ttest.Gibbs.AR: Obtain Bayesian t test and posterior distributions for single...

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

This function computes a Bayes factor for the mean difference between two phases of a single subject data sequence, using Gibbs sampling. Posterior samples of parameters are also provided.

Usage

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ttest.Gibbs.AR(before, after, iterations = 1000, areaNull = c(-0.2, 0.2), treat = NULL, r.scale = 1, alphaTheta = 1, 
		betaTheta = 5, sdMet = 0.3, progress = TRUE, return.chains = FALSE)

Arguments

before

A vector of observations, in time order, taken in Phase 1 (e.g., before the treatment).

after

A vector of observations, in time order, taken in Phase 2 (e.g., after the treatment).

iterations

Number of Gibbs sampler iterations to perform.

areaNull

Only used if return.chains=TRUE. Bounds for the interval null hypothesis for delta.

treat

Vector of dummy coding, indicating Phase 1 and Phase 2; default is -.5 for Phase 1 and .5 for Phase 2.

r.scale

Prior scale for delta (see Details below).

alphaTheta

The alpha parameter of the beta prior on theta (see Details below).

betaTheta

The beta parameter of the beta prior on theta (see Details below).

sdMet

Scale for the Metropolis-Hastings sampling of theta (see Details below).

progress

Report progress with a text progress bar?

return.chains

Return posterior samples of parameters?.

Details

This function computes a Bayes factor for the mean difference between two data sequences from a single subject, using Gibbs sampling. The Bayes factor compares the null hypothesis of no true mean difference against the alternative hypothesis of a true mean difference. A Bayes factor larger than 1 supports the null hypothesis, a Bayes factor smaller than 1 supports the alternative hypothesis. Auto-correlation of the errors is modeled by a first order auto-regressive process.

Posterior distributions of the model parameters can also be obtained. Model parameters of interest include mu0 (overall mean), delta (standardized mean difference), sig2 (variance of the random shocks), and rho (auto-correlation).

A Cauchy prior is placed on the standardized mean difference delta. The r.scale argument controls the scale of this Cauchy prior, with r.scale=1 yielding a standard Cauchy prior. A noninformative Jeffreys prior is placed on the variance of the random shocks of the auto-regressive process. A beta prior is placed on the auto-correlation rho. The alphaTheta and betaTheta arguments control the form of this beta prior.

Missing data are sampled from the likelihood function, conditioned at the observed data, at each iteration of the Gibbs sampler.

Value

if return.chains=FALSE: a scalar giving an MCMC estimate of the log Bayes factor, computed using the Savage-Dickey method (Morey, Rouder, Pratte, and Speckman, submitted) if return.chains=TRUE: a list containing the following:

logbf

An MCMC estimate of the log Bayes factor, computed using the Savage-Dickey method (Morey, Rouder, Pratte, and Speckman, submitted).

chains

Only returned if return.chains=TRUE. An object of type MCMC containing the chains for each parameter.

acc

Only returned if return.chains=TRUE. The Metropolis-Hastings acceptance rate.

logbfArea

Only returned if return.chains=TRUE. An MCMC estimate of the log interval null Bayes factor.

Note

For a more accurate method of computing the Bayes factor, see ttest.MCGQ.AR.

Author(s)

Richard D. Morey and Rivka de Vries

References

De Vries, R. M. \& Morey, R. D. (submitted). Bayesian hypothesis testing Single-Subject Data. Psychological Methods.

R code guide: http://drsmorey.org/research/rdmorey/

See Also

ttest.MCGQ.AR, trendtest.Gibbs.AR, trendtest.MC.AR

Examples

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## Define data
data = c(87.5, 82.5, 53.4, 72.3, 94.2, 96.6, 57.4, 78.1, 47.2,
 80.7, 82.1, 73.7, 49.3, 79.3, 73.3, 57.3, 31.7, 50.4, 77.8,
 67, 40.5, 1.6, 38.6, 3.2, 24.1)

## Obtain log Bayes factor
logBF = ttest.Gibbs.AR(data[1:10], data[11:25])

## Obtain log Bayes factor, chains, and log interval null Bayes factor
output = ttest.Gibbs.AR(data[1:10], data[11:25], return.chains = TRUE, areaNull = c(-0.2, 0.2))

## Look at the posterior distribution of the mean
plot(output$chains[,1])

## Obtain summary statistics of posterior distributions
summary(output$chains)

BayesSingleSub documentation built on May 2, 2019, 5:47 p.m.