Stereotypical Logit Example
This example demonstrates the use of a stereotypical multinomial logit model. It models grade (
ABC) achievement rates in a Economics course in relationship to cumulative grade point average (
GPA), literacy test score (
TUCE), and optional participation in a special economics course (
PSI).
The first step to setting up all Discrete Choice models is to declare and initialize the
dcControl structure:
struct dcControl dcCt;
dcCt = dcControlCreate();
Next, load and setup the model data using the
dcSet procedures:
loadm y = aldnel_mat;
dcSetYVar(&dcCt,y[.,1]);
dcsetYLabel(&dcCt,"ABC");
dcSetYCategoryLabels(&dcCt,"A,B,C");
dcSetXVars(&dcCt,y[.,2:4]);
dcsetXLabels(&dcCt,"GPA, TUCE, PSI");
Following data setup, declare the
dcOut structure:
struct dcout dcout1;
Finally, call the
stereoLogit procedure:
dcout1 = binaryLogit(dcCt);
call printDCOut(dcOut1);
The example prints the model and data description to screen:
Stereo Logistic Results
2015-05-21 07:09:28
Number of Observations: 32
Degrees of Freedom: 26
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
All coefficients, odds ratios, and marginal effects are printed:
COEFFICIENTS
Coefficient Estimates
---------------------------------------------------------------------------
Variables Coefficient se tstat pval
Constant: A 11.3** 4.93 2.3 0.0213
Constant: C 16** 6.28 2.55 0.0107
GPA -4.38** 2.1 -2.09 0.037
TUCE -0.0693 0.177 -0.391 0.695
PSI -2.54* 1.31 -1.94 0.0525
Distance: B 0.655** 0.259 2.53 0.0114
---------------------------------------------------------------------------
Estimate se in parentheses.
*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 0.012486 0.00020319 0.76723
TUCE 0.93308 0.65965 1.3198
PSI 0.078949 0.0060662 1.0275
Distance: B 1.9242 1.1586 3.1956
----------------------------------------------------------------------------
MARGINAL EFFECTS
Partial probability with respect to mean x
Marginal Effects for X Variables in A category
---------------------------------------------------------------------------
Variables Coefficient se tstat pval
GPA -0.644** ( 0.255) -2.53 0.0171
TUCE -0.0102 ( 0.0265) -0.384 0.704
PSI -0.373* ( 0.214) -1.75 0.0914
---------------------------------------------------------------------------
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 -2.79* ( 1.54) -1.82 0.0796
TUCE -0.0441 ( 0.119) -0.37 0.714
PSI -1.62 ( 1.21) -1.34 0.191
---------------------------------------------------------------------------
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 -1.38* ( 0.767) -1.8 0.0817
TUCE -0.0219 ( 0.0606) -0.36 0.721
PSI -0.801 ( 0.671) -1.19 0.242
---------------------------------------------------------------------------
Estimate se in parentheses.
*p-val<0.1 **p-val<0.05 ***p-val<0.001
In addition a number of summary statistics for model diagnostics are printed:
********************SUMMARY STATISTICS********************
MEASURES OF FIT:
-2 Ln(Lu): 52.3305
-2 Ln(Lr): All coeffs equal zero 70.3112
-2 Ln(Lr): J-1 intercepts 69.0937
LR Chi-Square (coeffs equal zero): 17.9806
d.f. 6.0000
p-value = 0.0000
LR Chi-Square (J-1 intercepts): 16.7631
d.f. 4.0000
p-value = 0.0021
Count R2, Percent Correctly Predicted: 20.0000
Adjusted Percent Correctly Predicted: 0.3684
Madalla's pseudo R-square: 0.4078
McFadden's pseudo R-square: 0.2426
Ben-Akiva and Lerman's Adjusted R-square: 0.1558
Cragg and Uhler's pseudo R-square: 0.0898
Akaike Information Criterion: 2.0103
Bayesian Information Criterion1: 0.2748
Hannan-Quinn Information Criterion: 2.1014
OBSERVED AND PREDICTED OUTCOMES
| Predicted
Observed | A B C Total
----------------------------------------------------------
A | 8 3 0 11
B | 2 9 2 13
C | 1 4 3 8
----------------------------------------------------------
Total | 11 16 5 32
