Discrete Choice Examples - Ordered Logit

Ordered Logit Example

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). The first step to performing analysis is to load the data:
new;
cls;
library dc;

//Load Data
loadm y = aldnel_mat;
Once this data is loaded, estimation features are specified using the dcControl structure. This structure must be declared then initialized:
//Step One: dcControl structure
//Declare dcControl structure
struct dcControl dcCt;

//Initialize dcControl structure 
dcCt = dcControlCreate();
Prior to estimation, the dcSet procedures are used to setup model parameters and data:
//Step Two: Describe 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");
Next, the dcOut structure is declared:
//Step Three: Declare dcOut structure 
struct dcout dcout1;
Finally, calling the orderedLogit procedure estimates the model and results are reported using the printDCOut procedure:
//Step Four: Call orderedLogit 
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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