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#---------------------------------------------
#' Variance-covariance matrix for a bellreg model
#'
#' @aliases vcov.bellreg
#' @description This function extracts and returns the variance-covariance matrix associated with the regression coefficients when the maximum likelihood estimation approach is used in the model fitting.
#' @export
#' @param object an object of the class bellreg.
#' @param ... further arguments passed to or from other methods.
#' @return the variance-covariance matrix associated with the regression coefficients.
#'
#' @examples
#' \donttest{
#' data(faults)
#' fit <- bellreg(nf ~ lroll, data = faults)
#' vcov(fit)
#' }
#'
vcov.bellreg <- function(object, ...){
Delta <- object$Delta
V <- MASS::ginv(object$fit$hessian)
V <- Delta%*%V%*%t(Delta)
colnames(V) <- object$labels
rownames(V) <- object$labels
return(V)
}
#---------------------------------------------
#' Covariance of the regression coefficients
#'
#' @aliases vcov.zibellreg
#' @export
#' @param object an object of the class bellreg
#' @param ... further arguments passed to or from other methods.
#' @return the variance-covariance matrix associated with the regression coefficients.
#'
#' @examples
#' \donttest{
#' data(cells)
#' fit <- zibellreg(cells ~ smoker + gender|smoker + gender, data = cells)
#' vcov(fit)
#' }
#'
vcov.zibellreg <- function(object, ...){
Delta <- object$Delta
V <- MASS::ginv(object$fit$hessian)
V <- Delta%*%V%*%t(Delta)
colnames(V) <- with(object, c(labels1, labels2))
rownames(V) <- with(object, c(labels1, labels2))
return(V)
}
#---------------------------------------------
#' Estimated regression coefficients for the bellreg model
#'
#' @aliases coef.bellreg
#' @export
#' @param object an object of the class bellreg.
#' @param ... further arguments passed to or from other methods.
#' @return a vector with the estimated regression coefficients.
#'
#' @examples
#' \donttest{
#' data(faults)
#' fit <- bellreg(nf ~ lroll, data=faults)
#' coef(fit)
#' }
#'
coef.bellreg <- function(object, ...){
coeffs <- object$fit$par
names(coeffs) <- object$labels
return(coeffs)
}
#---------------------------------------------
#' Estimated regression coefficients for zibellreg model
#'
#' @aliases coef.zibellreg
#' @export
#' @param object an object of the class bellreg
#' @param ... further arguments passed to or from other methods
#' @return a list containing the the estimated regression coefficients associated with the degenerated and Bell count distributions, respectively.
#'
#' @examples
#' \donttest{
#' data(cells)
#' fit <- zibellreg(cells ~ smoker + gender|smoker + gender, data = cells)
#' coef(fit)
#' }
#'
coef.zibellreg <- function(object, ...){
coefs <- object$fit$par
p <- object$p
q <- object$q
coeffs1 <- coefs[1:q]
coeffs2 <- coefs[(q+1):(q+p)]
names(coeffs1) <- object$labels1
names(coeffs2) <- object$labels2
coeffs1
coeffs2
coeffs <- list("Degenerated dist." = coeffs1, "Bell dist." = coeffs2)
return(coeffs)
}
#---------------------------------------------
#' Confidence intervals for the regression coefficients
#'
#' @aliases confint.bellreg
#' @export
#' @param object an object of the class bellreg
#' @param parm a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
#' @param level the confidence level required
#' @param ... further arguments passed to or from other methods
#' @return A matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labelled as (1-level)/2 and 1 - (1-level)/2 in \% (by default 2.5\% and 97.5\%).
#'
#' @examples
#' \donttest{
#' data(faults)
#' fit <- bellreg(nf ~ lroll, data = faults)
#' confint(fit)
#' }
#'
confint.bellreg <- function(object, parm = NULL, level=0.95, ...){
p <- object$p
q <- object$q
V <- vcov(object)
par.hat <- object$fit$par[1:p]
alpha <- 1-level
d <- stats::qnorm(1 - alpha/2)*sqrt(diag(V))
lower <- par.hat - d
upper <- par.hat + d
CI <- cbind(lower, upper)
labels <- round(100*(c(alpha/2, 1-alpha/2)),1)
colnames(CI) <- paste0(labels, "%")
if(is.null(parm)){
return(CI)
}else{
CI <- CI[parm, ,drop = FALSE]
return(CI)
}
}
#---------------------------------------------
#' Confidence intervals for the regression coefficients
#'
#' @aliases confint.zibellreg
#' @export
#' @param object an object of the class zibellreg
#' @param parm a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
#' @param level the confidence level required
#' @param ... further arguments passed to or from other methods
#' @return 100(1-alpha)% confidence intervals for the regression coefficients
#'
#' @examples
#' \donttest{
#' data(cells)
#' fit <- zibellreg(cells ~ smoker+gender|smoker+gender, data = cells, approach = "mle")
#' confint(fit)
#' }
#'
confint.zibellreg <- function(object, parm = NULL, level=0.95, ...){
p <- object$p
q <- object$q
V <- vcov(object)
par.hat <- object$fit$par
alpha <- 1-level
d <- stats::qnorm(1 - alpha/2)*sqrt(diag(V))
lower <- par.hat - d
upper <- par.hat + d
ci <- cbind(lower, upper)
labels <- round(100*(c(alpha/2, 1-alpha/2)),1)
colnames(ci) <- paste0(labels, "%")
# if(!is.null(parm)){
# ci <- ci[parm, ,drop = FALSE]
# }
CI <- list("Degenerated dist." = ci[1:p, ], "Bell dist." = ci[(q+1):(q+p),])
return(CI)
}
# estimates <- function(object, parm = NULL, conf.level = 0.95, ...) UseMethod("estimates")
#
# estimates.bellreg <- function(object, parm = NULL, conf.level = 0.95){
# Estimate <- coef(object)
# CI <- confint(object)
# return(cbind(Estimate, CI))
# }
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