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#' @title b_success_rate
#' @description Bayesian model for comparing test success rate.
#' @import rstan
#' @export
#' @param r a vector containing test results (0 - test was not solved successfully, 1 - test was solved successfully).
#' @param s a vector containing subject indexes. Starting index should be 1 and the largest subject index should equal the number of subjects.
#' @param priors List of parameters and their priors - b_prior objects. You can put a prior on the p (mean probability of success) and tau (variance) parameters (default = NULL).
#' @param warmup Integer specifying the number of warmup iterations per chain (default = 1000).
#' @param iter Integer specifying the number of iterations (including warmup, default = 2000).
#' @param chains Integer specifying the number of parallel chains (default = 4).
#' @param seed Random number generator seed (default = NULL).
#' @param refresh Frequency of output (default = NULL).
#' @param control A named list of parameters to control the sampler's behavior (default = NULL).
#' @param suppress_warnings Suppress warnings returned by Stan (default = TRUE).
#' @return An object of class `success_rate_class`.
#'
#' @examples
#' \donttest{
#' # priors
#' p_prior <- b_prior(family="beta", pars=c(1, 1))
#' tau_prior <- b_prior(family="uniform", pars=c(0, 500))
#'
#' # attach priors to relevant parameters
#' priors <- list(c("p", p_prior),
#' c("tau", tau_prior))
#'
#' # generate data
#' s <- rep(1:5, 20)
#' data <- rbinom(100, size=1, prob=0.6)
#'
#' # fit
#' fit <- b_success_rate(r=data, s=s, priors=priors, chains=1)
#' }
#'
b_success_rate <- function(r,
s,
priors=NULL,
warmup=1000,
iter=2000,
chains=4,
seed=NULL,
refresh=NULL,
control=NULL,
suppress_warnings=TRUE) {
# multi core
if (chains > 1) {
options(mc.cores = parallel::detectCores())
}
# prepare data
n <- length(r)
m <- length(unique(s))
# prior ids and values
p_ids <- rep(0, 2)
p_values <- rep(0, 4)
# parameter mapping
df_pars <- data.frame(par=c("p", "tau"), index=c(1, 2))
# priors
if (!is.null(priors)) {
for (p in priors) {
par <- p[[1]]
prior <- p[[2]]
# get parameter index
id <- 0
par_id <- df_pars[df_pars$par==par,]
if (nrow(par_id) > 0) {
id <- par_id$index
} else {
wrong_prior <- "Provided an unknown parameter for prior, use \"p\" or \"tau\"."
warning(wrong_prior)
return()
}
# set prior family id
p_ids[id] <- get_prior_id(prior)
if (p_ids[id] == 0) {
wrong_prior <- "Provided an unknown prior family, use \"uniform\", \"normal\", \"gamma\" or \"beta\"."
warning(wrong_prior)
return()
}
# set parameter values
if (length(prior@pars) != 2) {
wrong_pars <- "Incorrect prior parameters, provide a vector of 2 numerical values."
warning(wrong_pars)
return()
}
p_values[2*id-1] <- prior@pars[1]
p_values[2*id] <- prior@pars[2]
}
}
# put data together
stan_data <- list(n=n,
m=m,
r=r,
s=s,
p_ids = p_ids,
p_values = p_values)
# set seed
if (is.null(seed)) {
seed <- sample.int(.Machine$integer.max, 1)
}
# set output frequency
if (is.null(refresh)) {
refresh <- max(iter/10, 1)
}
# fit
if (suppress_warnings) {
fit <- suppressWarnings(sampling(stanmodels$success_rate,
data=stan_data,
iter=iter,
warmup=warmup,
chains=chains,
seed=seed,
refresh=refresh,
control=control))
} else {
fit <- sampling(stanmodels$success_rate,
data=stan_data,
iter=iter,
warmup=warmup,
chains=chains,
seed=seed,
refresh=refresh,
control=control)
}
# extract and parse into list
extract_raw <- extract(fit, permuted=FALSE)
# p0
i <- 1
p0 <- extract_raw[, 1, i]
# tau
i <- i + 1
tau <- extract_raw[, 1, i]
# p
i <- i + 1
j <- i + m - 1
p <- extract_raw[, 1, i:j]
# lp__
i <- i + m
lp__ <- extract_raw[, 1, i]
extract <- list(p0=p0,
tau=tau,
p=p,
lp__=lp__)
# create output class
out <- success_rate_class(extract=extract, data=stan_data, fit=fit)
# return
return(out)
}
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