.15   0.002     .4416471    1.895829
       dff_4820 |   .2926636   .3439681     0.85   0.395    -.3815015    .9668287
       dff_4821 |     .04455   .1979365     0.23   0.822    -.3433985    .4324984
       dff_4822 |    .513263   .2040231     2.52   0.012      .113385     .913141
       dff_4823 |    .655507   .2499663     2.62   0.009     .1655821    1.145432
       dff_4824 |   .3471894   .2018535     1.72   0.085    -.0484362     .742815
       dff_4825 |   1.436533   .2127431     6.75   0.000     1.019564    1.853502
       dff_4826 |    1.35246   .1701663     7.95   0.000      1.01894     1.68598
       dff_4827 |   .2629131   .2169667     1.21   0.226    -.1623338      .68816
       dff_4828 |   .3728516   .3416901     1.09   0.275    -.2968487    1.042552
       dff_4829 |  -.3755445   .2461308    -1.53   0.127     -.857952     .106863
       dff_4830 |          0  (omitted)
          _cons |  -11.82941   .6885259   -17.18   0.000    -13.17889   -10.47992
---------------------------------------------------------------------------------

. estimates store m3, title(Pooled Poisson)

. 
. *Negative Binomial regression
. nbreg ma_date $xlist dff_* $if, cluster(id)
note: friday_dummy omitted because of collinearity
note: dff_4830 omitted because of collinearity

Fitting Poisson model:

Iteration 0:   log pseudolikelihood = -614820.73  
... (omitted by me)
Iteration 11:  log pseudolikelihood = -84570.774  

Fitting constant-only model:

Iteration 0:   log pseudolikelihood = -111830.61  (not concave)
... (omitted by me)
Iteration 3:   log pseudolikelihood = -86895.686  

Fitting full model:

Iteration 0:   log pseudolikelihood = -80480.501  (not concave)
...(omitted by me)
Iteration 6:   log pseudolikelihood = -68702.281  

Negative binomial regression                    Number of obs     =    260,051
                                                Wald chi2(67)     =          .
Dispersion           = mean                     Prob > chi2       =          .
Log pseudolikelihood = -68702.281               Pseudo R2         =     0.2094

                                       (Std. Err. adjusted for 99 clusters in id)
---------------------------------------------------------------------------------
                |               Robust
        ma_date |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        pr_date |   2.247993   .1328436    16.92   0.000     1.987624    2.508362
   lag1_pr_date |   1.444228   .1049681    13.76   0.000     1.238494    1.649962
   lag2_pr_date |   .2211551   .0640249     3.45   0.001     .0956687    .3466415
   lag3_pr_date |    .078516   .0701399     1.12   0.263    -.0589558    .2159878
   lag4_pr_date |   .2084509   .1175018     1.77   0.076    -.0218484    .4387501
   lag5_pr_date |   .2452226   .0667983     3.67   0.000     .1143002    .3761449
   lag6_pr_date |   .0534334   .0452411     1.18   0.238    -.0352375    .1421043
   lag7_pr_date |   .1240363   .0634079     1.96   0.050     -.000241    .2483135
  lead1_pr_date |   .1473781    .049885     2.95   0.003     .0496054    .2451508
  NANAL_ALLFPIs |    .015404   .0050685     3.04   0.002     .0054699     .025338
        lnvolat |   .1290542   .0876203     1.47   0.141    -.0426785    .3007869
            lmc |   .8916833   .0456288    19.54   0.000     .8022525    .9811141
          b2m_w |   .9761746   .2225084     4.39   0.000     .5400662    1.412283
          lev_w |  -.1382236   .4507382    -0.31   0.759    -1.021654    .7452071
         turn_w |   .2546776    .062727     4.06   0.000     .1317349    .3776203
     car_3day_w |   12.28865   1.264065     9.72   0.000     9.811128    14.76617
            BAD |  -.0329519   .0252579    -1.30   0.192    -.0824565    .0165528
         CARBAD |  -27.07786   2.426125   -11.16   0.000    -31.83298   -22.32274
      jan_dummy |   .6726258   .1107412     6.07   0.000     .4555771    .8896746
      feb_dummy |   .6457852   .1210236     5.34   0.000     .4085832    .8829871
      mar_dummy |  -.0714396   .0788274    -0.91   0.365    -.2259383    .0830592
      apr_dummy |   .8291621   .1063276     7.80   0.000     .6207638     1.03756
      may_dummy |   .2520949   .1068045     2.36   0.018     .0427619     .461428
      jun_dummy |  -.1199021   .0952381    -1.26   0.208    -.3065654    .0667611
      jul_dummy |   .8227358   .1022923     8.04   0.000     .6222466    1.023225
      aug_dummy |    .261813    .102113     2.56   0.010     .0616752    .4619507
      sep_dummy |  -.0801642   .1087655    -0.74   0.461    -.2933408    .1330123
      oct_dummy |   .9066078   .1064598     8.52   0.000     .6979505    1.115265
      nov_dummy |   .3615638   .1014902     3.56   0.000     .1626466     .560481
   monday_dummy |   -.104886   .0532351    -1.97   0.049    -.2092249   -.0005471
  tuesday_dummy |   .0547453   .0548501     1.00   0.318    -.0527589    .1622494
wednesday_dummy |   .0930527   .0538107     1.73   0.084    -.0124144    .1985197
 thursday_dummy |   .1955793   .0434536     4.50   0.000     .1104117    .2807469
   friday_dummy |          0  (omitted)
          y2001 |   .2452011   .1025571     2.39   0.017     .0441928    .4462093
          y2002 |   .6857021   .0943363     7.27   0.000     .5008064    .8705979
          y2003 |   .5137892    .130987     3.92   0.000     .2570593     .770519
          y2004 |   .2659107   .1400178     1.90   0.058    -.0085191    .5403404
          y2005 |   .2113518    .157398     1.34   0.179    -.0971426    .5198462
          y2006 |  -.0305301   .1519179    -0.20   0.841    -.3282837    .2672234
          y2007 |   -.322139   .1590925    -2.02   0.043    -.6339546   -.0103234
          y2008 |  -.4808956    .133917    -3.59   0.000    -.7433682   -.2184231
          y2009 |   .1578829   .1357854     1.16   0.245    -.1082515    .4240174
          y2010 |   .4263938   .1392555     3.06   0.002     .1534579    .6993296
          y2011 |   .2782374   .1413439     1.97   0.049     .0012085    .5552664
          y2012 |   .4904513   .1653367     2.97   0.003     .1663974    .8145053
        dff_481 |   .8171322   .1358796     6.01   0.000     .5508131    1.083451
        dff_482 |   1.430244   .3111868     4.60   0.000     .8203296    2.040159
        dff_483 |   .9758514   .1511631     6.46   0.000     .6795771    1.272126
        dff_484 |   .7345527    .106276     6.91   0.000     .5262556    .9428499
        dff_485 |    1.22941   .1818537     6.76   0.000     .8729834    1.585837
        dff_486 |   .7718213   .2243806     3.44   0.001     .3320433    1.211599
        dff_487 |   .5162925   .1888825     2.73   0.006     .1460897    .8864954
        dff_488 |   .7295854   .0737029     9.90   0.000     .5851302    .8740405
        dff_489 |  -.3033605   .1329005    -2.28   0.022    -.5638407   -.0428802
       dff_4810 |  -.1291446   .3625409    -0.36   0.722    -.8397117    .5814226
       dff_4811 |   3.266223    .167148    19.54   0.000     2.938619    3.593827
       dff_4812 |   .3851765   .2509706     1.53   0.125    -.1067169    .8770698
       dff_4813 |  -.6001461   .1832771    -3.27   0.001    -.9593626   -.2409296
       dff_4814 |  -.4065606   .2632715    -1.54   0.123    -.9225632    .1094421
       dff_4815 |  -.2687441   .2247391    -1.20   0.232    -.7092247    .1717365
       dff_4816 |   .2166383   .1468606     1.48   0.140    -.0712032    .5044797
       dff_4817 |   .3932401   .1295183     3.04   0.002     .1393888    .6470913
       dff_4818 |   .9904419   .1990388     4.98   0.000     .6003331    1.380551
       dff_4819 |   1.452219   .2514482     5.78   0.000       .95939    1.945049
       dff_4820 |   .7469517   .2929905     2.55   0.011     .1727009    1.321203
       dff_4821 |   .1882909    .151817     1.24   0.215     -.109265    .4858468
       dff_4822 |    .440028   .1074251     4.10   0.000     .2294787    .6505774
       dff_4823 |    .696302   .2668276     2.61   0.009     .1733295    1.219275
       dff_4824 |   .5615763   .1235353     4.55   0.000     .3194516    .8037009
       dff_4825 |   1.317961   .1337195     9.86   0.000     1.055875    1.580046
       dff_4826 |   1.366076   .0926049    14.75   0.000     1.184574    1.547579
       dff_4827 |   .2569888   .1594787     1.61   0.107    -.0555836    .5695612
       dff_4828 |   .3208987   .2668197     1.20   0.229    -.2020584    .8438558
       dff_4829 |  -.3415261   .2603351    -1.31   0.190    -.8517736    .1687214
       dff_4830 |          0  (omitted)
          _cons |  -13.51136   .7012759   -19.27   0.000    -14.88583   -12.13688
----------------+----------------------------------------------------------------
       /lnalpha |   1.212884   .1799361                      .8602152    1.565552
----------------+----------------------------------------------------------------
          alpha |   3.363168   .6051555                      2.363669    4.785315
---------------------------------------------------------------------------------

. estimates store m4, title(Negative Binomial)

. 
end of do-file

[Carlo Lazzaro]

Nikos:
thanks for providing Stata codes and results in a readable way.
I would rule out OLS from the set of your models, as it seems the weakest one (by the way, did you try -xtpoisson-? Are you looking for fixed effect or conditional fixed effect specification?).
Just out of curiosity:
-do you really need so many predictors for your research purposes?
- which model favoured others in the past when faced with the same research topic? Could the literature in your research field help you out in this respect?

[Julian Pritsch]

Sorry Nikos for "invading" your post, but I have a similar question regarding a model and its marginal effects. Maybe (that reads hopefully) the following discussion helps you / me / and others who have similar questions.


I estimated a ordinal multilevel model with this command:

meologit foc ib0.sex c.agez##c.agez ib5.bildungr ib1.erwerbr01 ib4.einkr ///
vulnerz ib0.kv01 ib0.einbr01 ib0.raub01 ib0.diebst01 ib0.betrug01 ///
|| plz: ,or vce(robust) intpoints(30) baselevel level(99)

(Some of the variable names are in German!)

Of interest for this post:
foc = standard indicator for fear of crime (0-3 categories: 3=feeling very unsafe )
einbr01= dummy if some on experienced a burglary within the last 12 months


After the estimation I calculated the predicted probabilities for outcome 3 (and outcome 2; code not shown) via:

margins, dydx(kv01 einbr01 raub01 diebst01 betrug01) ///
at(agez=(-2(1)2)) over (sex) predict(outcome(3) fixedonly) post

I used Excel to produce the attached graph for the variable einbr01. It shows the predicted probabilities for outcome 2 (dashed line) and 3 (solid line) for females (gray) and males (black) for different ages (Alter=age; which is z-standardized and I used the range -2 SD to +2SD)

Coming to
Jeff Wooldridge: quote. Your stated the following:

Generally, for exponential models you can estimate the effect on the expected number of counts (.2 above) or the percentage effect (3% above). They're just two ways of measuring the effect. If you start at the mean count and go up by .2, that will be roughly a 3% increase.

Looking at the solid gray line for females, this is my interpretation (which I changed a bit since Jeff said: "If you start at the mean...")

1. Very young females (-2SD), who were victims of a burglary within the 12 months prior to the survey are more likely to respond that they feel very unsafe in their neighborhood than males who were victims of a burglary and they are more likely to feel very unsafe than middle age female who were victimized.
   • I can say that because the predicted probability is higher for females at age= -2SD than for man.
     • Is thast suprising, since females feel more unsafe on average than males anyway? (Same goes for the u-shaped distribution of fear of crime regarding age)

Question1:
How do I interpret the values on the y-axis? The predicted probabilities???

• Is it correct to say: The probability that very young females (-2SD) respond that they feel very unsafe increases by more than 5%-Points if they experienced a burglary. This increase of probability decreases if the female were middle aged and sharply inceases again up to 8%-Points when looking at very old females (+2SD age).

Question 2:
Who is the (imagined) person I am comparing this probabilities to? Is it a female with average fear of crime in my sample who never experienced a burglary?

[Nikos Tsileponis]

Hi Carlo,

I am using different model specifications to see what is happening and what is best to use. OLS is likely to provide biased results but at least it gives me some idea. As a matter of fact, I have tried both xtpoisson and xtnbreg. xtpoisson gives very similar results with poisson, and xtnbreg gives very similar results with nbreg.

Yes, I need all these regressors, as I am examining the relation between media articles and press releases, and, more specifically, I am examining the timing between them.
As for prior literature, most people seem to be using OLS even with count outcomes (which is clearly not the best solution...).

Have you got any idea why poisson and nbreg provide so different results ? In addition, is there a way to find out what is the "expected" coefficient for x1 (i.e. for pr_date) ? Because the interpretations across the models (see my post #2) are massively different !

Thank you once again.

Best,
Nikos

[Nikos Tsileponis]

Dear members,

Please allow me to add some feedback that I just received from my supervisor. He is very very experienced in general, but not experienced at all with count models. This is what he found:

"The count models were designed to model the time gap between events. I do not think that this is what we are trying to do.

Thus I doubt if a count model is the right model for us. We have no concept of the length of time between events in our model.

Try searching on "count models" in google

The model assumes that the probability of at least one occurrence of the event in a given time interval is proportional to the length of the interval,
AND the probability of two or more occurrences of the event in a very small time interval is negligible,
AND the number of occurrences of the event in disjoint time intervals are mutually independent."

As far as I am concerned, based on what I have studied so far (J. Wooldridge, Long and Freese 2013 'Regression Models for Categorical Dependent Variables Using Stata', and Cameron and Trivedi 'Microeconometrics Using Stata' revised edition) I disagree and have reached the opposite conclusion: OLS is not suitable and I should be using count models (e.g. Poisson or Negative binomial).

I would appreciate your views.

Thank you.

Best,
Nikos

[Nikos Tsileponis]

Dear members,

Is there anyone who is familiar with the Poisson and Negative Binomial models? For some reason these 2 models provide very different results. I have even started to question the suitability of the models for my research. I describe everything above. My output is in #7.


I appreciate your help!

PS. Julian I think you shoud create a separate post for your question in order to get a reply. My questions are not very similar.

Best,
Nikos

[Richard Williams]

Nikos, A few thoughts that may or may not be helpful:

* Is there any particular reason you aren't using xtpoisson and xtnbreg?
* I would not create all these dummies. Instead I would use factor variable notation, e.g. I would have i.month i.day i.year. See -help fvvarlist-
* Also see -help tsvarlist- for simpler ways of specifying the lagged variables.
* This is a pretty complicated model. Can you simplify it? Or start simple and gradually build it up. Then maybe you can identify what is causing you grief.
* Note that you don't get a value reported for Wald Chi-Square. If you click on the dot that is reported you may get more info. This post may help: http://www.stata.com/statalist/archi.../msg00344.html

I don't usually see that big of discrepancies between poisson and nbreg but then I don't usually see models that are as complicated as yours.

[Nikos Tsileponis]

Nikos, A few thoughts that may or may not be helpful:

* Is there any particular reason you aren't using xtpoisson and xtnbreg?
* I would not create all these dummies. Instead I would use factor variable notation, e.g. I would have i.month i.day i.year. See -help fvvarlist-
* Also see -help tsvarlist- for simpler ways of specifying the lagged variables.
* This is a pretty complicated model. Can you simplify it? Or start simple and gradually build it up. Then maybe you can identify what is causing you grief.
* Note that you don't get a value reported for Wald Chi-Square. If you click on the dot that is reported you may get more info. This post may help: http://www.stata.com/statalist/archi.../msg00344.html

I don't usually see that big of discrepancies between poisson and nbreg but then I don't usually see models that are as complicated as yours.

Dear Prof. Williams,

Thank you for your reply. This is very helpful to me.
- As a matter of fact, xtpoisson and xtnbreg might be a much better solution to my model. Now, the Wald Chi-square is NOT missing! E.g. for the xtnbreg after running the command xtnbreg y $xlist weekday_dummies month_dummies year_dummies, i(id) fe it is :

Wald chi2(45)      =  27597.35
 Prob > chi2        =    0.0000

- Thank you about your comment about fvvarlist. As a matter of fact, there is a detailed discussion about it in Long and Freese (2014) ' Regression Models for Categorical Dependent Variables' 3rd edition. I strongly advise this book to students with similar research interests.
- I would really like to ask your opinion about the suitability of Poisson and Neg. Binomial model in my research. I have to investigate why these 2 models give me different results. In any case, do you think that I should be using a Poisson and Neg. Binomial model in the first place? I think YES after a lot of studying, although my supervisor does not share the same opinion (I give more details in #11). My dependent variable is a COUNT variable, i.e. number of media articles on day t. My main independent variable is the number of Corporate Disclosures on day t. However, I am also using lags of the independent variable (lag1, lag2, lag3, ..., lag7 and lead1). Do the lags / leads violate any assumption of these models ? I have not found anything relevant in Wooldridge, Cameron and Trivedi, and Long and Freese.




More importantly, does the fact that I have TOO MANY ZEROS in my sample affect the reliability of the models (Poisson and Neg. Binomial)? Let me give you an idea of y and x1:

. tab y

    y |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |    243,207       93.52       93.52
          1 |      9,718        3.74       97.26
          2 |      3,139        1.21       98.47
          3 |      1,460        0.56       99.03
          4 |        806        0.31       99.34
          5 |        525        0.20       99.54
          6 |        327        0.13       99.67
          7 |        218        0.08       99.75
          8 |        164        0.06       99.81
          9 |        126        0.05       99.86
         10 |         64        0.02       99.89
         11 |         71        0.03       99.91
         12 |         56        0.02       99.93
         13 |         38        0.01       99.95
         14 |         32        0.01       99.96
         15 |         21        0.01       99.97
         16 |         22        0.01       99.98
         17 |         10        0.00       99.98
         18 |          9        0.00       99.99
         19 |          5        0.00       99.99
         20 |          7        0.00       99.99
         21 |          6        0.00       99.99
         22 |          5        0.00       99.99
         24 |          4        0.00      100.00
         25 |          2        0.00      100.00
         26 |          2        0.00      100.00
         28 |          1        0.00      100.00
         29 |          2        0.00      100.00
         30 |          2        0.00      100.00
         36 |          2        0.00      100.00
------------+-----------------------------------
      Total |    260,051      100.00

 tab x1

    x1 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |    249,981       96.13       96.13
          1 |      9,420        3.62       99.75
          2 |        596        0.23       99.98
          3 |         36        0.01       99.99
          4 |         14        0.01      100.00
          5 |          4        0.00      100.00
------------+-----------------------------------
      Total |    260,051      100.00

Thank you once again.

Best,
Nikos

[Richard Williams]

You also have zip and zinb. Also see http://statisticalhorizons.com/zero-inflated-models. I would not use plain old poisson though.

I hesitate to advise you too much just because I have never worked with models quite like this. Perhaps others will chime in.

I don't really understand your dependent variable but I wonder how horrible it would be to recode it into 0/not 0 and just use logit. Less than 3% of the records are getting recoded if you did that.