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
