# ivbma: Instrumental Variable Bayesian Model Averaging via... In ivbma: Bayesian Instrumental Variable Estimation and Model Determination via Conditional Bayes Factors

## Description

This function estimates an Instrumental Variable (IV) system while incorporating model uncertainty and performing model averaging using an MC3-within-Gibbs Sampler.

## Usage

 ```1 2``` ```ivbma(Y, X, Z, W, s = 1000, b = round(s/10), full = FALSE, odens = min(c(5000, s - b)), print.every = round(s/10), run.diagnostics = FALSE) ```

## Arguments

 `Y` n x 1 matrix. Response variable `X` n x r matrix. Endogenous variables `W` n x p matrix. Further explanatory variables. You are responsible for including an intercept. `Z` n x q matrix. Instrumental variables `s` integer. Number of iterations `b` integer. Number of iterations to discard as burn-in. `full` If full is TRUE then model selection is not performed `odens` Output density. How many samples from the posterior should be returned? Note that posterior expectations are taken over every sample after burn-in `print.every` After how many iterations should the progress be printed? `run.diagnostics` If TRUE, this will compute experimental diagnostics to assess the validity of the instruments in use. Note that this adds a non-negligible amount of computing time.

## Details

The function estimates the parameters based on the model

Y = [X W] * ρ + ε

X = [Z W] * λ + η

with

(ε_i, η_i)^T \sim N_2 ( 0,Σ)

and its extension to multiple endogenous variables. If `full` is set to `FALSE` model uncertainty is included using conditional Bayes factors.

## Value

 `rho` An odens x (r + p) matrix with sampled values for the outcome stage. Endogenous variables come first. `rho.bar` Posterior expectation of the outcome stage taken over all iterations `lambda` A (p + q) x r x odens array with sampled values for the parameters of the first stage regressions. Instruments come first. `lambda.bar` Posterior expectation of each first stage taken over all iterations `Sigma` odens sampled realizations of Sigma `Sigma.bar` Posterior expectation of Sigma taken over all iterations `M` Sampled first stage models `M.bar` Posterior first stage inclusion probabilities `L` Sampled second stage models `L.bar` Posterior second stage inclusion probabilities

If run.diagnostics was set to TRUE then you also receive

 `Sargan` Model averaged Sargan p-values. Lower values indicate lack of instrument validity `Bayesian.Sargan` An _Experimental_ Bayesian Sargan diagnostic based on Conditional Bayes Factors. Same direction as above

## Author(s)

Alex Lenkoski ([email protected])

## References

Anna Karl and Alex Lenkoski (2012). "Instrumental Variable Bayesian Model Averaging via Conditional Bayes Factors" http://arxiv.org/abs/1202.5846

`summary.ivbma` `ivbma.cv.study`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```set.seed(1) data(growth) attach(growth) ## To replicate KL, set s to 1e5 a <- ivbma(Y, X, Z, W, s = 1e2) summary(a, nms.U = c(names(Z), names(W)),nms.V = c(names(X), names(W))) detach(growth) set.seed(1) data(margarine) attach(margarine) ## To replicate KL, set s to 2.5e5 a <- ivbma(Y, X, Z, W, s=1e2) summary(a, nms.U = c(names(Z), names(W)),nms.V = c(names(X), names(W))) detach(margarine) ```

ivbma documentation built on May 29, 2017, 12:31 p.m.