# Obtain Bayesian trend test or 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 Monte Carlo integration.

### Usage

1 2 3 4 | ```
trendtest.MC.AR(before, after, iterations = 1000,
r.scaleInt = 1, r.scaleSlp = 1,
alphaTheta = 1, betaTheta = 5,
progress = TRUE)
``` |

### 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. |

`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? |

### Details

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.

### Value

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

### Note

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

`trendtest.Gibbs.AR`

, `ttest.Gibbs.AR`

, `ttest.MCGQ.AR`

### Examples

1 2 3 4 5 6 7 | ```
## 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])
``` |