BayesSingleSub (version 0.6.2)

trendtest.Gibbs.AR: Obtain Bayesian trend test and posterior distributions for single case data

Description

This function computes Bayes factors for the trend and intercept differences between two phases of a single subject data sequence, using Gibbs sampling. Posterior samples of parameters are also provided.

Usage

trendtest.Gibbs.AR(before, after, iterations = 1000,  intArea = c(-0.2,0.2), slpArea = c(-0.2, 0.2),  leftSidedInt = TRUE, leftSidedSlp = TRUE,  r.scaleInt = 1, r.scaleSlp = 1, 
		  alphaTheta = 1, betaTheta = 5, sdMet = 0.3,  progress = TRUE, return.chains = FALSE, return.onesided = 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.

intArea

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

slpArea

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

leftSidedInt

Only used if return.onesided = TRUE. Should the one sided Bayes factor for the intercept difference be one sided?

leftSidedSlp

Only used if return.onesided = TRUE. Should the one sided Bayes factor for the trend difference be one sided?

r.scaleInt

Prior scale for the intercept difference (see Details below).

r.scaleSlp

Prior scale for the trend difference (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?.

return.onesided

Return one sided Bayes factors?

Value

A list containing the following:

logbf

MCMC estimates of the log two sided point null Bayes factors, 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. MCMC estimates of the log two sided interval null Bayes factors.

logbfOnesided

Only returned if return.onesided=TRUE. MCMC estimates of the log one sided point null Bayes factors.

Details

This function computes Bayes factors for the differences in trend and intercept between two data sequences from a single subject, using Gibbs sampling. The Bayes factor for trend difference compares the null hypothesis of no true trend difference against the alternative hypothesis of a true trend difference. The Bayes factor for intercept difference compares the null hypothesis of no true intercept difference against the alternative hypothesis of a true intercept difference. Also, a joined Bayes factor for the trend and intercept combined is provided. Bayes factors larger than 1 support the null hypothesis, Bayes factors smaller than 1 support 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), sig*delta (difference between intercepts), beta0 (overall trend), sig*beta1 (difference between trends), sig2 (variance of the random shocks), and rho (auto-correlation).

Cauchy priors are placed on the standardized trend and intercept differences. The r.scaleInt and r.scaleSlp arguments control the scales of these Cauchy priors, with r.scaleInt = 1 and r.scaleSlp = 1 yielding standard Cauchy priors. 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 theta. 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.

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

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

Examples

## 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 factors
logBFs = trendtest.Gibbs.AR(data[1:10], data[11:25])

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