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