ttest.MCGQ.AR: Obtain Bayesian t test for 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

View source: R/notrendAR.R

This function computes a Bayes factor for the mean difference between two phases of a single subject data sequence, using Monte Carlo integration or Gaussian quadrature.

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ttest.MCGQ.AR(before, after, iterations = 1000, treat = NULL, 
            method = "MC", r.scale = 1, 
            alphaTheta = 1, betaTheta = 5)

`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.
`treat`	Vector of dummy coding, indicating Phase 1 and Phase 2; default is -.5 for Phase 1 and .5 for Phase 2.
`method`	Method to be used to compute the Bayes factor; "MC" is monte carlo integration, "GQ" is gaussian quadrature.
`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).

This function computes a Bayes factor for the mean difference between two data sequences from a single subject, using monte carlo integration or Gaussian quadrature. 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.

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 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 scalar giving the monte carlo or Gaussian quadrature estimate of the log Bayes factor.

To obtain posterior distributions and interval null Bayes factors, see ttest.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/

ttest.Gibbs.AR, trendtest.Gibbs.AR, trendtest.MC.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 factor
logBF = ttest.MCGQ.AR(data[1:10], data[11:25])