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

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