# Discrete Choice Examples - Ordered Logit

### 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;

## 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     1.0000```
In 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
--------------------------------------------------------------
*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
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

----------------------------------------------------------
Total |      11       15        6       32```

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