Introduction
This ordered logit example uses the Greene course performance data.The independent data, ABC, categorizes student grades in an economics course as A,B,or C. The dependent variables are cumulative grade point average (GPA), literacy test scores (TUCE), and participation in a special economics course (PSI).
Step 1: Load the data
new;
cls;
library dc;
// Load Data
loadm y = aldnel_mat;Step 2: Initialize control structure
Once this data is loaded, estimation features are specified using the dcControl structure. This structure must be declared then initialized:
// Declare dcControl structure
struct dcControl dcCt;
// Fill with default settings
dcCt = dcControlCreate();Step 3: Specify model parameters and data
Prior to estimation, the dcSet procedures are used to setup model parameters and data:
// Dependent variable
dcSetYVar(&dcCt,y[.,1]);
dcSetYLabels(&dcCt,"ABC");
// Category Labels
dcSetYCategoryLabels(&dcCt,"A,B,C");
// Independent variables
dcSetXVars(&dcCt,y[.,2:4]);
dcSetXLabels(&dcCt,"GPA,TUCE,PSI");Step 4: Declare results structure
Next, the dcOut structure is declared:
// Declare dcOut structure to hold results
struct dcout dcout1;Step 5: Perform estimation and print results
Finally, calling the orderedLogit procedure estimates the model and results are reported using the printDCOut procedure:
// Estimate ordered logit model
dcout1 = orderedLogit(dcCt);
// Print Results
call printDCOut(dcout1);The printDCOut procedure prints a model and data summary to the output screen:
Ordered Probit Results Number of Observations: 32 Degrees of Freedom: 27 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 1.0000In addition, coefficient estimates, odds ratios, and marginal effects are printed:
COEFFICIENTS
Coefficient Estimates
--------------------------------------------------------------
Variables Coefficient se tstat pval
GPA -3.23** 1.07 -3.03 0.00245
TUCE 0.00499 0.106 0.047 0.963
PSI -1.44* 0.824 -1.75 0.08
Threshold : 1 -11.5** 3.56 -3.24 0.00119
Threshold : 2 -8.89** 3.23 -2.75 0.00589
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*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 0.23615 0.046937 1.1881
TUCE 9.8391e-006 9.2206e-009 0.010499
PSI 0.0001372 2.4458e-007 0.076969
-------------------------------------------------------------
MARGINAL EFFECTS
Partial probability with respect to mean x
Marginal Effects for X Variables in A category
-------------------------------------------------------------
Variables Coefficient se tstat pval
GPA -0.914** (0.394) -2.32 0.0274
TUCE 0.00141 (0.0301) 0.0469 0.963
PSI -0.408 (0.272) -1.5 0.144
--------------------------------------------------------------
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 -1.82** (0.819) -2.22 0.0341
TUCE 0.00281 (0.0598) 0.047 0.963
PSI -0.813 (0.525) -1.55 0.132
-----------------------------------------------------------
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 -0.497** (0.226) -2.2 0.0357
TUCE 0.000768 (0.0164) 0.047 0.963
PSI -0.222 (0.133) -1.67 0.105
----------------------------------------------------------
Estimate se in parentheses.
*p-val<0.1 **p-val<0.05 ***p-val<0.001
Finally, the example also returns a number of summary statistics for model diagnostics:
********************SUMMARY STATISTICS********************
MEASURES OF FIT:
-2 Ln(Lu): 52.3256
-2 Ln(Lr): All coeffs equal zero 70.3112
-2 Ln(Lr): J-1 intercepts 69.0937
LR Chi-Square (coeffs equal zero): 17.9855
d.f. 5.0000
p-value = 0.0000
LR Chi-Square (J-1 intercepts): 16.7680
d.f. 3.0000
p-value = 0.0008
Count R2, Percent Correctly Predicted: 20.0000
Adjusted Percent Correctly Predicted: 0.3684
Madalla's pseudo R-square: 0.4079
McFadden's pseudo R-square: 0.2427
Ben-Akiva and Lerman's Adjusted R-square: 0.1558
Cragg and Uhler's pseudo R-square: 0.0899
Akaike Information Criterion: 1.9477
Bayesian Information Criterion1: 0.2290
Hannan-Quinn Information Criterion: 2.0236
OBSERVED AND PREDICTED OUTCOMES
| Predicted
Observed | Y01 Y02 Y03 Total
----------------------------------------------------------
Y01 | 8 3 0 11
Y02 | 3 8 2 13
Y03 | 0 4 4 8
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Total | 11 15 6 32