GAUSS Bayesian Estimation Tools

GAUSS Bayesian Estimation Tools

Posterior distribution of lambda
The GAUSS Bayesian Estimation Tools package provides a suite of tools for estimation and analysis of a number of pre-packaged models. The internal GAUSS Bayesian models provide quickly accessible, full-stage modeling including data generation, estimation, and post-estimation analysis. Modeling flexibility is provided through control structures for setting modeling parameters, such as burn-in periods, total iterations and others.

GAUSS Bayesian internal models include

  • Univariate and multivariate linear models
  • Linear models with auto-correlated error terms
  • HB Interaction and HB mixture models
  • Probit models
  • Logit models
  • Dynamic two-factor model
  • SVAR models with sign restrictions

Data loading and data generation

Users may load data into GAUSS for estimation and analysis using standard intrinsic GAUSS procedures. However, in addition, the Bayesian Analysis Module includes a data generation feature that allows users to specify true data parameters to build hypothetical data sets for analysis.

Individual modeling

Users can meet individual modeling needs by specifying key controls for the estimation algorithm including:

  • Number of saved iterations
  • Number of iterations to skip
  • Number of burn-in iterations
  • Total number of iterations
  • Inclusion of an intercept

Easy to interpret stored results

Posterior distribution of sigma

The Bayesian application module stores all results in a single output structure. In addition the Bayesian module graphs draws of all parameters and the posterior distributions for all parameters.

  • Draws for all parameters at each iteration
  • Posterior mean for all parameters
  • Posterior standard deviation for all parameters
  • Predicted values
  • Residuals
  • Correlation matrix between Y and Yhat
  • PDF values and corresponding PDF grid for all posterior distributions
  • Log-likelihood value (when applicable)

Sample output report for probit model

Model Type: Probit regression model
*************************************************************
Possible underlying (unobserved) choice generation:
Agent selects one alternative:
Y[ij] = X[j]*beta_i + epsilon[ij]
epsilon[ij]~N(0,Sigma)
*************************************************************
Y[ij] is mvar vector
Y[ij] is utility from subject i, choice set j, alternative k
where	i = 1, ..., numSubjects
			j = 1, ..., numChoices
			k = 1, ..., numAlternatives - 1
*************************************************************
X[j] is numAlternative x rankX for choice j
*************************************************************
Pick alternative k if:
Y[ijk] > max( Y[ijl] )
for all k < mvar+1 and l not equal to k
Select base alternative if max(Y)<0
*************************************************************
Observed model:
*************************************************************
Choice vector C[ij] is a numAlternative vector of 0/1
beta_i = Theta'Z[i] + delta[i]
delta[i]~N(0,Lambda)
*************************************************************

Summary stats of independent data

*****************************************
Summary stats for X variables
*****************************************

        Variable             Mean              STD              MIN              MAX 
              X1          0.33333          0.47538                0                1 
              X2          0.33333          0.47538                0                1 
              X3          0.33333          0.47538                0                1 
              X4          0.28648          0.20641        -0.083584          0.71157 
              X5         0.083333          0.59065               -1                1 

*****************************************
Summary stats for Z variables
*****************************************

        Variable             Mean              STD              MIN              MAX 
              Y1         -0.10328           1.1582          -6.1714           3.7266 
              Y2         -0.23821           1.1428          -6.1295           3.2853 
              Y3         -0.28473           1.2776          -5.4752             4.58 

*****************************************
Summary stats for dependent variables
*****************************************

        Variable             Mean              STD              MIN              MAX 
              Y1         -0.10328           1.1582          -6.1714           3.7266 
              Y2         -0.23821           1.1428          -6.1295           3.2853 
              Y3         -0.28473           1.2776          -5.4752             4.58 

***********************************
MCMC Analysis Setup
***********************************
Total number of iterations:     1100.0 
Total number of saved iterations:     1000.0 
Number of iterations in transition period:     100.00 
Number of iterations between saved iterations:     0.0000 
Number of obs:    60.000 
Number of independent variables:    5.0000 
(excluding deterministic terms)
Number of dependent variables:    3.0000 


********************************
MCMC Analysis Results
********************************

***********************************
Error Standard Deviation
***********************************
Variance-Covariance Means(Sigma)

        Equation               Y1               Y2               Y3 
              Y1          0.20831         0.078641         -0.12772 
              Y2         0.078641          0.26217        -0.078051 
              Y3         -0.12772        -0.078051                1 

***********************************
Error Standard Deviation
***********************************
Variance-Covariance Means (Lambda)

        Equation            Beta1            Beta2            Beta3            Beta4            Beta5 
           Beta1         0.038024        0.0084823        0.0050414        -0.010463       -0.0044786 
           Beta2        0.0084823         0.038058        0.0061952       -0.0098521        0.0017846 
           Beta3        0.0050414        0.0061952         0.080755       -0.0086755         0.016158 
           Beta4        -0.010463       -0.0098521       -0.0086755          0.10271        -0.010493 
           Beta5       -0.0044786        0.0017846         0.016158        -0.010493         0.046216 

***********************************
Theta for Z Equation     1.0000 
***********************************

        Variable         PostMean          PostSTD 
          Theta1          0.53176          0.43012 
          Theta2          0.43195          0.35411 
          Theta3        -0.011848       0.00015526 
          Theta4          -2.0511          -1.9772 
          Theta5           1.0605           1.1038 

***********************************
Theta for Z Equation     2.0000 
***********************************

        Variable         PostMean          PostSTD 
          Theta1          0.90016          0.79037 
          Theta2          0.37388          0.19278 
          Theta3         -0.32424         -0.37066 
          Theta4          0.69154          0.85307 
          Theta5         -0.26623         -0.19126 

***********************************
Theta for Z Equation     3.0000 
***********************************

        Variable         PostMean          PostSTD 
          Theta1         -0.24998          -0.2454 
          Theta2         -0.22883         -0.19728 
          Theta3        -0.043585         0.026509 
          Theta4         -0.29718         -0.30046 
          Theta5          0.52032          0.50741 

Platform: Windows, Mac, and Linux

Requirements: GAUSS/GAUSS Engine/GAUSS Light v13.1 or higher