# Binary panel logistic regression (xtlogit fixed effects) is not converging in Stata, how to resolve?

I have a panel dataset with a sample of 800 groups, each having between 200-500 observations. The data looks like this:

The dependent variable is binomial: close_gp30_f30.

The independent variables are continous growth rates. An example summary of one of these is:

                          close_g1
-------------------------------------------------------------
Percentiles      Smallest
1%    -.0789325      -.9908884
5%    -.0396762      -.9907975
10%    -.0256917       -.990625       Obs             2993902
25%    -.0096911      -.9904597       Sum of Wgt.     2993902

50%            0                      Mean           .0015124
Largest       Std. Dev.      .3472223
75%      .009676         103.25
90%     .0253968       103.3333       Variance       .1205633
95%     .0399516          104.5       Skewness       436.1726
99%     .0841585       309.3899       Kurtosis       266732.5


I would like to run this experimental regression:

xtset ticker_id date
xtlogit close_gp30_f30 close_g1 close_g10 close_g15 close_g30 close_g60 close_g120 if ticker_grp == 0, fe


However, when I add more than about 5 variables the regression never converges and I seem to get stuck in a loop of "backed up iterations", like so:

. xtlogit close_gp30_f30 close_g1 close_g10 close_g15 close_g30 close_g60 close_g120 if ticker_grp == 0, fe
note: multiple positive outcomes within groups encountered.
note: 11 groups (272 obs) dropped because of all positive or
all negative outcomes.

Iteration 0:   log likelihood = -175837.76
Iteration 1:   log likelihood = -175015.93
Iteration 2:   log likelihood = -175006.84
Iteration 3:   log likelihood =  -175002.6
Iteration 4:   log likelihood = -175001.69  (backed up)
Iteration 5:   log likelihood = -175001.69  (backed up)
Iteration 6:   log likelihood = -175001.69  (backed up)
Iteration 7:   log likelihood = -175001.69  (backed up)
Iteration 8:   log likelihood = -175001.69  (backed up)
Iteration 9:   log likelihood = -175001.69  (backed up)
Iteration 10:  log likelihood = -175001.69  (backed up)
Iteration 11:  log likelihood = -175001.69  (backed up)
Iteration 12:  log likelihood = -175001.69  (backed up)
Iteration 13:  log likelihood = -175001.69  (backed up)
Iteration 14:  log likelihood = -175001.69  (backed up)
Iteration 15:  log likelihood = -175001.69  (backed up)
Iteration 16:  log likelihood = -175001.69  (backed up)
Iteration 17:  log likelihood = -175001.69  (backed up)
Iteration 18:  log likelihood = -175001.69  (backed up)
Iteration 19:  log likelihood = -175001.69  (backed up)
Iteration 20:  log likelihood = -175001.69  (backed up)
Iteration 21:  log likelihood = -175001.69  (backed up)
Iteration 22:  log likelihood = -175001.69  (backed up)
Iteration 23:  log likelihood = -175001.69  (backed up)
Iteration 24:  log likelihood = -175001.69  (backed up)
Iteration 25:  log likelihood = -175001.69  (backed up)
Iteration 26:  log likelihood = -175001.69  (backed up)
Iteration 27:  log likelihood = -175001.69  (backed up)
Iteration 28:  log likelihood = -175001.69  (backed up)
Iteration 29:  log likelihood = -175001.69  (backed up)
Iteration 30:  log likelihood = -175001.69  (backed up)
Iteration 31:  log likelihood = -175001.69  (backed up)
Iteration 32:  log likelihood = -175001.69  (backed up)
Iteration 33:  log likelihood = -175001.69  (backed up)
Iteration 34:  log likelihood = -175001.69  (backed up)
Iteration 35:  log likelihood = -175001.69  (backed up)
Iteration 36:  log likelihood = -175001.69  (backed up)
--Break--
r(1);


I have also rerun this regression with all debugging information enabled, this is a lot of information but may provide the answer on why it is not converging. Note that here I regressed on the standardized values of the independent variables, but this had exactly the same effect (for some reason I hoped that it would solve my problem).

http://pastebin.com/YU0EEkJt

My main questions are:

1. Why is it not converging?
2. How can I resolve this situation?

Update: multicollinearity checks

. collin close_g1 close_g3 close_g5 close_g15 close_g30 close_g60 close_g70 close_g80 close_g90 close_g100
(obs=3146949)

Collinearity Diagnostics

SQRT                   R-
Variable      VIF     VIF    Tolerance    Squared
----------------------------------------------------
close_g1      1.17    1.08    0.8564      0.1436
close_g3      1.22    1.11    0.8169      0.1831
close_g5      1.25    1.12    0.7979      0.2021
close_g15      1.35    1.16    0.7396      0.2604
close_g30      1.48    1.22    0.6767      0.3233
close_g60      1.87    1.37    0.5343      0.4657
close_g70      1.97    1.40    0.5074      0.4926
close_g80      2.06    1.43    0.4857      0.5143
close_g90      2.03    1.43    0.4915      0.5085
close_g100      1.89    1.38    0.5280      0.4720
----------------------------------------------------
Mean VIF      1.63

Cond
Eigenval          Index
---------------------------------
1     4.0898          1.0000
2     1.4492          1.6799
3     0.9965          2.0259
4     0.7954          2.2675
5     0.7143          2.3928
6     0.6716          2.4677
7     0.5801          2.6552
8     0.5096          2.8328
9     0.4174          3.1303
10     0.3970          3.2096
11     0.3791          3.2847
---------------------------------
Condition Number         3.2847
Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept)
Det(correlation matrix)    0.0422


This too does not seem to be a problem.

Update 2: with gradient option and modified "limits":

. xtlogit close_gp30_f30 close_g1 close_g10 close_g15 close_g30 close_g60 close_g80 close_g100 if ticker_grp == 0, fe ltol(0) tol(1e-7) gradi
> ent
note: multiple positive outcomes within groups encountered.
note: 10 groups (240 obs) dropped because of all positive or
all negative outcomes.

---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 0:
log likelihood = -186484.82
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -145.9671      -491.122     -628.1631      -548.698     -1291.774     -2406.543     -2847.761
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 1:
log likelihood =  -185998.3
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -93.28661     -296.7566     -370.1424     -292.3351     -675.5539     -1381.919     -1716.862
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 2:
log likelihood = -185954.74
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -88.19199     -278.7058      -347.356     -273.7588      -633.336     -1296.948     -1610.864
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 3:
log likelihood = -185934.48
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -85.68227     -270.0902     -336.5747      -265.113     -613.5868     -1256.742     -1560.826
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 4:
log likelihood = -185929.57
(backed up)
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -85.03234     -267.9852     -333.9495     -263.0359     -608.7964     -1246.943      -1548.65
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 5:
log likelihood = -185927.13
(backed up)
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -84.55817     -266.8118     -332.5234     -262.1772     -606.6421     -1241.936     -1542.494
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 6:
log likelihood = -185926.38
(backed up)
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -79.15747     -261.7075     -327.7218     -267.7253     -612.7412      -1235.74     -1536.582
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 7:
log likelihood = -185925.91
(backed up)
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -72.14189     -254.8101     -321.5761     -276.4171     -622.5654     -1228.224     -1528.416
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 8:
log likelihood = -185925.59
(backed up)
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -67.13769     -250.2303     -317.4594     -280.2288      -626.198      -1222.17     -1525.716
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 9:
log likelihood = -185925.59
(backed up)
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -67.13769     -250.2303     -317.4594     -280.2288      -626.198      -1222.17     -1525.716
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 10:
log likelihood = -185925.59
(backed up)
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -67.13769     -250.2303     -317.4594     -280.2288      -626.198      -1222.17     -1525.716
---------------------------------------------------------------------------------------------------------------------------------------------
Iteration 11:
log likelihood = -185925.59
(backed up)
close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:  close_g~f30:
close_g1     close_g10     close_g15     close_g30     close_g60     close_g80    close_g100
r1     -67.13769     -250.2303     -317.4594     -280.2288      -626.198      -1222.17     -1525.716


Update 3:

I don't know if this helps, but when I do xtdata indepvars, i(ticker_id) fe clear followed by a logit depvar indepvar (which normally worked just fine), the logit seems to get stuck too. I therefore believe that it has something to do with fixed effects and/or panel data. Does this make sense?

Update 4:

This seems to be a problem with Stata's background to double recast, please see my follow-up question xtlogit: panel data transformation's recast to double makes model incomputable (STATA)

• I find that Stata is more likely to fail to converge with complex problems than other software - is there anything else you can try? – Jeremy Miles Mar 30 '13 at 21:44
• What kind of things? I have no idea really, that's why I'm here. – Tom Mar 30 '13 at 22:07
• Sorry, I meant other software. SAS proc glimmix and Mplus are my usual go-to's when Stata fails. – Jeremy Miles Mar 30 '13 at 22:33
• I don't have any experience with those. Moreover, I am so dependent on do-files of thousands of lines that for me it really is worth it to resolve the problem in STATA. If I have to use other software than all the time invested in those do-files will be for nothing. – Tom Mar 30 '13 at 22:34

There are 2 possibilities. One is that Stata has found a perfect max and cannot get to a better point. This is pretty unlikely, but a fellow can still dream.

The second, and more likely, scenario is that the optimizer wound up in a bad concave part where the computed gradient and Hessian give a bad direction for stepping.

Here are some possible solutions. Use the gradient max option. If the gradient is zero, the optimizer found a max that may not be unique, but is a max. This is a valid result. If the gradient is not zero, that is not a valid result. You can try tightening up the convergence criterion, or try ltol(0) tol(1e-7) to see if the optimizer can work its way out of the bad region.

Also, sometime adding the difficult max option helps.

• Option 1 is probably ruled out. Did you see pastebin.com/YU0EEkJt? I have enabled gradient there. How does this help me? I'm now adding the ltol(0) tol(1e-7) and running the regression again. Unfortunately the difficult option doesn't seem to help. – Tom Mar 30 '13 at 22:02
• I have now added the output of your suggested changes -- see my original question. Unfortunately it does not seem to help. Do you have any more advice? – Tom Mar 30 '13 at 22:17
• Gradient allows you to distinguish between (1) and (2). I don't see difficult as one of the options in your updated code. That is my only remaining suggestion. – Dimitriy V. Masterov Mar 30 '13 at 22:38
• As mentioned I already tried difficult, with no effect. I still don't understand why this is happening. Is it my data? How do I determine which variable is causing this? Can I transform it to resolve the problem? Do you want me to run it again with difficult on and post the new log file? The regression is at iteration 34 now and the gradient is still 2111.886 – Tom Mar 30 '13 at 22:42
• Another note is that I am not getting these problems when just using logit (no panel data), and random effects. – Tom Mar 30 '13 at 22:59

A short answer is that complicated models are often difficult to fit!

You should try a much simpler model first. Perhaps there are problems because of high correlations between predictors. Sometimes using the difficult option helps.

(UPDATE)

The point of trying a simpler model first is twofold. If you can't get a simpler model to fit, a more complicated model is even less likely to fit. More specifically, it may be possible to identify which predictors are problematic: as you add them, things detectably stall.

Sometimes people try transforming growth rates with some sign-preserving transformation such as cube root or an inverse hyperbolic function. This is suggested because your sample predictor is enormously skew with very high kurtosis, given outliers of very high growth rates. That could be seriously problematic.

Also, a rough guess is that although your response is 0,1 it appears of the same kind as the others: did your dichotomise something as (value > threshold)?

If so, you may have discarded most of the information in the original response, and you are trying to explain that by noise plus outliers. That's a highly pessimistic reading, but it appears entirely consistent with what you are telling us.

Do you have prior experience fitting similar models with similar data, or is there literature implying that they work?

• When I try less variables like g1, g3, g10, g15 it does work. But when I start adding more than about 5 it doesn't converge. How does this help me? I need to include all variables and see their significance. I have updated my original question with a multicollinearity check: this does not seem to be the problem. I also tried the difficult option, but it did not help. – Tom Mar 30 '13 at 21:55
• In response to your update: I did dichotomise the dependent variable. It is one when the future growth rate is positive and zero when it is negative or zero. My reasons for this are grounded because it I do not need to know more than this up or downward behavior, and it allows me to use a logistic model with laxer assumptions than OLS regressions. My initial results seem to confirm this, because the predictions made by OLS regression are much more often invalid (even when looking solely at the sign of growth) than the predictions made by the fixed effects logistic regression. – Tom Mar 31 '13 at 15:07
• Could you tell me why dichotomising the dependent variable could cause issues? – Tom Mar 31 '13 at 15:08
• Noted. There is no easy trade-off here. I would still suggest a sign-preserving transformation of growth rate. – Nick Cox Mar 31 '13 at 16:19
• This seems to be a problem with STATA's background to double recast, please see my follow-up question stats.stackexchange.com/questions/54952/… – Tom Apr 2 '13 at 10:58