# R/confidence-interval-functions.R In scdhlm: Estimating Hierarchical Linear Models for Single-Case Designs

#### Defines functions CI_g.g_HPSCI_g.g_REMLcoverageCI_SMDCI_SMD_single

```CI_SMD_single <- function(delta, kappa, nu, V_delta, cover, bound) {
start_val <- suppressWarnings(J(nu) * (delta + c(-1, 1) * qt(1 - (1 - cover) / 2, df = nu) * sqrt(V_delta)) / kappa)
L <- kappa * nlminb(start = start_val[1],
objective = function(ncp) suppressWarnings((qt((1 - cover) / 2, df = nu, ncp=-ncp) + delta / kappa)^2),
lower = -bound, upper = bound)\$par
U <- kappa * nlminb(start = start_val[2],
objective = function(ncp) suppressWarnings((qt((1 - cover)  / 2, df = nu, ncp=ncp) - delta / kappa)^2),
lower = -bound, upper = bound)\$par
if (L == -bound * kappa) L <- start_val[1] * kappa
if (U == bound * kappa) U <- start_val[2] * kappa
c(L,U)
}

CI_SMD <- function(delta, kappa, nu, cover = 0.95, bound = 35) {
nu <- pmax(nu, 2.001)
V_delta = kappa^2 * nu / (nu - 2) + delta^2 * (nu / (nu - 2) - 1 / J(nu)^2)
mapply(CI_SMD_single, delta = delta, kappa = kappa, nu = nu, V_delta = V_delta,
MoreArgs = list(cover = cover, bound = bound))
}

coverage <- function(delta, CI) CI[1,] < delta & CI[2,] > delta

#' @method CI_g g_REML
#' @export

CI_g.g_REML <- function(g, cover = 0.95, bound = 35, symmetric = TRUE) {
delta <- g\$delta_AB
g_AB <- g\$g_AB
V_g_AB <- g\$V_g_AB
kappa <- g\$kappa
nu <- g\$nu
V_delta <- kappa^2 * nu / (nu - 2) + delta^2 * (nu / (nu - 2) - 1 / J(nu)^2)

if (symmetric) {

suppressWarnings(g_AB + c(-1, 1) * stats::qt(1 - (1 - cover) / 2, df = nu) * sqrt(V_g_AB))

} else{

CI_SMD_single(delta = delta, kappa = kappa, nu = nu, V_delta = V_delta,
cover = cover, bound = bound)

}

}

#' @method CI_g g_HPS
#' @export

CI_g.g_HPS <- function(g, cover = 0.95, bound = 35, symmetric = TRUE) {
kappa <- g\$theta
nu <- g\$nu
V_delta <- kappa^2 * nu / (nu - 2) + delta^2 * (nu / (nu - 2) - 1 / J(nu)^2)

if (symmetric) {

suppressWarnings(delta_adj + c(-1, 1) * stats::qt(1 - (1 - cover) / 2, df = nu) * sqrt(V_delta_adj))

} else {

CI_SMD_single(delta=delta, kappa=kappa, nu=nu, V_delta=V_delta,
cover=cover, bound=bound)

}

}
```

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scdhlm documentation built on March 31, 2023, 10:55 p.m.