Discrete Choice Examples - Ordered Logit

Introduction

This ordered logit example uses the Greene course performance data.The independent data, ABC, categorizes student grades in an economics course as A,B,or C. The dependent variables are cumulative grade point average (GPA), literacy test scores (TUCE), and participation in a special economics course (PSI).

Step 1: Load the data

new;
cls;
library dc;

// Load Data
loadm y = aldnel_mat;

Step 2: Initialize control structure

Once this data is loaded, estimation features are specified using the dcControl structure. This structure must be declared then initialized:

// Declare dcControl structure
struct dcControl dcCt;

// Fill with default settings
dcCt = dcControlCreate();

Step 3: Specify model parameters and data

Prior to estimation, the dcSet procedures are used to setup model parameters and data:

// Dependent variable
dcSetYVar(&dcCt,y[.,1]);
dcSetYLabels(&dcCt,"ABC");

// Category Labels
dcSetYCategoryLabels(&dcCt,"A,B,C");

// Independent variables 
dcSetXVars(&dcCt,y[.,2:4]);
dcSetXLabels(&dcCt,"GPA,TUCE,PSI");

Step 4: Declare results structure

Next, the dcOut structure is declared:

// Declare dcOut structure to hold results
struct dcout dcout1;

Step 5: Perform estimation and print results

Finally, calling the orderedLogit procedure estimates the model and results are reported using the printDCOut procedure:

// Estimate ordered logit model
dcout1 = orderedLogit(dcCt);

// Print Results
call printDCOut(dcout1);

The printDCOut procedure prints a model and data summary to the output screen:

Ordered Probit Results

Number of Observations:   32
Degrees of Freedom:       27


  1 - A
  2 - B
  3 - C


Distribution Among Outcome Categories For ABC 


Dependent Variable     Proportion  
A                       0.3438     
B                       0.4063     
C                       0.2500     



Descriptive Statistics (N=32):


Independent Vars.      Mean     Std Dev    Minimum    Maximum  
GPA                  3.1172     0.4521     2.0600     4.0000     
TUCE                 21.9375    3.7796     12.0000    29.0000    
PSI                  0.4375     0.4883     0.0000     1.0000
In addition, coefficient estimates, odds ratios, and marginal effects are printed:
COEFFICIENTS

Coefficient Estimates
--------------------------------------------------------------

    Variables    Coefficient         se      tstat       pval 
          GPA        -3.23**       1.07      -3.03    0.00245 
         TUCE        0.00499      0.106      0.047      0.963 
          PSI         -1.44*      0.824      -1.75       0.08 
Threshold : 1        -11.5**       3.56      -3.24    0.00119 
Threshold : 2        -8.89**       3.23      -2.75    0.00589 
--------------------------------------------------------------
*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 
      GPA          0.23615         0.046937           1.1881 
     TUCE      9.8391e-006      9.2206e-009         0.010499 
      PSI        0.0001372      2.4458e-007         0.076969 
-------------------------------------------------------------

MARGINAL EFFECTS  
             Partial probability with respect to mean x
Marginal Effects for X Variables in A category
-------------------------------------------------------------

Variables     Coefficient    se            tstat       pval            
GPA           -0.914**       (0.394)      -2.32        0.0274         
TUCE           0.00141       (0.0301)      0.0469      0.963          
PSI           -0.408         (0.272)      -1.5         0.144          
--------------------------------------------------------------

Estimate se in parentheses. 
*p-val<0.1 **p-val<0.05 ***p-val<0.001

Marginal Effects for X Variables in B category
-----------------------------------------------------------

Variables     Coefficient    se           tstat      pval            
GPA           -1.82**        (0.819)     -2.22       0.0341         
TUCE           0.00281       (0.0598)     0.047      0.963          
PSI           -0.813         (0.525)     -1.55       0.132          
-----------------------------------------------------------

Estimate se in parentheses. 
*p-val<0.1 **p-val<0.05 ***p-val<0.001  

Marginal Effects for X Variables in C category
----------------------------------------------------------

Variables     Coefficient    se          tstat      pval            
GPA           -0.497**       (0.226)    -2.2        0.0357         
TUCE           0.000768      (0.0164)    0.047      0.963          
PSI           -0.222         (0.133)    -1.67       0.105          
----------------------------------------------------------

Estimate se in parentheses. 
*p-val<0.1 **p-val<0.05 ***p-val<0.001
Finally, the example also returns a number of summary statistics for model diagnostics:
********************SUMMARY STATISTICS********************

MEASURES OF FIT:

  -2 Ln(Lu):                                    52.3256 
  -2 Ln(Lr): All coeffs equal zero              70.3112 
  -2 Ln(Lr): J-1 intercepts                     69.0937 
  LR Chi-Square (coeffs equal zero):            17.9855 
       d.f.                                      5.0000 
       p-value =                                 0.0000 
  LR Chi-Square (J-1 intercepts):               16.7680 
       d.f.                                      3.0000 
       p-value =                                 0.0008 
  Count R2, Percent Correctly Predicted:        20.0000 
  Adjusted Percent Correctly Predicted:          0.3684 
  Madalla's pseudo R-square:                     0.4079 
  McFadden's pseudo R-square:                    0.2427 
  Ben-Akiva and Lerman's Adjusted R-square:      0.1558 
  Cragg and Uhler's pseudo R-square:             0.0899 
  Akaike Information Criterion:                  1.9477 
  Bayesian Information Criterion1:               0.2290 
  Hannan-Quinn Information Criterion:            2.0236 


OBSERVED AND PREDICTED OUTCOMES

           |           Predicted
  Observed |     Y01      Y02      Y03    Total 
  ----------------------------------------------------------
       Y01 |       8        3        0       11 
       Y02 |       3        8        2       13 
       Y03 |       0        4        4        8 

  ----------------------------------------------------------
     Total |      11       15        6       32

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