postPPalpha {ppRep}

Marginal posterior distribution of power parameter

Description

These functions compute the marginal posterior of the power parameter \alpha. 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

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

postPPalphaHPD(level = 0.95, tr, sr, to, so, x = 1, y = 1, m = 0, v = Inf, ...)

Arguments

alpha

Power parameter. Can be a vector.

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 \alpha. Defaults to 1.

y

Number of failures parameter of beta prior \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.

level

Credibility level of the highest posterior density interval. Defaults to 0.95.

Value

postPPalpha returns the marginal posterior density of the power parameter.

postPPalphaHPD returns the highest marginal posterior density interval of the power parameter.

Author(s)

Samuel Pawel

See Also

postPP, postPPtheta, plotPP

Examples

alpha <- seq(0, 1, 0.001)
margpostdens <- postPPalpha(alpha = alpha, tr = 0.1, to = 0.2, sr = 0.05, so = 0.05)
plot(alpha, margpostdens, type = "l", xlab = bquote("Power parameter" ~ alpha),
     ylab = "Marginal posterior density", las = 1)