Not concave issue with multinomiallogit regression

[Rabab Al hasni]

Dear Satalis,

I hope you are well. I would like to ask please regarding the problem of 'not concave' iteration. I have a dataset for 300 firms, one of the firms appears to be an outlier. When I excluded the outlier (i.e. to be only 299 firms) from the multinomial regression analysis (mlogit) the analysis iteration took a long time to perform the iteration and showed non-concavity in some iteration process. How to solve this problem please? Important to mention that when the outlier is not excluded the regression runs perfect but I got small value for the marginal effects results (for instance, 3.94E) for only one of the dependent variable estimation.



mlogit App_status i.I_sec i.AF_LEG i.AF_AGE i.AF_SIZE i.I_loct2 i.I_expt2 i.AF_GRWT i.BO_GEN i.BO_CIT i.BO_AGE i.ow_Exper2 i.BO_FINT i.BO_EDU i.CR_LEN i.CRBS1 i.CR_BS2 i.CR_BS3 i.CR_BS4 i.CR_BS5 i.CR_BS6 i.CR_BS7 i.CR_BS8 i.CR_SAT i.DE_ADS1 i.DE_ADS2 i.DE_ADS3 i.DE_ADS4 i.DE_ADS5 i.DE_ADS6 i.DE_ADS72 i.EI_BP i.EI_AUDFR

Iteration 0: log likelihood = -376.13767
Iteration 1: log likelihood = -240.52371
Iteration 2: log likelihood = -204.10375
Iteration 3: log likelihood = -190.49561
Iteration 4: log likelihood = -182.16412
Iteration 5: log likelihood = -174.29973
Iteration 6: log likelihood = -169.14731
Iteration 7: log likelihood = -167.60249
Iteration 8: log likelihood = -167.36518
Iteration 9: log likelihood = -167.30934
Iteration 10: log likelihood = -167.29729
Iteration 11: log likelihood = -167.29478
Iteration 12: log likelihood = -167.29422
Iteration 13: log likelihood = -167.29408
Iteration 14: log likelihood = -167.29405
Iteration 15: log likelihood = -167.29405 (not concave)
Iteration 16: log likelihood = -167.29405 (not concave)
Iteration 17: log likelihood = -167.29405 (not concave)
Iteration 18: log likelihood = -167.29405 (not concave)
Iteration 19: log likelihood = -167.29405 (not concave)
Iteration 20: log likelihood = -167.29405 (not concave)
Iteration 21: log likelihood = -167.29405 (not concave)
Iteration 22: log likelihood = -167.29405 (not concave)
Iteration 23: log likelihood = -167.29405 (not concave)
Iteration 24: log likelihood = -167.29405 (not concave)
Iteration 25: log likelihood = -167.29405 (not concave)
Iteration 26: log likelihood = -167.29405 (not concave)
Iteration 27: log likelihood = -167.29405 (not concave)
Iteration 28: log likelihood = -167.29405 (not concave)
Iteration 29: log likelihood = -167.29405 (not concave)
Iteration 30: log likelihood = -167.29405 (not concave)
Iteration 31: log likelihood = -167.29405 (not concave)
Iteration 32: log likelihood = -167.29405 (not concave)
Iteration 33: log likelihood = -167.29405 (not concave)
Iteration 34: log likelihood = -167.29405 (not concave)
Iteration 35: log likelihood = -167.29405 (not concave)
Iteration 36: log likelihood = -167.29405 (not concave)
Iteration 37: log likelihood = -167.29405 (not concave)
Iteration 38: log likelihood = -167.29405 (not concave)
Iteration 39: log likelihood = -167.29405 (not concave)
Iteration 40: log likelihood = -167.29405 (not concave)
Iteration 41: log likelihood = -167.29405 (not concave)
Iteration 42: log likelihood = -167.29405 (not concave)
Iteration 43: log likelihood = -167.29405 (not concave)
Iteration 44: log likelihood = -167.29405 (not concave)
Iteration 45: log likelihood = -167.29405 (not concave)
Iteration 46: log likelihood = -167.29405 (not concave)
Iteration 47: log likelihood = -167.29405 (not concave)
Iteration 48: log likelihood = -167.29405 (not concave)
Iteration 49: log likelihood = -167.29405 (not concave)
Iteration 50: log likelihood = -167.29405 (not concave)
Iteration 51: log likelihood = -167.29405 (not concave)
Iteration 52: log likelihood = -167.29405 (not concave)
Iteration 53: log likelihood = -167.29405 (not concave)
Iteration 54: log likelihood = -167.29405 (not concave)
Iteration 55: log likelihood = -167.29405 (not concave)
Iteration 56: log likelihood = -167.29405 (not concave)
Iteration 57: log likelihood = -167.29405 (not concave)
Iteration 58: log likelihood = -167.29405 (not concave)

--Break--
r(1);




Could you please advise on how to solve the problem of the non-concavity with mlogit analysis?
In case if I got small value such as 3.94E for the marginal effect, can I interpret these results to explain the relationship between the dependent and independent variables or should I exclude them (i.e. results) from the discussion part as they not given sense? in other words, what I should do when I got results for the marginal effect with very small values? How I should deal with?


Appreciate your kind help and cooperation

Best regards,
Rabab

[Marcos Almeida]

You may try to add the option - difficult - for that matter.

[Rabab Al hasni]

You may try to add the option - difficult - for that matter.

Dear Marcos,

Many thanks for your reply. I added the option difficult but still I have the problem as below shows:

mlogit App_status i.I_secr i.AF_LEG i.AF_AGE i.AF_SIZE i.I_loct2 i.I_expt2 i.AF_GRWT i.BO_GEN i.BO_CIT i.BO_AGE i.ow_Exper2 i.BO_FINT i.BO_EDU i.CR_LEN i.CR_BS1 i.CR_BS2 i.CR_BS3 i.CR_BS4 i.CR_BS5 i.CR_BS6 i.CR_BS7 i.CR_BS8 i.CR_SAT i.DE_ADS1 i.DE_ADS2 i.DE_ADS3 i.DE_ADS4 i.DE_ADS5 i.DE_ADS6 i.DE_ADS72 i.EI_BP i.EI_AUDFR, difficult

Iteration 0: log likelihood = -240.93338
Iteration 1: log likelihood = -151.62102
Iteration 2: log likelihood = -120.08411
Iteration 3: log likelihood = -109.30193
Iteration 4: log likelihood = -100.87127
Iteration 5: log likelihood = -93.535301
Iteration 6: log likelihood = -88.861266
Iteration 7: log likelihood = -87.941263
Iteration 8: log likelihood = -87.795143
Iteration 9: log likelihood = -87.760216
Iteration 10: log likelihood = -87.751991
Iteration 11: log likelihood = -87.75031
Iteration 12: log likelihood = -87.750035
Iteration 13: log likelihood = -87.749969
Iteration 14: log likelihood = -87.749955 (not concave)
Iteration 15: log likelihood = -87.749954 (not concave)
Iteration 16: log likelihood = -87.749954 (not concave)
Iteration 17: log likelihood = -87.749953 (not concave)
Iteration 18: log likelihood = -87.749953 (not concave)
Iteration 19: log likelihood = -87.749953 (not concave)
Iteration 20: log likelihood = -87.749953 (not concave)
Iteration 21: log likelihood = -87.749953 (not concave)
Iteration 22: log likelihood = -87.749953 (not concave)
Iteration 23: log likelihood = -87.749953 (not concave)
Iteration 24: log likelihood = -87.749953 (not concave)
Iteration 25: log likelihood = -87.749953 (not concave)
Iteration 26: log likelihood = -87.749953 (not concave)
Iteration 27: log likelihood = -87.749953 (not concave)
Break--
r(1);

I am wondering if the sample size is the issue the cause this problem where the unorder dependent variable consist of A 197 firms, B 83 firms, and C 19 firms.
Any suggestions please for the issue of non-concavity.

Thank you very much

Best regards,
Rabab

[FernandoRios]

Hi Rabab
The problem is that your model has too many explanatory variables. Most of them dummies, from the looks of it, and a small sample. That is why the estimator is having difficulties finding a solution to the maximization problem.
Start by estimating simpler models, and build from there.
Fernando

[Rabab Al hasni]

Hi

I have tried other option called 'nonrtolerance' and tech(dfp nr). The regression run good but when it comes to apply the marginal effect for only the category C that has 19 firms the results appear as the following:

Code1

mlogit M_App_status i.I_sec i.AF_LEG i.AF_AGE i.AF_SIZE i.I_loct2 i.I_export2 i.AF_GRWT i.BO_GEN i.BO_CIT i.BO_AGE i.ow_Exp2 i.BO_FINT i.BO_EDU i.CR_LEN i.CR_BS1 i.CR_BS2 i.CR_BS3 i.CR_BS4 i.CR_BS5 i.CR_BS6 i.CR_BS7 i.CR_BS8 i.CR_SAT i.DE_ADS1 i.DE_ADS2 i.DE_ADS3 i.DE_ADS4 i.DE_ADS5 i.DE_ADS6 i.DE_ADS72 i.EI_BP i.EI_AUDFR, nonrtolerance



Code2

. margins, dydx(*) atmeans predict(pr outcome(1))
Warning: variance matrix is nonsymmetric or highly singular

Conditional marginal effects Number of obs = 299
Model VCE : OIM

	dy/dx	Delta-methodStd. Err.	z	P>z	[95% Cof. Interval]
I_sec
X1	-4.34E-94	.	.		.	.
X3	-4.34E-94	.	.		.	.
AF_LEG
X	2.46E-71	.	.		.	.
X2	1.13E-72	.	.		.	.
AF_AGE
X1	1.91E-95	.	.		.	.
X2	-4.00E-112	.	.		.	.
X3	9.12E-97	.	.		.	.
AF_SIZE
X1	-2.59E-50	.	.		.	.
X2	-2.59E-50	.	.		.	.
X3	-2.59E-50	.	.		.	.

What do the dots in the above table means? Could you please help?

Best regards,
Rabab

[Rabab Al hasni]

Hi Rabab
The problem is that your model has too many explanatory variables. Most of them dummies, from the looks of it, and a small sample. That is why the estimator is having difficulties finding a solution to the maximization problem.
Start by estimating simpler models, and build from there.
Fernando

Dear FernandoRios,

Thank you for your advice. I will check my model and try to reduce unnecessary explanatory variables.

Best regards,
Rabab

[Marcos Almeida]

All the tips and ticks won't be enough to tackle the issue when there is a core problem in the model, such as excessive number of predictors, small sample size, etc.

[Rabab Al hasni]

All the tips and ticks won't be enough to tackle the issue when there is a core problem in the model, such as excessive number of predictors, small sample size, etc.

Many thanks Marcos for your advice

Kind regards
Rabab