Binary Logit Example

This example demonstrates the use of a binary logit model. It models grade (A) achievement rates in a Economics course in relationship to cumulative grade point average (GPA), literacy test score (TUCE), and optional participation in a special economics course (PSI). The first step to setting up all Discrete Choice models is to declare and initialize the dcControl structure:

//Step one: Declare dc control structure
struct dcControl dcCt;

//Initialize dc control structure
dcCt = dcControlCreate();

Next, load and setup the model data using the dcSet procedures:

//Load data
loadm y = aldnel_mat;

//Step two: Describe data names
//Name of dependent variable
dcSetYVar(&dcCt,y[.,5]);
dcsetYLabel(&dcCt,"A");

//Name of independent variable
dcSetXVars(&dcCt,y[.,2:4]);
dcsetXLabels(&dcCt,"GPA,TUCE,PSI");

Following data setup, declare the dcOut structure:

//Step three: Declare dcOut struct
struct dcout dcout1;

Finally, call the binaryLogit procedure:

//Step four: Call binary logit procedure
dcout1 = binaryLogit(dcCt);
call printDCOut(dcOut1);

The example prints the model and data description to screen:

Binary Logit Results
                       2015-05-14 14:56:37

Number of Observations:   32
Degrees of Freedom:       28


  1 - Y0
  2 - Y1


Distribution Among Outcome Categories For A 


Dependent Variable       Proportion  
Y0                        0.6563     
Y1                        0.3438     



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     

All coefficients, odds ratios, and marginal effects are printed:

COEFFICIENTS

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

       Variables      Coefficient               se            tstat             pval 
    Constant: Y0            -13**             4.93            -2.64          0.00828 
             GPA           2.83**             1.26             2.24           0.0252 
            TUCE           0.0952            0.142            0.672            0.501 
             PSI           2.38**             1.06             2.23           0.0255 
--------------------------------------------------------------------------------
*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            16.88           1.4201           200.63 
            TUCE           1.0998          0.83336           1.4515 
             PSI           10.791           1.3393           86.941 
----------------------------------------------------------------------------
                 





                           MARGINAL EFFECTS  
             Partial probability with respect to mean x
Marginal Effects for X Variables in Y1 category
---------------------------------------------------------------------------

Variables       Coefficient     se              tstat           pval            
GPA              0.534**        ( 0.237)         2.25            0.0321         
TUCE             0.018          ( 0.0262)        0.685           0.499          
PSI              0.449**        ( 0.197)         2.28            0.0299         
---------------------------------------------------------------------------

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

In addition a number of summary statistics for model diagnostics are printed:

********************SUMMARY STATISTICS********************

MEASURES OF FIT:

  -2 Ln(Lu):                                    25.7793 
  -2 Ln(Lr): All coeffs equal zero              44.3614 
  -2 Ln(Lr): J-1 intercepts                     41.1835 
  LR Chi-Square (coeffs equal zero):            18.5822 
       d.f.                                      4.0000 
       p-value =                                 0.0000 
  LR Chi-Square (J-1 intercepts):               15.4042 
       d.f.                                      3.0000 
       p-value =                                 0.0015 
  Count R2, Percent Correctly Predicted:        26.0000 
  Adjusted Percent Correctly Predicted:          0.4545 
  Madalla's pseudo R-square:                     0.3821 
  McFadden's pseudo R-square:                    0.3740 
  Ben-Akiva and Lerman's Adjusted R-square:      0.2283 
  Cragg and Uhler's pseudo R-square:             0.2358 
  Akaike Information Criterion:                  1.0556 
  Bayesian Information Criterion1:               0.1832 
  Hannan-Quinn Information Criterion:            1.1163 


OBSERVED AND PREDICTED OUTCOMES

           |       Predicted
  Observed |     Y01      Y02    Total 
  -------------------------------------------------
       Y01 |      18        3       21 
       Y02 |       3        8       11 

  -------------------------------------------------
     Total |      21       11       32