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).
My main questions are:
- Why is it not converging?
- 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
Gradient vector (length = 4065.469):
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
Gradient vector (length = 2373.377):
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
Gradient vector (length = 2226.909):
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
Gradient vector (length = 2157.759):
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)
Gradient vector (length = 2140.928):
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)
Gradient vector (length = 2132.452):
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)
Gradient vector (length = 2125.423):
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)
Gradient vector (length = 2117.104):
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)
Gradient vector (length = 2111.886):
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)
Gradient vector (length = 2111.886):
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)
Gradient vector (length = 2111.886):
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)
Gradient vector (length = 2111.886):
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)
Best Answer
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
gradientmax 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 tryltol(0) tol(1e-7)to see if the optimizer can work its way out of the bad region.Also, sometime adding the
difficultmax option helps.