Model Estimation and Analysis:

Multinomial Choice Models

The features described below are for LIMDEP’s CLOGIT command for estimation of the canonical (McFadden) conditional logit model. Many options are available for this framework. But, CLOGIT is also the gateway to NLOGIT, LIMDEP’s companion program for estimation for estimation of discrete choice models. NLOGIT contains all of the features noted below and supports many additional forms of the discrete choice model, such as nested logit and multinomial probit.

Conditional logit estimator

  • Extreme value model with flexible utility functions (user specified)
    • Utilities specified individually or with generic attributes
    • Random utility or random regret
    • Parameters specified generically or by name
    • Within and cross equation constraints
    • Interactions and choice specific constants
    • Box-Cox transformations
    • Fixed coefficients
    • Up to 300 coefficients in utility functions
    • LM, Wald and LR specification tests
  • Marginal effects and elasticities
  • Robust covariance matrix
  • Predictions and predicted probabilities
  • Inclusive values
  • Model simulation for ‘what if’ scenarios
  • Choice sets
    • Up to 500 choices
    • Restricted choice sets
    • Hausman test for IIA
    • Small/Hsiao test for IIA
    • Variable sized choice sets
    • Conditional choice model based on specified choices
  • Data types
    • Individual choice, proportions or frequencies
    • Ranks (complete and incomplete rankings)
    • Stated and revealed preferences (merge data sets)
    • Automatic scaling for stated choice data sets
    • Weighting
    • Choice based sampling and robust covariance matrix

Example: Choice of travel mode

The following estimates a model for travel mode choice. The four choice model is fit with two attributes and choice specific constants. One of the attributes is generalized cost (operating plus time). The simulation examines the predicted outcomes that would result if the generalized cost of driving a car rose 25% for all individuals. The scenario suggests how many drivers would choose some other mode and which mode would be chosen.


CLOGIT	; Lhs = mode
	; Rhs = one,gc,ttme
	; Choices = air,train,bus,car ; Effects: gc(car) ; full
	; Simulation = *  ? * means simulate all choices
	; Scenario: gc(car) = [*] 1.25$

-----------------------------------------------------------------------------
Discrete choice (multinomial logit) model
Dependent variable               Choice
Log likelihood function      -199.97662
Estimation based on N =    210, K =   5
Inf.Cr.AIC  =    410.0 AIC/N =    1.952
R2=1-LogL/LogL* Log-L fncn R-sqrd R2Adj
Constants only   -283.7588  .2953 .2896
Chi-squared[ 2]          =    167.56429
Prob [ chi squared > value ] =   .00000
Response data are given as ind. choices
Number of obs.=   210, skipped    0 obs
--------+--------------------------------------------------------------------
        |                  Standard            Prob.      95% Confidence
    MODE|  Coefficient       Error       z    |z|>Z*         Interval
--------+--------------------------------------------------------------------
      GC|    -.01578***      .00438    -3.60  .0003     -.02437   -.00719
    TTME|    -.09709***      .01044    -9.30  .0000     -.11754   -.07664
   A_AIR|    5.77636***      .65592     8.81  .0000     4.49078   7.06193
 A_TRAIN|    3.92300***      .44199     8.88  .0000     3.05671   4.78929
   A_BUS|    3.21073***      .44965     7.14  .0000     2.32943   4.09204
--------+--------------------------------------------------------------------
Note: ***, **, * ==>  Significance at 1%, 5%, 10% level.
-----------------------------------------------------------------------------

+---------------------------------------------------+
| Elasticity             averaged over observations.|
| Effects on probabilities of all choices in model: |
| * = Direct Elasticity effect of the attribute.    |
+---------------------------------------------------+

-----------------------------------------------------------------------------
Average elasticity      of prob(alt) wrt GC       in CAR
--------+--------------------------------------------------------------------
        |                  Standard            Prob.      95% Confidence
  Choice|  Coefficient       Error       z    |z|>Z*         Interval
--------+--------------------------------------------------------------------
     AIR|     .42429***      .02386    17.78  .0000      .37752    .47106
   TRAIN|     .42429***      .02386    17.78  .0000      .37752    .47106
     BUS|     .42429***      .02386    17.78  .0000      .37752    .47106
     CAR|   -1.08170***      .04303   -25.14  .0000    -1.16604   -.99736
--------+--------------------------------------------------------------------
Note: ***, **, * ==>  Significance at 1%, 5%, 10% level.
-----------------------------------------------------------------------------

Elasticity wrt change of X in row choice on Prob[column choice]
--------+-----------------------------------
GC      |     AIR    TRAIN      BUS      CAR
--------+-----------------------------------
     CAR|   .4243    .4243    .4243  -1.0817

-------------------------------------------------------------------------
Simulations of Probability Model
Model: Discrete Choice (One Level) Model
Simulated choice set may be a subset of the choices.
Number of individuals is the probability times the
number of observations in the simulated sample.
Column totals may be affected by rounding error.
The model used was simulated with    210 observations.
-------------------------------------------------------------------------
Specification of scenario 1 is:
Attribute  Alternatives affected            Change type             Value
---------  -------------------------------  ------------------- ---------
GC         CAR                              Scale base by value     1.250
-------------------------------------------------------------------------

The simulator located    210 observations for this scenario.
Simulated Probabilities (shares) for this scenario:
+----------+--------------+--------------+------------------+
|Choice    |     Base     |   Scenario   | Scenario - Base  |
|          |%Share Number |%Share Number |ChgShare ChgNumber|
+----------+--------------+--------------+------------------+
|AIR       | 27.619    58 | 30.191    63 |  2.572%        5 |
|TRAIN     | 30.000    63 | 32.126    67 |  2.126%        4 |
|BUS       | 14.286    30 | 15.504    33 |  1.218%        3 |
|CAR       | 28.095    59 | 22.180    47 | -5.916%      -12 |
|Total     |100.000   210 |100.000   210 |   .000%        0 |
+----------+--------------+--------------+------------------+