postPP {ppRep}

Posterior density of effect size and power parameter

Description

This function computes the posterior density of effect size \theta and power parameter \alpha assuming a normal likelihood for original and replication effect estimate. A power prior for \theta is constructed by updating an initial normal prior \theta \sim \mathrm{N}(\code{m}, \code{v}) with the likelihood of the original data raised to the power of \alpha. A marginal beta prior \alpha \sim \mbox{Beta}(\code{x},\code{y}) is assumed.

Usage

postPP(theta, alpha, tr, sr, to, so, x = 1, y = 1, m = 0, v = Inf, ...)

Arguments

theta

Effect size. Has to be of length one or the same length as alpha.

alpha

Power parameter. Has to be of length one or the same length as theta.

tr

Effect estimate of the replication study.

sr

Standard error of the replication effect estimate.

to

Effect estimate of the original study.

so

Standard error of the replication effect estimate.

x

Number of successes parameter of beta prior for \alpha. Defaults to 1.

y

Number of failures parameter of beta prior for \alpha. Defaults to 1.

m

Mean parameter of initial normal prior for \theta. Defaults to 0.

v

Variance parameter of initial normal prior for \theta. Defaults to Inf (uniform prior).

...

Additional arguments passed to stats::integrate.

Value

Posterior density

Author(s)

Samuel Pawel

See Also

postPPalpha, postPPtheta, plotPP

Examples

alpha <- seq(0, 1, length.out = 200)
theta <- seq(0, 0.3, length.out = 200)
parGrid <- expand.grid(alpha = alpha, theta = theta)
postdens <- postPP(theta = parGrid$theta, alpha = parGrid$alpha, tr = 0.1,
                   sr = 0.05, to = 0.2, so = 0.05)
postdensMat <- matrix(data = postdens, ncol = 200, byrow = TRUE)
filled.contour(x = theta, y = alpha, z = postdensMat,
               xlab = bquote("Effect size" ~ theta),
               ylab = bquote("Power parameter" ~ alpha), nlevels = 15,
               color.palette = function(n) hcl.colors(n = n, palette = "viridis"))