GAUSS Binary Logit Model

This example runs the binary logit model using the GAUSS DC application. It uses a version of the education program effectiveness data originally collected by Spector and Mazzeo (1980). The dataset includes 32 observations of 6 different variables: letter grade (ABC), grade point average (GPA ), an indicator of participation in a personalized system of instruction (PSI), student test scores on an economics test (TUCE), and indicators of if the student received an A (A) or A+ (APLUS1).

Load the data

This example uses the formula string syntax to load data using loadd. The formula string syntax syntax allows users to load, transform and analyze data in one line.

new;
cls;
library dc;

//Load data
fname = getGAUSShome() $+ "examples/dc/aldnel.dat";
y = loadd(fname);

Set up the model parameters

The Discrete Choice Module uses a suite of dcSet functions to set various features of the model. An instance of the dcControl structure must be declared for storing all parameters prior to calling any dcSet functions.

//Step one: Declare dc control structure
struct dcControl dcCt;
//Initialize dc control structure
dcCt = dcControlCreate();

//Step two: Describe data names
//Name of dependent variable
dcSetYVar(&dcCt,y[.,5]);
dcSetYLabel(&dcCt,"A");

//Name of independent variable
dcSetXVars(&dcCt,y[.,2:4]);
dcSetXLabels(&dcCt,"GPA, TUCE, PSI");

Estimate the Model

The binary logit model can be estimated using the binaryLogit procedure. This function takes a dcControl structure as an input and returns all output to a dcOut structure. In addition, a complete report of results can be printed to screen using the printDCOut procedure.

//Step three: Declare dcOut struct 
struct dcout dcout1;

//Step four: Call binary logit procedure
dcout1 = binaryLogit(dcCt);

//Print Results
call printDCOut(dcOut1);

Output

The output from binaryLogit model reads

Binary Logit Results
Number of Observations:   32
Degrees of Freedom:       28

  1 - Y0
  2 - Y1

Distribution Among Outcome Categories For A
Dependent Variable       Proportion
Y0 0.6563
Y1 0.3438
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
COEFFICIENTS Coefficient Estimates -------------------------------------------------------------------------------- Variables Coefficient se tstat pval Constant: Y0 -13** 4.93 -2.64 0.00828 GPA 2.83** 1.26 2.24 0.0252 TUCE 0.0952 0.142 0.672 0.501 PSI 2.38** 1.06 2.23 0.0255 -------------------------------------------------------------------------------- *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 16.88 1.4201 200.63 TUCE 1.0998 0.83336 1.4515 PSI 10.791 1.3393 86.941 ---------------------------------------------------------------------------- MARGINAL EFFECTS
Partial probability with respect to mean x Marginal Effects for X Variables in Y1 category --------------------------------------------------------------------------- Variables Coefficient se tstat pval
GPA 0.534** ( 0.237) 2.25 0.0321
TUCE 0.018 ( 0.0262) 0.685 0.499
PSI 0.449** ( 0.197) 2.28 0.0299
--------------------------------------------------------------------------- Estimate se in parentheses. *p-val<0.1 **p-val<0.05 ***p-val<0.001
********************SUMMARY STATISTICS******************** MEASURES OF FIT: -2 Ln(Lu): 25.7793 -2 Ln(Lr): All coeffs equal zero 44.3614 -2 Ln(Lr): J-1 intercepts 41.1835 LR Chi-Square (coeffs equal zero): 18.5822 d.f. 4.0000 p-value = 0.0000 LR Chi-Square (J-1 intercepts): 15.4042 d.f. 3.0000 p-value = 0.0015 Count R2, Percent Correctly Predicted: 26.0000 Adjusted Percent Correctly Predicted: 0.4545 Madalla's pseudo R-square: 0.3821 McFadden's pseudo R-square: 0.3740 Ben-Akiva and Lerman's Adjusted R-square: 0.2283 Cragg and Uhler's pseudo R-square: 0.2358 Akaike Information Criterion: 1.0556 Bayesian Information Criterion: 1.2388 Hannan-Quinn Information Criterion: 1.1163 OBSERVED AND PREDICTED OUTCOMES | Predicted Observed | Y0 Y1 Total ------------------------------------------------- Y0 | 18 3 21 Y1 | 3 8 11 ------------------------------------------------- Total | 21 11 32

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