pprior: Prior Cumulative Distribution Function (CDF)

In quentingronau/abtest: Bayesian A/B Testing

Description

Function for evaluating the prior cumulative distribution function (CDF).

Usage

pprior(
  q,
  prior_par = list(mu_psi = 0, sigma_psi = 1, mu_beta = 0, sigma_beta = 1),
  what = "logor",
  hypothesis = "H1"
)

Arguments

q	numeric vector with quantiles.
prior_par	list with prior parameters. This list needs to contain the following elements: mu_psi (prior mean for the normal prior on the test-relevant log odds ratio), sigma_psi (prior standard deviation for the normal prior on the test-relevant log odds ratio), mu_beta (prior mean for the normal prior on the grand mean of the log odds), sigma_beta (prior standard deviation for the normal prior on the grand mean of the log odds). Each of the elements needs to be a real number (the standard deviations need to be positive). The default are standard normal priors for both the log odds ratio parameter and the grand mean of the log odds parameter.
what	character specifying for which quantity the prior CDF should be evaluated. Either "logor" (i.e., log odds ratio) , "or" (i.e., odds ratio), "rrisk" (i.e., relative risk, the ratio of the "success" probability in the experimental and the control condition), or "arisk" (i.e., absolute risk, the difference of the "success" probability in the experimental and control condition).
hypothesis	character specifying whether to evaluate the CDF for a two-sided prior (i.e., "H1"), a one-sided prior with lower truncation point (i.e., "H+"), or a one-sided prior with upper truncation point (i.e., "H-").

Value

numeric vector with the values of the prior CDF.

Note

Internally, the test-relevant prior is always a normal prior on the log odds ratio, consequently, if what is not "logor", the implied prior CDF for the quantity is returned.

Author(s)

Quentin F. Gronau

Examples

# prior parameters
prior_par <- list(mu_psi = 0, sigma_psi = 1,
                  mu_beta = 0, sigma_beta = 1)

# evaluate prior CDF
pprior(q = 0.1, prior_par = prior_par, what = "logor")
pprior(q = 1.1, prior_par = prior_par, what = "or")
pprior(q = 1.05, prior_par = prior_par, what = "rrisk")
pprior(q = 0.02, prior_par = prior_par, what = "arisk")

# also works for vectors
pprior(q = c(-0.1, 0, 0.1, 0.2), prior_par = prior_par, what = "logor")

quentingronau/abtest documentation built on Nov. 23, 2021, 1:43 a.m.