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:
struct dcControl dcCt;
Next, the
dcSet procedures are used for data setup:
dcSetYVar(&dcCt,y[.,1]);
dcSetYLabels(&dcCt,"occatt");
dcSetXVars(&dcCt,y[.,2:4]);
dcSetXLabels(&dcCt,"exper,educ,white");
dcSetReferenceCategory(&dcCt,1);
The
dcOut structure is declared:
struct dcout dcout1;
Finally, calling the
adjacentCategories procedure estimates the model and results are reported using the
printDCOut procedure:
dcout1 = adjacentCategories(dcCt);
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