BAYESIAN ESTIMATION TOOLS
The 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.
DATA GENERATION TOOLS FOR BUILDING HYPOTHETICAL DATA SETS:
- Univariate and multivariate linear models
- Autoregressive error terms (AR)
- Hierarchical Bayes (HB)
- Probit and logit data
SUPPORTED MODELS FOR MARKOV CHAIN MONTE CARLO (MCMC) ESTIMATION:
- Univariate and multivariate linear models
- Autoregressive error terms (AR)
- Hierarchical Bayes (HB)
- Probit model
- Dynamic two-factor model
- Structural vector autoregressive (SVAR)
FLEXIBLE, USER DEFINED MCMC ESTIMATION PARAMETERS INCLUDING:
- Number of saved iterations
- Skipped iterations
- Burn-in iterations
- Total number of iterations
- Inclusion of intercept
- Optional graph and results output
- Elective maximum likelihood estimation (MLE) initialization
THOROUGH COMPUTATIONS INCLUDING:
- Draws for all parameters at each iteration
- Posterior mean of parameters
- Posterior standard deviation of parameters
- Predicted variable values and residuals
- Correlation matrix between observed and predicted data
- PDF values and corresponding PDF graphs
- Log-likelihood values (when applicable)
SAMPLE OUTPUT REPORT FOR PROBIT MODEL
Model Type: Probit regression model
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Possible underlying (unobserved) choice generation:
Agent selects one alternative:
Y[ij] = X[j]*beta_i + epsilon[ij]
epsilon[ij]~N(0,Sigma)
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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
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X[j] is numAlternative x rankX for choice j
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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
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Observed model:
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Choice vector C[ij] is a numAlternative vector of 0/1
beta_i = Theta'Z[i] + delta[i]
delta[i]~N(0,Lambda)
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Summary stats of independent data
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Summary stats for X variables
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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
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Summary stats for Z variables
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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
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Summary stats for dependent variables
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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
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MCMC Analysis Setup
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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
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MCMC Analysis Results
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Error Standard Deviation
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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
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Error Standard Deviation
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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
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Theta for Z Equation 1.0000
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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
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Theta for Z Equation 2.0000
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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
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Theta for Z Equation 3.0000
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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
