Discrete Choice Example: Adjacent Categories Logit

Adjacent Categories Logit Example

The Adjacent Categories Logit example uses General Social Survey occupational outcomes data included with the Discrete Choice examples. This model includes the independent data, occatt, and the dependent variables, exper, educ, and white. Once data is loaded, estimation features are specified using the dcControl structure:
//Step One: dcControl structure
//Declare dcControl structure
struct dcControl dcCt;
Next, the dcSet procedures are used for data setup:
//Step Two: Describe data names
//Dependent variable
dcSetYVar(&dcCt,y[.,1]); 
dcSetYLabels(&dcCt,"occatt");


//Independent variable
dcSetXVars(&dcCt,y[.,2:4]);
dcSetXLabels(&dcCt,"exper,educ,white");

//Reference category excluded from regression
dcSetReferenceCategory(&dcCt,1);
The dcOut structure is declared:
//Step Three: Declare dcOut structure
struct dcout dcout1;
Finally, calling the adjacentCategories procedure estimates the model and results are reported using the printDCOut procedure:
//Step Four: Call AdjacentCategories
dcout1 = adjacentCategories(dcCt);

//Print Results
call printDCOut(dcout1);
Running printDcOut prints the model and data summary to the output screen:
Adjacent Categories Results

Number of Observations:   337
Degrees of Freedom:       321


  1 - Menial
  2 - BC
  3 - Craft
  4 - WC
  5 - Pro


Distribution Among Outcome Categories For occatt 


Dependent Variable       Proportion  
Menial                    0.0920     
BC                        0.2047     
Craft                     0.2493     
WC                        0.1217     
Pro                       0.3323     



Descriptive Statistics (N=337):


Independent Vars.          Mean             Std Dev          Minimum          Maximum  
exper                    20.5015          13.9179          2.0000           66.0000    
educ                     13.0950          2.9377           3.0000           20.0000    
white                    0.9169           0.2756           0.0000           1.0000
All coefficients, odds ratios, and marginal effect tables are printed:
COEFFICIENTS

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

       Variables      Coefficient               se            tstat             pval 
    Constant: BC            0.741             1.52            0.488            0.626 
 Constant: Craft            -1.83             1.19            -1.55            0.122 
    Constant: WC          -5.15**             1.59            -3.23          0.00125 
   Constant: Pro          -5.28**             1.68            -3.14          0.00172 
      exper : BC          0.00472           0.0174            0.271            0.786 
   exper : Craft           0.023*           0.0126             1.83           0.0674 
      exper : WC          0.00691            0.014            0.495            0.621 
     exper : Pro          0.00106           0.0144           0.0735            0.941 
       educ : BC          -0.0994            0.102           -0.972            0.331 
    educ : Craft          0.193**           0.0775             2.49           0.0126 
       educ : WC          0.259**           0.0935             2.77          0.00555 
      educ : Pro         0.426***           0.0922             4.62        3.91e-006 
      white : BC            1.24*            0.724             1.71           0.0878 
   white : Craft           -0.764            0.632            -1.21            0.227 
      white : WC              1.1            0.819             1.34            0.179 
     white : Pro            0.203            0.869            0.233            0.815 
-----------------------------------------------------------------------------------------------
Comparisons to Menial
*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 
      exper : BC           1.0047          0.97105           1.0396 
   exper : Craft           1.0232          0.99836           1.0487 
      exper : WC           1.0069          0.97974           1.0349 
     exper : Pro           1.0011          0.97328           1.0296 
       educ : BC          0.90536           0.7409           1.1063 
    educ : Craft           1.2132           1.0422           1.4122 
       educ : WC           1.2961            1.079           1.5568 
      educ : Pro           1.5307           1.2775           1.8339 
      white : BC           3.4435          0.83244           14.245 
   white : Craft          0.46573          0.13484           1.6086 
      white : WC           3.0013          0.60334            14.93 
     white : Pro            1.225          0.22293           6.7313 
----------------------------------------------------------------------------
Comparisons to Menial

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

Variables       Coefficient     se              tstat           pval            
exper            0.00113        ( 0.000788)      1.43            0.153          
educ             0.0211***      ( 0.00491)       4.29            2.33e-005      
white            0.0468         ( 0.0386)        1.21            0.227          
---------------------------------------------------------------------------
Comparisons to Menial 
Estimate se in parentheses.
*p-val<0.1 **p-val<0.05 ***p-val<0.001

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

Variables       Coefficient     se              tstat           pval            
exper            0.00357        ( 0.00646)       0.553           0.581          
educ             0.0124         ( 0.0346)        0.357           0.721          
white            0.449          ( 0.289)         1.56            0.121          
---------------------------------------------------------------------------
Comparisons to Menial 
Estimate se in parentheses.
*p-val<0.1 **p-val<0.05 ***p-val<0.001

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

Variables       Coefficient     se              tstat           pval            
exper            0.00723*       ( 0.00401)       1.8             0.0722         
educ             0.0793**       ( 0.0347)        2.28            0.023          
white           -0.106          ( 0.173)        -0.614           0.54           
---------------------------------------------------------------------------
Comparisons to Menial 
Estimate se in parentheses.
*p-val<0.1 **p-val<0.05 ***p-val<0.001

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

Variables       Coefficient     se              tstat           pval            
exper            0.00118        ( 0.00107)       1.1             0.272          
educ             0.0326**       ( 0.0109)        2.99            0.00301        
white            0.115*         ( 0.0648)        1.77            0.0774         
---------------------------------------------------------------------------
Comparisons to Menial 
Estimate se in parentheses. 
*p-val<0.1 **p-val<0.05 ***p-val<0.001

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

Variables       Coefficient     se              tstat           pval            
exper            0.00212        ( 0.00434)       0.489           0.625          
educ             0.139***       ( 0.0337)        4.13            4.63e-005      
white            0.127          ( 0.256)         0.497           0.619          
---------------------------------------------------------------------------
Comparisons to Menial 
Estimate se in parentheses. 
*p-val<0.1 **p-val<0.05 ***p-val<0.001
In addition, the mode produces a number of summary statistics for diagnostics:
********************SUMMARY STATISTICS********************

MEASURES OF FIT:

  -2 Ln(Lu):                                   853.6010 
  -2 Ln(Lr): All coeffs equal zero            1084.7612 
  -2 Ln(Lr): J-1 intercepts                   1019.6881 
  LR Chi-Square (coeffs equal zero):           231.1602 
       d.f.                                     16.0000 
       p-value =                                 0.0000 
  LR Chi-Square (J-1 intercepts):              166.0872 
       d.f.                                     12.0000 
       p-value =                                 0.0000 
  Count R2, Percent Correctly Predicted:       147.0000 
  Adjusted Percent Correctly Predicted:          0.1556 
  Madalla's pseudo R-square:                     0.3891 
  McFadden's pseudo R-square:                    0.1629 
  Ben-Akiva and Lerman's Adjusted R-square:      0.1570 
  Cragg and Uhler's pseudo R-square:             0.0325 
  Akaike Information Criterion:                  2.6279 
  Bayesian Information Criterion1:               0.1814 
  Hannan-Quinn Information Criterion:            2.7002 


OBSERVED AND PREDICTED OUTCOMES

           |                    Predicted
  Observed |     Y01      Y02      Y03      Y04      Y05    Total 
  ----------------------------------------------------------------------------
       Y01 |       0       21        6        0        4       31 
       Y02 |       0       57        6        0        6       69 
       Y03 |       0       60       10        0       14       84 
       Y04 |       0       24        3        0       14       41 
       Y05 |       0       24        8        0       80      112 

  ----------------------------------------------------------------------------
     Total |       0      186       33        0      118      337 

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