trendtest.MC.AR: Obtain Bayesian trend test or single case data
In BayesSingleSub: Computation of Bayes factors for interrupted time-series designs

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

This function computes Bayes factors for the trend and intercept differences between two phases of a single subject data sequence, using Monte Carlo integration.

1	trendtest.MC.AR(before, after, iterations = 1000, r.scaleInt = 1, r.scaleSlp = 1, alphaTheta = 1, betaTheta = 5, progress = TRUE)

`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.
`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).
`progress`	Report progress with a text progress bar?

This function computes Bayes factors for the differences in trend and intercept between two data sequences from a single subject, using monte carlo integration. 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.

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 handled by removing the locations of the missing data from the design matrix and error covariance matrix.

A matrix containing the Monte carlo estimates of the log Bayes factors.

To obtain posterior distributions and interval null Bayes factors, see trendtest.Gibbs.AR.

Richard D. Morey and Rivka de Vries

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

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

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

## 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.MC.AR(data[1:10], data[11:25])

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