Discrete Choice Example: Stereotypical Multinomial Logit

Stereotypical Logit Example

This example demonstrates the use of a stereotypical multinomial logit model. It models grade (ABC) 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[.,1]);
dcsetYLabel(&dcCt,"ABC");

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

//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 stereoLogit procedure:
//Step four: Call stereo logit procedure
dcout1 = binaryLogit(dcCt);
call printDCOut(dcOut1);
The example prints the model and data description to screen:
Stereo Logistic Results
                       2015-05-21 07:09:28

Number of Observations:   32
Degrees of Freedom:       26


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

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

       Variables      Coefficient               se            tstat             pval 
     Constant: A           11.3**             4.93              2.3           0.0213 
     Constant: C             16**             6.28             2.55           0.0107 
             GPA          -4.38**              2.1            -2.09            0.037 
            TUCE          -0.0693            0.177           -0.391            0.695 
             PSI           -2.54*             1.31            -1.94           0.0525 
     Distance: B          0.655**            0.259             2.53           0.0114 
---------------------------------------------------------------------------
Estimate se in parentheses. 
*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         0.012486       0.00020319          0.76723 
            TUCE          0.93308          0.65965           1.3198 
             PSI         0.078949        0.0060662           1.0275 
     Distance: B           1.9242           1.1586           3.1956 
----------------------------------------------------------------------------

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

Variables       Coefficient     se              tstat           pval            
GPA             -0.644**        ( 0.255)        -2.53            0.0171         
TUCE            -0.0102         ( 0.0265)       -0.384           0.704          
PSI             -0.373*         ( 0.214)        -1.75            0.0914         
---------------------------------------------------------------------------
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             -2.79*          ( 1.54)         -1.82            0.0796         
TUCE            -0.0441         ( 0.119)        -0.37            0.714          
PSI             -1.62           ( 1.21)         -1.34            0.191          
---------------------------------------------------------------------------
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             -1.38*          ( 0.767)        -1.8             0.0817         
TUCE            -0.0219         ( 0.0606)       -0.36            0.721          
PSI             -0.801          ( 0.671)        -1.19            0.242          
---------------------------------------------------------------------------
Estimate se in parentheses. 
*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):                                    52.3305 
  -2 Ln(Lr): All coeffs equal zero              70.3112 
  -2 Ln(Lr): J-1 intercepts                     69.0937 
  LR Chi-Square (coeffs equal zero):            17.9806 
       d.f.                                      6.0000 
       p-value =                                 0.0000 
  LR Chi-Square (J-1 intercepts):               16.7631 
       d.f.                                      4.0000 
       p-value =                                 0.0021 
  Count R2, Percent Correctly Predicted:        20.0000 
  Adjusted Percent Correctly Predicted:          0.3684 
  Madalla's pseudo R-square:                     0.4078 
  McFadden's pseudo R-square:                    0.2426 
  Ben-Akiva and Lerman's Adjusted R-square:      0.1558 
  Cragg and Uhler's pseudo R-square:             0.0898 
  Akaike Information Criterion:                  2.0103 
  Bayesian Information Criterion1:               0.2748 
  Hannan-Quinn Information Criterion:            2.1014 


OBSERVED AND PREDICTED OUTCOMES

           |           Predicted
  Observed |       A        B        C    Total 
  ----------------------------------------------------------
         A |       8        3        0       11 
         B |       2        9        2       13 
         C |       1        4        3        8 

  ----------------------------------------------------------
     Total |      11       16        5       32 

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