Multinomial Choice in 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 | +----------+--------------+--------------+------------------+