GAUSS Nested Logit Model

This example runs the Nested Logit model using GAUSS DC application. It uses the Greene and Hensher dataset with 810 observations of on 4 modes of transportation: air, train, bus, or car. The features in the dataset include terminal waiting time ( ttme ), in vehicle cost for all stages ( invc ), in vehicle time ( invt ), generalized costs measure ( gc ), household income ( hinc), and traveling group size ( psize ).

Load the data

This example uses the formula string syntax to load data using loadd. The formula string syntax syntax allows users to load, transform and analyze data in one line.

new;
cls;
library dc;

//Load data
fname = getGAUSShome() $+ "examples/dc/hensher.dat";
y = loadd(fname);

Set up the model parameters

The Discrete Choice Module uses a suite of dcSet functions to set various features of the model. An instance of the dcControl structure must be declared for storing all parameters prior to calling any dcSet functions.

//Step One: Declare dc dcCtrol structure
struct dcControl dcCt;
//Initialize dc dcCtrol structure
dcCt = dcControlCreate();

//Step Two:Describe data 
//Name of dependent variable
dcSetYVar(&dcCt,y[.,1]);
dcSetYLabel(&dcCt,"Mode");

//Y Category Labels
dcSetYCategoryLabels(&dcCt,"Air,Train,Bus,Car");
//Specify reference category (excluded)
dcSetReferenceCategory(&dcCt, "Car");

//Name of independent variable
varlist = "TTME,GC,AIRHINC";
dcSetAttributeVars(&dcCt,y[.,2]~y[.,5]~y[.,8]);
dcSetAttributeLabels(&dcCt,"TTME,GC,AIRHINC");

//Set-up nested levels
dcMakeLogitNests(&dcCt,2);

//Set attributes and categories for lower nest (Nest One)
dcSetLogitNestAttributes(&dcCt,1,"TTME,GC");
dcSetLogitNestCategories(&dcCt,1,"Air,Train,Bus,Car");

//Reference category is car (last column)
mask = { 1  1  1 0,
      1  1  1 0,
      1  1  1 0};

//Intercepts for three categories at first nest level
b0 = { 1  1  1 0};
dcCt.startValues = 
  pvPackmi(dcCt.startValues,
  b0,"b0",mask[1,.],1);

//Two attribute variables at first level nest                           
g1 = { .1, 
    .1 };
dcCt.startValues =
  pvPackmi(dcCt.startValues,
  g1,"g1",mask[1:2,2],3);

//One attribute variable in second level nest                       
g2 = { .1 };
dcCt.startValues =
  pvPackmi(dcCt.startValues,
  g2,"g2",mask[1,3],4);

//Two categories at second level - interaction terms                    
t2 = { .1, 
    .1 };
dcCt.startValues =
  pvPackmi(dcCt.startValues,
  t2,"t2",mask[1:2,2],5);

//Set attributes and categories for lower nest (Nest Two)
dcSetLogitNestAttributes(&dcCt,2,"AIRHINC");
dcSetLogitNestCategories(&dcCt,2,"Fly,Ground");

//Make nest assignments
dcAssignLogitNests(&dcCt , 1 , "Air,Train,Bus,Car", "Fly,Ground,Ground,Ground");

Estimate the Model

The Nested Logit Model can be estimated using the nestedLogit function. This function takes a dcControl structure as an input and returns all output to a dcOut structure. In addition, a complete report of results can be printed to screen using the printDCOut procedure.

//Step Three: Declare output structure
struct dcout dcout1;

//Step Four: Call NestedLogit
dcout1 = nestedLogit(dcCt);

//Print Results
call printDCOut(dcOut1);

Output

The output from nestedLogit reads

Nested Logit Results

Number of Observations:   210
Degrees of Freedom:       202

  1 - Air
  2 - Train
  3 - Bus
  4 - Car

Distribution Among Outcome Categories For Mode
Dependent Variable       Proportion
Air 0.2762
Train 0.3000
Bus 0.1429
Car 0.2810
COEFFICIENTS Coefficient Estimates ----------------------------------------------------------------------------------------------- Variables Coefficient se tstat pval Constant: Air 6.04*** 1.33 4.54 5.66e-06 Constant: Train 5.06*** 0.676 7.49 6.79e-14 Constant: Bus 4.1*** 0.629 6.51 7.33e-11 TTME -0.113*** 0.0118 -9.52 1.68e-21 GC -0.0316*** 0.00743 -4.25 2.15e-05 AIRHINC 0.0153 0.0111 1.38 0.168 Corr: Fly 0.586*** 0.113 5.18 2.18e-07 Corr: Ground 0.389** 0.158 2.46 0.0138 ----------------------------------------------------------------------------------------------- *p-val<0.1 **p-val<0.05 ***p-val<0.001
ODDS RATIO Odds Ratio ---------------------------------------------------------------------------- Variables Odds Ratio 95% Lower Bound 95% Upper Bound TTME 0.89349 0.87302 0.91444 GC 0.96891 0.95489 0.98313 AIRHINC 1.0154 0.99355 1.0378 Corr: Fly 1.7968 1.4397 2.2425 Corr: Ground 1.4754 1.0827 2.0106 ---------------------------------------------------------------------------- MARGINAL EFFECTS
Partial probability with respect to mean attributes Marginal Effects for Attribute: TTME --------------------------------------------------------------------------- Variables Air Train Bus Car
Air -0.013*** 0.00364** 0.00113 0.00384
( 0.00326) ( 0.0013) ( 0.00147) ( 2.93)
Train 0.00549** -0.0216*** 0.00409* 0.0139
( 0.00166) ( 0.00341) ( 0.00214) ( 1.85)
Bus 0.00171** 0.00409** -0.00954*** 0.00432
( 0.000597) ( 0.00125) ( 0.00269) ( 1.4)
Car 0.00579*** 0.0139*** 0.00432** -0.022
( 0.0015) ( 0.00346) ( 0.00192) ( 1.8)
--------------------------------------------------------------------------- Attribute equations in separate columns Estimate se in parentheses. *p-val<0.1 **p-val<0.05 ***p-val<0.001
Marginal Effects for Attribute: GC --------------------------------------------------------------------------- Variables Air Train Bus Car
Air -0.00364** 0.00102* 0.000318 0.00108*
( 0.00135) ( 0.000576) ( 0.000421) ( 0.000596)
Train 0.00154** -0.00606*** 0.00115* 0.00389**
( 0.000488) ( 0.00181) ( 0.000613) ( 0.00158)
Bus 0.000479** 0.00115** -0.00268** 0.00121*
( 0.000233) ( 0.000431) ( 0.00089) ( 0.000616)
Car 0.00162* 0.00389** 0.00121 -0.00618***
( 0.000869) ( 0.00132) ( 0.000942) ( 0.000969)
--------------------------------------------------------------------------- Attribute equations in separate columns Estimate se in parentheses. *p-val<0.1 **p-val<0.05 ***p-val<0.001
MARGINAL EFFECTS
Partial probability with respect to mean attributes Marginal Effects for Attribute: AIRHINC ------------------------------------------ Variables Fly Ground
Fly 0.00302 -0.00302**
( 0.00326) ( 0.0013)
Ground -0.00128 0.00128
( 0.00166) ( 0.00341)
------------------------------------------ Attribute equations in separate columns Estimate se in parentheses. *p-val<0.1 **p-val<0.05 ***p-val<0.001
********************SUMMARY STATISTICS******************** MEASURES OF FIT: -2 Ln(Lu): 387.3123 -2 Ln(Lr): All coeffs equal zero 582.2436 -2 Ln(Lr): J-1 intercepts 567.5175 LR Chi-Square (coeffs equal zero): 194.9313 d.f. 8.0000 p-value = 0.0000 LR Chi-Square (J-1 intercepts): 180.2052 d.f. 5.0000 p-value = 0.0000 Count R2, Percent Correctly Predicted: 148.0000 Adjusted Percent Correctly Predicted: 0.5782 Madalla's pseudo R-square: 0.5760 McFadden's pseudo R-square: 0.3175 Ben-Akiva and Lerman's Adjusted R-square: 0.3175 Cragg and Uhler's pseudo R-square: 0.0976 Akaike Information Criterion: 1.9205 Bayesian Information Criterion: 2.0480 Hannan-Quinn Information Criterion: 1.9721 OBSERVED AND PREDICTED OUTCOMES | Predicted Observed | Air Train Bus Car Total ------------------------------------------------------------------- Air | 37 3 2 16 58 Train | 2 49 1 11 63 Bus | 0 3 23 4 30 Car | 5 14 1 39 59 ------------------------------------------------------------------- Total | 44 69 27 70 210

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