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R: Approximate BCEE Implementation

ABCEE

R Documentation

Approximate BCEE Implementation

Description

A-BCEE implementation of the BCEE algorithm.

Usage

ABCEE(X, Y, U, omega, forX = NA, niter = 5000, nburn = 500, nthin = 10,
 maxmodelY = NA, OR = 20, family.X = "gaussian")

Arguments

`X`	A vector of observed values for the exposure.
`Y`	A vector of observed values for the continuous outcome.
`U`	A matrix of observed values for the `M` potential confounding covariates, where each column contains observed values for a potential confounding factor. A recommended implementation is to only consider pre-exposure covariates.
`omega`	The value of the hyperparameter omega in the BCEE's outcome model prior distribution. A recommended implementation is to take `omega` `=` `sqrt(n)*c`, where `n` is the sample size and `c` is a user-supplied constant value. Simulation studies suggest that values of `c` between 100 and 1000 yield good results.
`forX`	A Boolean vector of size `M`, where the `m`th element indicates whether or not the `m`th potential confounding covariate should be considered in the exposure modeling step of the BCEE algorithm. The default for `forX` is `NA`, which indicates that all potential confounding covariates should be considered in the exposure modeling step.
`niter`	The number of post burn-in iterations in the Markov chain Monte Carlo model composition (MC^3) algorithm (Madigan et al. 1995), prior to applying thinning. The default is 5000.
`nburn`	The number of burn-in iterations (prior to applying thinning). The default is 500.
`nthin`	The thinning of the chain. The default is 10.
`maxmodelY`	The maximum number of distinct outcome models that the algorithm can explore. Choosing a smaller value can shorten computing time. However, choosing a value that is too small will cause the algorithm to crash. The default is `NA`; the maximum number of outcome models that can be explored is then set to the minimum of `niter + nburn` and `2^M`.
`OR`	A number specifying the maximum ratio for excluding models in Occam's window for the exposure modeling step (see the `bic.glm` help file, and Madigan & Raftery, 1994). The default is 20.
`family.X`	A description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See `family` for details of family functions.) The default is `"gaussian"`

Details

The ABCEE function first computes the exposure model's posterior distribution using the bic.glm function. The outcome model's posterior distribution is then computed using MC^3 (Madigan et al., 1995) as described in Talbot et al. (2015).

ABCEE assumes there are no missing values in the objects X, Y and U. The na.omit function which removes cases with missing data or an imputation package might be helpful.

Value

`betas`	A vector containing the sampled values for the exposure effect.
`models.X`	A matrix giving the posterior distribution of the exposure model. Each row corresponds to an exposure model. Within each row, the first `M` elements are Booleans indicating the inclusion (1) or the exclusion (0) of each potential confounding factor. The last element gives the posterior probability of the exposure model.
`models.Y`	A Boolean matrix identifying the sampled outcome models. Each row corresponds to a sampled outcome model. Within each row, the `m`th element equals 1 if and only if the `m`th potential confounding covariate is included in the sampled outcome model (and 0 otherwise).

Author(s)

Denis Talbot, Genevieve Lefebvre, Juli Atherton.

References

Madigan, D., York, J., Allard, D. (1995) Bayesian graphical models for discrete data, International Statistical Review, 63, 215-232.

Madigan, D., Raftery, A. E. (1994) Model selection and accounting for model uncertainty in graphical models using Occam's window, Journal of the American Statistical Association, 89 (428), 1535-1546.

Talbot, D., Lefebvre, G., Atherton, J. (2015) The Bayesian causal effect estimation algorithm, Journal of Causal Inference, 3(2), 207-236.

Examples

# In this example, U1 and U2 are potential confounding covariates
# generated as independent N(0,1).
# X is generated as a function of both U1 and U2 with a N(0,1) error.
# Y is generated as a function of X and U1 with a N(0,1) error.
# Variable U1 is the only confounder.
# The causal effect of X on Y equals 1. 
# The exposure effect estimator (beta hat) in the outcome model  
# including U1 and U2 or including U1 only is unbiased.
# The sample size is n = 200.

# Generating the data
set.seed(418949); 
U1 = rnorm(200); 
U2 = rnorm(200);
X = 0.5*U1 + 1*U2 + rnorm(200);
Y = 1*X + 0.5*U1 + rnorm(200);

# Using ABCEE to estimate the causal exposure effect
n = 200;
omega.c = 500;
results = ABCEE(X,Y,cbind(U1,U2), omega = omega.c*sqrt(n),
 niter = 1000, nthin = 5, nburn = 20);

# The posterior mean of the exposure effect:
mean(results$betas);
# The posterior standard deviation of the exposure effect:
sd(results$betas);
# The posterior distribution of the exposure model:
results$models.X;
# The posterior probability of inclusion of each covariate:
colMeans(results$models.Y);
# The posterior distribution of the outcome model:
table(apply(results$models.Y, 1, paste0, collapse = ""));

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(BCEE)
Loading required package: BMA
Loading required package: survival
Loading required package: leaps
Loading required package: robustbase

Attaching package: 'robustbase'

The following object is masked from 'package:survival':

    heart

Loading required package: inline
Loading required package: rrcov
Scalable Robust Estimators with High Breakdown Point (version 1.3-11)

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/BCEE/ABCEE.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ABCEE
> ### Title: Approximate BCEE Implementation
> ### Aliases: ABCEE
> ### Keywords: causal confounding model average
> 
> ### ** Examples
> 
> # In this example, U1 and U2 are potential confounding covariates
> # generated as independent N(0,1).
> # X is generated as a function of both U1 and U2 with a N(0,1) error.
> # Y is generated as a function of X and U1 with a N(0,1) error.
> # Variable U1 is the only confounder.
> # The causal effect of X on Y equals 1. 
> # The exposure effect estimator (beta hat) in the outcome model  
> # including U1 and U2 or including U1 only is unbiased.
> # The sample size is n = 200.
> 
> # Generating the data
> set.seed(418949); 
> U1 = rnorm(200); 
> U2 = rnorm(200);
> X = 0.5*U1 + 1*U2 + rnorm(200);
> Y = 1*X + 0.5*U1 + rnorm(200);
> 
> # Using ABCEE to estimate the causal exposure effect
> n = 200;
> omega.c = 500;
> results = ABCEE(X,Y,cbind(U1,U2), omega = omega.c*sqrt(n),
+  niter = 1000, nthin = 5, nburn = 20);
> 
> # The posterior mean of the exposure effect:
> mean(results$betas);
[1] 0.9615841
> # The posterior standard deviation of the exposure effect:
> sd(results$betas);
[1] 0.05521132
> # The posterior distribution of the exposure model:
> results$models.X;
     [,1] [,2] [,3]
[1,]    1    1    1
> # The posterior probability of inclusion of each covariate:
> colMeans(results$models.Y);
[1] 1.000 0.375
> # The posterior distribution of the outcome model:
> table(apply(results$models.Y, 1, paste0, collapse = ""));

 10  11 
125  75 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>