BayesMed (version 1.0.1)

jzs_partcorSD: A default Bayesian hypothesis test for partial correlation using the Savage-Dickey method.

Description

This function can be used to perform a default Bayesian hypothesis test for partial correlation, using the Savage-Dickey method (Dickey & Lientz, 1970). The test uses a Jeffreys-Zellner-Siow prior set-up (Liang et al., 2008).

Usage

jzs_partcorSD(V1, V2, control,  SDmethod = c("fit.st", "dnorm", "splinefun", "logspline"), alternative = c("two.sided", "less", "greater"), n.iter=10000,n.burnin=500,standardize=TRUE)

Arguments

V1

a numeric vector.

V2

a numeric vector of the same length as V1.

control

a numeric vector of the same length as V1 and V2. This variable is partialled out of the correlation between V1 and V2.

SDmethod

specify the precise method with which the density of the posterior distribution will be estimated in order to compute the Savage-Dickey ratio.

alternative

specify the alternative hypothesis for the correlation coefficient: two.sided, greater than zero, or less than zero.

n.iter

number of total iterations per chain (see the package R2jags). Defaults to 10000.

n.burnin

length of burn in, i.e. number of iterations to discard at the beginning(see the package R2jags). Defaults to 500.

standardize

logical. Should the variables be standardized? Defaults to TRUE.

Value

PartCoef

Mean of the posterior samples of the unstandardized partial correlation (the regression coefficient beta in the equation V2 = intercept + alpha*control + beta*V1).

BayesFactor

The Bayes factor for the correlation coefficient. A value greater than one indicates evidence in favor of correlation, a value smaller than one indicates evidence against correlation.

PosteriorProbability

The posterior probability for the existence of a correlation between V1 and V2.

beta

The posterior samples for the regression coefficient beta. This is the unstandardized partial correlation.

jagssamples

The JAGS output for the MCMC estimation of the path. This object can be used to construct a traceplot.

Warning

In some cases the SDmethod fit.st will fail to converge. If so, another optimization method is used, using different starting values. If the other optimization method does not converge either or gives you a negative Bayes factor (which is meaningless), you could try one of the other SDmethod options or see jzs_partcor.

References

Dickey, J. M., & Lientz, B. P. (1970). The weighted likelihood ratio, sharp hypotheses about chances, the order of a Markov chain. The Annals of Mathematical Statistics, 214-226.

Liang, F., Paulo, R., Molina, G., Clyde, M. A., & Berger, J. O. (2008). Mixtures of g priors for Bayesian variable selection. Journal of the American Statistical Association, 103(481), 410-423.

Nuijten, M. B., Wetzels, R., Matzke, D., Dolan, C. V., & Wagenmakers, E.-J. (2014). A default Bayesian hypothesis test for mediation. Behavior Research Methods. doi: 10.3758/s13428-014-0470-2

Wetzels, R., & Wagenmakers, E.-J. (2012). A Default Bayesian Hypothesis Test for Correlations and Partial Correlations. Psychonomic Bulletin & Review, 19, 1057-1064.

See Also

jzs_partcor, jzs_corSD

Examples

# simulate partially correlated data
X <- rnorm(50,0,1)
C <- .5*X + rnorm(50,0,1)
Y <- .3*X + .6*C + rnorm(50,0,1)

# run jzs_partcor
(res <- jzs_partcorSD(X,Y,C))

# plot posterior samples
plot(res$beta_samples)

# plot traceplot
plot(res$jagssamples)
# where the first chain (theta[1]) is for tau' and the second chain (theta[2]) for beta