6. The Multinomial Logit Regression Model
Suppose we have a nominal dependent variable such as the mode of transportation (walk, bike, bus, and car). The multinomial logit and conditional logit models are commonly used; the multinomial probit model is not often used mainly due to the practical difficulty in estimation. However, STATA does have the .mprobit command to fit the model.
In the multinomial logit model, the independent variables contain characteristics of individuals, while they are the attributes of the choices in the conditional logit model. In other words, the conditional logit estimates how alternative-specific, not individual-specific, variables affect the likelihood of observing a given outcome (Long 2003). Therefore, data need to be appropriately arranged in advance.
6.1 Multinomial Logit/Probit in STATA (.mlogit and .mprobit)
STATA has the .mlogit command for the multinomial logit model. The base() option indicates the value of the dependent variable to be used as the base category for the estimation. You may omit the default option, base(0).
. mlogit transmode income age male, base(0)
Iteration
0: log likelihood = -444.84113
Iteration 1: log likelihood = -411.18604
Iteration 2: log likelihood = -406.36474
Iteration 3: log likelihood = -406.3251
Iteration 4: log likelihood = -406.32509
Multinomial logistic regression Number of obs = 437
LR chi2(9) = 77.03
Prob > chi2 = 0.0000
Log likelihood = -406.32509 Pseudo R2 = 0.0866
------------------------------------------------------------------------------
transmode | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1 |
income | 4.018021 1.34443 2.99 0.003 1.382986 6.653057
age | .1915917 .1392928 1.38 0.169 -.0814172 .4646006
male | .2582886 .4039971 0.64 0.523 -.5335311 1.050108
_cons | -6.903473 2.97678 -2.32 0.020 -12.73785 -1.069091
-------------+----------------------------------------------------------------
2 |
income | 8.951041 1.338539 6.69 0.000 6.327552 11.57453
age | .1374997 .1451938 0.95 0.344 -.1470749 .4220742
male | .1573179 .4191014 0.38 0.707 -.6641057 .9787415
_cons | -9.091051 3.088123 -2.94 0.003 -15.14366 -3.038442
-------------+----------------------------------------------------------------
3 |
income | 4.210485 1.032024 4.08 0.000 2.187755 6.233215
age | .3457236 .0995071 3.47 0.001 .1506932 .540754
male | .5402549 .2769887 1.95 0.051 -.0026329 1.083143
_cons | -8.388756 2.135792 -3.93 0.000 -12.57483 -4.202681
------------------------------------------------------------------------------
(transmode==0 is the base outcome)
Iteration 1: log likelihood = -411.18604
Iteration 2: log likelihood = -406.36474
Iteration 3: log likelihood = -406.3251
Iteration 4: log likelihood = -406.32509
Multinomial logistic regression Number of obs = 437
LR chi2(9) = 77.03
Prob > chi2 = 0.0000
Log likelihood = -406.32509 Pseudo R2 = 0.0866
------------------------------------------------------------------------------
transmode | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1 |
income | 4.018021 1.34443 2.99 0.003 1.382986 6.653057
age | .1915917 .1392928 1.38 0.169 -.0814172 .4646006
male | .2582886 .4039971 0.64 0.523 -.5335311 1.050108
_cons | -6.903473 2.97678 -2.32 0.020 -12.73785 -1.069091
-------------+----------------------------------------------------------------
2 |
income | 8.951041 1.338539 6.69 0.000 6.327552 11.57453
age | .1374997 .1451938 0.95 0.344 -.1470749 .4220742
male | .1573179 .4191014 0.38 0.707 -.6641057 .9787415
_cons | -9.091051 3.088123 -2.94 0.003 -15.14366 -3.038442
-------------+----------------------------------------------------------------
3 |
income | 4.210485 1.032024 4.08 0.000 2.187755 6.233215
age | .3457236 .0995071 3.47 0.001 .1506932 .540754
male | .5402549 .2769887 1.95 0.051 -.0026329 1.083143
_cons | -8.388756 2.135792 -3.93 0.000 -12.57483 -4.202681
------------------------------------------------------------------------------
(transmode==0 is the base outcome)
Let us see if the base outcome changes. As shown in the following, the parameter estimates and standard errors are changed, whereas the goodness-of-fit remains unchanged. The two .mlogit commands with different bases fit the same model but present the result in different manner. The SAS CATMOD procedure in the next section uses the largest value as the base outcome.
. mlogit transmode income age male, base(3)
Iteration
0: log likelihood = -444.84113
Iteration 1: log likelihood = -411.18604
Iteration 2: log likelihood = -406.36474
Iteration 3: log likelihood = -406.3251
Iteration 4: log likelihood = -406.32509
Multinomial logistic regression Number of obs = 437
LR chi2(9) = 77.03
Prob > chi2 = 0.0000
Log likelihood = -406.32509 Pseudo R2 = 0.0866
------------------------------------------------------------------------------
transmode | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
0 |
income | -4.210485 1.032024 -4.08 0.000 -6.233215 -2.187755
age | -.3457236 .0995071 -3.47 0.001 -.540754 -.1506932
male | -.5402549 .2769887 -1.95 0.051 -1.083143 .0026329
_cons | 8.388756 2.135792 3.93 0.000 4.202681 12.57483
-------------+----------------------------------------------------------------
1 |
income | -.1924639 1.00606 -0.19 0.848 -2.164305 1.779377
age | -.154132 .1131506 -1.36 0.173 -.3759031 .0676392
male | -.2819663 .3443963 -0.82 0.413 -.9569706 .3930379
_cons | 1.485283 2.430912 0.61 0.541 -3.279216 6.249783
-------------+----------------------------------------------------------------
2 |
income | 4.740556 .9447126 5.02 0.000 2.888953 6.592158
age | -.2082239 .1164954 -1.79 0.074 -.4365507 .0201028
male | -.382937 .3490247 -1.10 0.273 -1.067013 .3011389
_cons | -.7022953 2.460119 -0.29 0.775 -5.52404 4.119449
------------------------------------------------------------------------------
(transmode==3 is the base outcome)
Iteration 1: log likelihood = -411.18604
Iteration 2: log likelihood = -406.36474
Iteration 3: log likelihood = -406.3251
Iteration 4: log likelihood = -406.32509
Multinomial logistic regression Number of obs = 437
LR chi2(9) = 77.03
Prob > chi2 = 0.0000
Log likelihood = -406.32509 Pseudo R2 = 0.0866
------------------------------------------------------------------------------
transmode | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
0 |
income | -4.210485 1.032024 -4.08 0.000 -6.233215 -2.187755
age | -.3457236 .0995071 -3.47 0.001 -.540754 -.1506932
male | -.5402549 .2769887 -1.95 0.051 -1.083143 .0026329
_cons | 8.388756 2.135792 3.93 0.000 4.202681 12.57483
-------------+----------------------------------------------------------------
1 |
income | -.1924639 1.00606 -0.19 0.848 -2.164305 1.779377
age | -.154132 .1131506 -1.36 0.173 -.3759031 .0676392
male | -.2819663 .3443963 -0.82 0.413 -.9569706 .3930379
_cons | 1.485283 2.430912 0.61 0.541 -3.279216 6.249783
-------------+----------------------------------------------------------------
2 |
income | 4.740556 .9447126 5.02 0.000 2.888953 6.592158
age | -.2082239 .1164954 -1.79 0.074 -.4365507 .0201028
male | -.382937 .3490247 -1.10 0.273 -1.067013 .3011389
_cons | -.7022953 2.460119 -0.29 0.775 -5.52404 4.119449
------------------------------------------------------------------------------
(transmode==3 is the base outcome)
The SPost .mlogtest command conducts a variety of statistical tests for the multinomial logit model. This command supports not only Wald and likelihood ratio tests, but also Hausman and Small-Hsiao tests for the independence of irrelevant alternatives (IIA) assumption. The .mlogtest command works with the .mlogit command only.
. mlogtest, hausman smhsiao base
****
Hausman tests of IIA assumption
Ho: Odds(Outcome-J vs Outcome-K) are independent of other alternatives.
Omitted | chi2 df P>chi2 evidence
---------+------------------------------------
0 | 0.260 8 1.000 for Ho
1 | -3.307 8 1.000 for Ho
2 | -0.319 8 1.000 for Ho
3 | 2.315 8 0.970 for Ho
----------------------------------------------
**** Small-Hsiao tests of IIA assumption
Ho: Odds(Outcome-J vs Outcome-K) are independent of other alternatives.
Omitted | lnL(full) lnL(omit) chi2 df P>chi2 evidence
---------+---------------------------------------------------------
0 | -120.685 -116.139 9.092 4 0.059 for Ho
1 | -131.938 -128.574 6.728 4 0.151 for Ho
2 | -155.078 -150.308 9.540 4 0.049 against Ho
3 | -71.735 -67.571 8.327 4 0.080 for Ho
-------------------------------------------------------------------
Ho: Odds(Outcome-J vs Outcome-K) are independent of other alternatives.
Omitted | chi2 df P>chi2 evidence
---------+------------------------------------
0 | 0.260 8 1.000 for Ho
1 | -3.307 8 1.000 for Ho
2 | -0.319 8 1.000 for Ho
3 | 2.315 8 0.970 for Ho
----------------------------------------------
**** Small-Hsiao tests of IIA assumption
Ho: Odds(Outcome-J vs Outcome-K) are independent of other alternatives.
Omitted | lnL(full) lnL(omit) chi2 df P>chi2 evidence
---------+---------------------------------------------------------
0 | -120.685 -116.139 9.092 4 0.059 for Ho
1 | -131.938 -128.574 6.728 4 0.151 for Ho
2 | -155.078 -150.308 9.540 4 0.049 against Ho
3 | -71.735 -67.571 8.327 4 0.080 for Ho
-------------------------------------------------------------------
The STATA .mprobit command fits the multinomial probit model. The model took longer time to converge than the multinomial logit model.
. mprobit transmode income age male
Iteration
0: log likelihood = -425.2053
Iteration 1: log likelihood = -407.95972
Iteration 2: log likelihood = -406.38652
Iteration 3: log likelihood = -406.38431
Iteration 4: log likelihood = -406.38431
Multinomial probit regression Number of obs = 437
Wald chi2(9) = 64.47
Log likelihood = -406.38431 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
transmode | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_outcome_2 |
income | 2.651949 .8328566 3.18 0.001 1.01958 4.284318
age | .1501467 .0903614 1.66 0.097 -.0269584 .3272519
male | .1967795 .262047 0.75 0.453 -.3168232 .7103822
_cons | -5.075328 1.953866 -2.60 0.009 -8.904835 -1.245822
-------------+----------------------------------------------------------------
_outcome_3 |
income | 5.757611 .8443105 6.82 0.000 4.102793 7.412429
age | .1218625 .0942662 1.29 0.196 -.0628959 .3066209
male | .1662947 .2772189 0.60 0.549 -.3770444 .7096339
_cons | -6.547874 2.031953 -3.22 0.001 -10.53043 -2.565319
-------------+----------------------------------------------------------------
_outcome_4 |
income | 2.751622 .6936632 3.97 0.000 1.392067 4.111177
age | .2760071 .074178 3.72 0.000 .1306208 .4213933
male | .4232271 .2086763 2.03 0.043 .0142289 .8322252
_cons | -6.375609 1.598767 -3.99 0.000 -9.509134 -3.242083
------------------------------------------------------------------------------
Iteration 1: log likelihood = -407.95972
Iteration 2: log likelihood = -406.38652
Iteration 3: log likelihood = -406.38431
Iteration 4: log likelihood = -406.38431
Multinomial probit regression Number of obs = 437
Wald chi2(9) = 64.47
Log likelihood = -406.38431 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
transmode | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_outcome_2 |
income | 2.651949 .8328566 3.18 0.001 1.01958 4.284318
age | .1501467 .0903614 1.66 0.097 -.0269584 .3272519
male | .1967795 .262047 0.75 0.453 -.3168232 .7103822
_cons | -5.075328 1.953866 -2.60 0.009 -8.904835 -1.245822
-------------+----------------------------------------------------------------
_outcome_3 |
income | 5.757611 .8443105 6.82 0.000 4.102793 7.412429
age | .1218625 .0942662 1.29 0.196 -.0628959 .3066209
male | .1662947 .2772189 0.60 0.549 -.3770444 .7096339
_cons | -6.547874 2.031953 -3.22 0.001 -10.53043 -2.565319
-------------+----------------------------------------------------------------
_outcome_4 |
income | 2.751622 .6936632 3.97 0.000 1.392067 4.111177
age | .2760071 .074178 3.72 0.000 .1306208 .4213933
male | .4232271 .2086763 2.03 0.043 .0142289 .8322252
_cons | -6.375609 1.598767 -3.99 0.000 -9.509134 -3.242083
------------------------------------------------------------------------------
SAS has the CATMOD procedure for the multinomial logit model. In the CATMOD procedure, the RESPONSE statement is used to specify the functions of response probabilities.
PROC CATMOD DATA = masil.students;
DIRECT income age male;
RESPONSE LOGITS;
MODEL transmode = income age male /NOPROFILE;
RUN;
The CATMOD Procedure
Data Summary
Response transmode Response Levels 4
Weight Variable None Populations 414
Data Set STUDENTS Total Frequency 437
Frequency Missing 0 Observations 437
Maximum Likelihood Analysis
Maximum likelihood computations converged.
Maximum Likelihood Analysis of Variance
Source DF Chi-Square Pr > ChiSq
--------------------------------------------------
Intercept 3 15.91 0.0012
income 3 45.72 <.0001
age 3 14.66 0.0021
male 3 4.73 0.1927
Likelihood Ratio 1E3 778.33 1.0000
Analysis of Maximum Likelihood Estimates
Function Standard Chi-
Parameter Number Estimate Error Square Pr > ChiSq
-------------------------------------------------------------------
Intercept 1 8.3888 2.1358 15.43 <.0001
2 1.4853 2.4309 0.37 0.5412
3 -0.7023 2.4601 0.08 0.7753
income 1 -4.2105 1.0320 16.65 <.0001
2 -0.1925 1.0061 0.04 0.8483
3 4.7406 0.9447 25.18 <.0001
age 1 -0.3457 0.0995 12.07 0.0005
2 -0.1541 0.1132 1.86 0.1731
3 -0.2082 0.1165 3.19 0.0739
male 1 -0.5403 0.2770 3.80 0.0511
2 -0.2820 0.3444 0.67 0.4129
3 -0.3829 0.3490 1.20 0.2726
Data Summary
Response transmode Response Levels 4
Weight Variable None Populations 414
Data Set STUDENTS Total Frequency 437
Frequency Missing 0 Observations 437
Maximum Likelihood Analysis
Maximum likelihood computations converged.
Maximum Likelihood Analysis of Variance
Source DF Chi-Square Pr > ChiSq
--------------------------------------------------
Intercept 3 15.91 0.0012
income 3 45.72 <.0001
age 3 14.66 0.0021
male 3 4.73 0.1927
Likelihood Ratio 1E3 778.33 1.0000
Analysis of Maximum Likelihood Estimates
Function Standard Chi-
Parameter Number Estimate Error Square Pr > ChiSq
-------------------------------------------------------------------
Intercept 1 8.3888 2.1358 15.43 <.0001
2 1.4853 2.4309 0.37 0.5412
3 -0.7023 2.4601 0.08 0.7753
income 1 -4.2105 1.0320 16.65 <.0001
2 -0.1925 1.0061 0.04 0.8483
3 4.7406 0.9447 25.18 <.0001
age 1 -0.3457 0.0995 12.07 0.0005
2 -0.1541 0.1132 1.86 0.1731
3 -0.2082 0.1165 3.19 0.0739
male 1 -0.5403 0.2770 3.80 0.0511
2 -0.2820 0.3444 0.67 0.4129
3 -0.3829 0.3490 1.20 0.2726
As mentioned before, the CATMOD procedure uses the largest value of the dependent variable as a base outcome. Accordingly, you need to compare the above with the STATA output of the base(3) option. The two outputs are the same except for the likelihood ratio.
6.3 Multinomial Logit in LIMDEP (Mlogit$)
In LIMDEP, you may use either the Mlogit$ or simply the Logit$ commands to fit the multinomial logit model. Both commands produce the identical result. Like STATA, LIMDEP by default uses the smallest value as the base outcome.
MLOGIT;
Lhs=transmod;
Rhs=ONE,income,age,male$
Or,
LOGIT;
Lhs=transmod;
Rhs=ONE,income,age,male$
Normal
exit from iterations. Exit status=0.
+---------------------------------------------+
| Multinomial Logit Model |
| Maximum Likelihood Estimates |
| Model estimated: Sep 19, 2005 at 09:19:23AM.|
| Dependent variable TRANSMOD |
| Weighting variable None |
| Number of observations 437 |
| Iterations completed 6 |
| Log likelihood function -406.3251 |
| Restricted log likelihood -444.8411 |
| Chi squared 77.03209 |
| Degrees of freedom 9 |
| Prob[ChiSqd > value] = .0000000 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Characteristics in numerator of Prob[Y = 1]
Constant -6.903472671 2.9767801 -2.319 .0204
INCOME 4.018021309 1.3444306 2.989 .0028 .61683982
AGE .1915916653 .13929281 1.375 .1690 20.691076
MALE .2582886230 .40399708 .639 .5226 .57208238
Characteristics in numerator of Prob[Y = 2]
Constant -9.091051495 3.0881231 -2.944 .0032
INCOME 8.951040805 1.3385396 6.687 .0000 .61683982
AGE .1374996725 .14519378 .947 .3436 20.691076
MALE .1573178944 .41910143 .375 .7074 .57208238
Characteristics in numerator of Prob[Y = 3]
Constant -8.388756169 2.1357918 -3.928 .0001
INCOME 4.210485161 1.0320242 4.080 .0000 .61683982
AGE .3457236198 .99507140E-01 3.474 .0005 20.691076
MALE .5402549359 .27698869 1.950 .0511 .57208238
(Note: E+nn or E-nn means multiply by 10 to + or -nn power.)
+--------------------------------------------------------------------+
| Information Statistics for Discrete Choice Model. |
| M=Model MC=Constants Only M0=No Model |
| Criterion F (log L) -406.32509 -444.84113 -605.81064 |
| LR Statistic vs. MC 77.03209 .00000 .00000 |
| Degrees of Freedom 9.00000 .00000 .00000 |
| Prob. Value for LR .00000 .00000 .00000 |
| Entropy for probs. 406.32509 444.84113 605.81064 |
| Normalized Entropy .67071 .73429 1.00000 |
| Entropy Ratio Stat. 398.97109 321.93900 .00000 |
| Bayes Info Criterion 867.36958 944.40167 1266.34067 |
| BIC - BIC(no model) 398.97109 321.93900 .00000 |
| Pseudo R-squared .08658 .00000 .00000 |
| Pct. Correct Prec. 64.98856 .00000 25.00000 |
| Means: y=0 y=1 y=2 y=3 yu=4 y=5, y=6 y>=7 |
| Outcome .1648 .0892 .0961 .6499 .0000 .0000 .0000 .0000 |
| Pred.Pr .1648 .0892 .0961 .6499 .0000 .0000 .0000 .0000 |
| Notes: Entropy computed as Sum(i)Sum(j)Pfit(i,j)*logPfit(i,j). |
| Normalized entropy is computed against M0. |
| Entropy ratio statistic is computed against M0. |
| BIC = 2*criterion - log(N)*degrees of freedom. |
| If the model has only constants or if it has no constants, |
| the statistics reported here are not useable. |
+--------------------------------------------------------------------+
Frequencies of actual & predicted outcomes
Predicted outcome has maximum probability.
Predicted
------ -------------------- + -----
Actual 0 1 2 3 | Total
------ -------------------- + -----
0 5 0 0 67 | 72
1 0 0 1 38 | 39
2 0 0 1 41 | 42
3 6 0 0 278 | 284
------ -------------------- + -----
Total 11 0 2 424 | 437
+---------------------------------------------+
| Multinomial Logit Model |
| Maximum Likelihood Estimates |
| Model estimated: Sep 19, 2005 at 09:19:23AM.|
| Dependent variable TRANSMOD |
| Weighting variable None |
| Number of observations 437 |
| Iterations completed 6 |
| Log likelihood function -406.3251 |
| Restricted log likelihood -444.8411 |
| Chi squared 77.03209 |
| Degrees of freedom 9 |
| Prob[ChiSqd > value] = .0000000 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Characteristics in numerator of Prob[Y = 1]
Constant -6.903472671 2.9767801 -2.319 .0204
INCOME 4.018021309 1.3444306 2.989 .0028 .61683982
AGE .1915916653 .13929281 1.375 .1690 20.691076
MALE .2582886230 .40399708 .639 .5226 .57208238
Characteristics in numerator of Prob[Y = 2]
Constant -9.091051495 3.0881231 -2.944 .0032
INCOME 8.951040805 1.3385396 6.687 .0000 .61683982
AGE .1374996725 .14519378 .947 .3436 20.691076
MALE .1573178944 .41910143 .375 .7074 .57208238
Characteristics in numerator of Prob[Y = 3]
Constant -8.388756169 2.1357918 -3.928 .0001
INCOME 4.210485161 1.0320242 4.080 .0000 .61683982
AGE .3457236198 .99507140E-01 3.474 .0005 20.691076
MALE .5402549359 .27698869 1.950 .0511 .57208238
(Note: E+nn or E-nn means multiply by 10 to + or -nn power.)
+--------------------------------------------------------------------+
| Information Statistics for Discrete Choice Model. |
| M=Model MC=Constants Only M0=No Model |
| Criterion F (log L) -406.32509 -444.84113 -605.81064 |
| LR Statistic vs. MC 77.03209 .00000 .00000 |
| Degrees of Freedom 9.00000 .00000 .00000 |
| Prob. Value for LR .00000 .00000 .00000 |
| Entropy for probs. 406.32509 444.84113 605.81064 |
| Normalized Entropy .67071 .73429 1.00000 |
| Entropy Ratio Stat. 398.97109 321.93900 .00000 |
| Bayes Info Criterion 867.36958 944.40167 1266.34067 |
| BIC - BIC(no model) 398.97109 321.93900 .00000 |
| Pseudo R-squared .08658 .00000 .00000 |
| Pct. Correct Prec. 64.98856 .00000 25.00000 |
| Means: y=0 y=1 y=2 y=3 yu=4 y=5, y=6 y>=7 |
| Outcome .1648 .0892 .0961 .6499 .0000 .0000 .0000 .0000 |
| Pred.Pr .1648 .0892 .0961 .6499 .0000 .0000 .0000 .0000 |
| Notes: Entropy computed as Sum(i)Sum(j)Pfit(i,j)*logPfit(i,j). |
| Normalized entropy is computed against M0. |
| Entropy ratio statistic is computed against M0. |
| BIC = 2*criterion - log(N)*degrees of freedom. |
| If the model has only constants or if it has no constants, |
| the statistics reported here are not useable. |
+--------------------------------------------------------------------+
Frequencies of actual & predicted outcomes
Predicted outcome has maximum probability.
Predicted
------ -------------------- + -----
Actual 0 1 2 3 | Total
------ -------------------- + -----
0 5 0 0 67 | 72
1 0 0 1 38 | 39
2 0 0 1 41 | 42
3 6 0 0 278 | 284
------ -------------------- + -----
Total 11 0 2 424 | 437
Note that the variable name TRANSMOD was truncated because LIMDEP allows up to eight characters for a variable name. LIMDEP and STATA produce the same result of the multinomial logit model.
SPSS has the Nomreg command to estimate the multinomial logit model. Like SAS, SPSS by default uses the largest value as the base outcome.
NOMREG transmode WITH income age male
/CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20) LCONVERGE(0)
PCONVERGE(0.000001) SINGULAR(0.00000001)
/MODEL /INTERCEPT INCLUDE /PRINT PARAMETER SUMMARY LRT .
Up: Table of Contents
Next: The Conditional Logit Model
Prev: Ordered Logit/Probit Models
