GAUSS Stereotypical Multinomial Logit Example

This example runs the stereotypical multinomial 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 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 
//Dependent variable
dcSetYVar(&dcCt,y[.,1]);
dcSetYLabel(&dcCt,"ABC");

//Independent variables 
dcSetXVars(&dcCt,y[.,2:4]);
dcSetXLabels(&dcCt,"GPA,TUCE,PSI");

//Category Labels
dcSetYCategoryLabels(&dcCt,"A,B,C");

Estimate the Model

The Ordered Logit Model can be estimated using the stereoLogit. 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 stereoLogit
dcout1 = stereoLogit(dcCt);

//Print Results
call printDCOut(dcOut1);

Output

The output from stereoLogit reads

Stereo Logistic Results
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
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 --------------------------------------------------------------------------- *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
********************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 Criterion: 2.2852 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

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