Multinomial Choice Modeling with NLOGIT: Simulation

After estimation of any model, you can simulate the probabilities computed by the model using the same or a different data set. The simulation can restrict the choice set or use the original one. Scenarios in the simulations involve changing attributes and recomputing probabilities and sample shares so as to examine the effect of the change on aggregate. The simulator may be used with any model. The example below shows an analysis of the effect of changing one of the attributes in two of the four choices in a multinomial logit model.

+------------------------------------------------------+
|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
---------  ---------------------- ------------------- -------
TTME       AIR                    Scale base by value   1.250
TTME       TRAIN                  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 | 16.731    35 |-10.888%      -23 |
|TRAIN     | 30.000    63 | 23.242    49 | -6.758%      -14 |
|BUS       | 14.286    30 | 19.444    41 |  5.159%       11 |
|CAR       | 28.095    59 | 40.583    85 | 12.488%       26 |
|Total     |100.000   210 |100.000   210 |   .000%        0 |
+----------+--------------+--------------+------------------+

The simulator provides several options for constructing the scenarios to be simulated.

  • Simulate full choice set or only a subset of the choices
  • Simulate any set of appropriately structured observations, whether used to fit the model or not
  • Merge revealed and stated preference data for simulations
  • Vary specific attributes of specific choices for simulations, proportional changes or add or subtract specific amounts
  • Construct scenarios of one or more changes in specific attributes
  • Compare two or more different scenarios in the same simulation

In the example below, a discrete choice model is fit to a mixed RP and SP data set. Two different scenarios are computed based on different changes in a price and an income variable and changes in the attributes of different choices in the two scenarios.

+---------------------------------------------+
| Discrete Choice (One Level) Model           |
| Model Simulation Using Previous Estimates   |
| Number of observations             1259     |
+---------------------------------------------+
+------------------------------------------------------+
|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   1259 observations.|
|RP and SP data are merged for this set of simulations.|
+------------------------------------------------------+
------------------------------------------------------------------
Specification of scenario 1 is:
Attribute  Alternatives affected            Change type      Value
---------  --------------------------  ------------------- -------
PRICEZ     E1       E2       E3  more  Scale base by value    .500
PRINC      E1       E2       E3  more  Scale base by value    .500
-----------------------------------------------------------------
+-------------------------------------------------------+
|REVEALED PREFERENCE (RP) / STATED PREFERENCE (SP) DATA |
+-------------------------------------------------------+
| This scenario is based on merged RP and SP data sets  |
| The sample contains    494 observations marked as RP. |
| Data search located    744 SP scenarios that matched  |
| IDs with an RP observation and     21 SP scenarios    |
| with IDs that did not match any RP observation in the |
| full sample of   1259 total observations. Any remain- |
| ing observations were erroneous or unusable.          |
+-------------------------------------------------------+
Simulated Probabilities (shares) for this scenario:
+----------+--------------+--------------+------------------+
|Choice    |     Base     |   Scenario   | Scenario - Base  |
|          |%Share Number |%Share Number |ChgShare ChgNumber|
+----------+--------------+--------------+------------------+
|E1        | 11.836    88 | 16.127   120 |  4.290%       32 |
|E2        |  8.470    63 | 12.072    90 |  3.602%       27 |
|E3        |  5.979    44 |  9.653    72 |  3.674%       28 |
|E4        |  4.412    33 |  7.144    53 |  2.732%       20 |
|A1        | 12.831    95 | 10.225    76 | -2.606%      -19 |
|A2        | 10.010    74 |  8.000    60 | -2.010%      -14 |
|A3        |  9.012    67 |  7.245    54 | -1.767%      -13 |
|A4        |  6.961    52 |  5.597    42 | -1.365%      -10 |
|MC        |  2.320    17 |  1.817    14 |  -.504%       -3 |
|SM        |  8.269    62 |  6.491    48 | -1.778%      -14 |
|MD        |  7.116    53 |  5.585    42 | -1.531%      -11 |
|UA        |  2.040    15 |  1.603    12 |  -.437%       -3 |
|UB        |  6.460    48 |  5.072    38 | -1.388%      -10 |
|LG        |  1.069     8 |   .838     6 |  -.231%       -2 |
|LX        |   .499     4 |   .402     3 |  -.097%       -1 |
|LC        |  1.482    11 |  1.160     9 |  -.322%       -2 |
|FD        |   .808     6 |   .636     5 |  -.173%       -1 |
|LT        |   .426     3 |   .334     2 |  -.092%       -1 |
|Total     |100.000   743 |100.000   746 |   .000%        3 |
+----------+--------------+--------------+------------------+
--------------------------------------------------------------------
Specification of scenario 2 is:
Attribute  Alternatives affected       Change type           Value
---------  --------------------------  ------------------- -------
PRICEZ     MC       SM       MD  more  Scale base by value   1.500
PRINC      MC       SM       MD  more  Scale base by value    .500
------------------------------------------------------------------
+-------------------------------------------------------+
| This scenario is based on merged RP and SP data sets  |
+-------------------------------------------------------+
Simulated Probabilities (shares) for this scenario:
+----------+--------------+--------------+------------------+
|Choice    |     Base     |   Scenario   | Scenario - Base  |
|          |%Share Number |%Share Number |ChgShare ChgNumber|
+----------+--------------+--------------+------------------+
|E1        | 11.836    88 | 13.176    98 |  1.340%       10 |
|E2        |  8.470    63 |  9.429    70 |   .960%        7 |
|E3        |  5.979    44 |  6.638    49 |   .659%        5 |
|E4        |  4.412    33 |  4.900    36 |   .488%        3 |
|A1        | 12.831    95 | 14.298   106 |  1.468%       11 |
|A2        | 10.010    74 | 11.173    83 |  1.162%        9 |
|A3        |  9.012    67 | 10.050    75 |  1.038%        8 |
|A4        |  6.961    52 |  7.745    58 |   .783%        6 |
|MC        |  2.320    17 |  1.964    15 |  -.356%       -2 |
|SM        |  8.269    62 |  6.367    47 | -1.902%      -15 |
|MD        |  7.116    53 |  5.130    38 | -1.985%      -15 |
|UA        |  2.040    15 |  1.442    11 |  -.597%       -4 |
|UB        |  6.460    48 |  4.744    35 | -1.716%      -13 |
|LG        |  1.069     8 |   .758     6 |  -.311%       -2 |
|LX        |   .499     4 |   .121     1 |  -.378%       -3 |
|LC        |  1.482    11 |  1.206     9 |  -.276%       -2 |
|FD        |   .808     6 |   .536     4 |  -.273%       -2 |
|LT        |   .426     3 |   .322     2 |  -.104%       -1 |
|Total     |100.000   743 |100.000   743 |   .000%        0 |
+----------+--------------+--------------+------------------+

Pairwise Comparisons of  Specified Scenarios
Base     for this comparison is scenario 1.
Scenario for this comparison  is scenario 2.

+----------+--------------+--------------+------------------+
|Choice    |     Base     |   Scenario   | Scenario - Base  |
|          |%Share Number |%Share Number |ChgShare ChgNumber|
+----------+--------------+--------------+------------------+
|E1        | 16.127   120 | 13.176    98 | -2.950%      -22 |
|E2        | 12.072    90 |  9.429    70 | -2.642%      -20 |
|E3        |  9.653    72 |  6.638    49 | -3.016%      -23 |
|E4        |  7.144    53 |  4.900    36 | -2.244%      -17 |
|A1        | 10.225    76 | 14.298   106 |  4.073%       30 |
|A2        |  8.000    60 | 11.173    83 |  3.173%       23 |
|A3        |  7.245    54 | 10.050    75 |  2.805%       21 |
|A4        |  5.597    42 |  7.745    58 |  2.148%       16 |
|MC        |  1.817    14 |  1.964    15 |   .147%        1 |
|SM        |  6.491    48 |  6.367    47 |  -.124%       -1 |
|MD        |  5.585    42 |  5.130    38 |  -.454%       -4 |
|UA        |  1.603    12 |  1.442    11 |  -.160%       -1 |
|UB        |  5.072    38 |  4.744    35 |  -.328%       -3 |
|LG        |   .838     6 |   .758     6 |  -.080%        0 |
|LX        |   .402     3 |   .121     1 |  -.281%       -2 |
|LC        |  1.160     9 |  1.206     9 |   .046%        0 |
|FD        |   .636     5 |   .536     4 |  -.100%       -1 |
|LT        |   .334     2 |   .322     2 |  -.012%        0 |
|Total     |100.000   746 |100.000   743 |   .000%       -3 |
+----------+--------------+--------------+------------------+