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R/Hartley.R
In Frames2: Estimation in Dual Frame Surveys
#' @name Hartley
#' @aliases Hartley
#' @title Hartley estimator
#'
#' @description Produces estimates for population totals and means using Hartley estimator from survey data obtained
#' from a dual frame sampling design. Confidence intervals are also computed, if required.
#'
#' @usage Hartley(ysA, ysB, pi_A, pi_B, domains_A, domains_B, conf_level = NULL)
#' @param ysA A numeric vector of length \eqn{n_A} or a numeric matrix or data frame of dimensions \eqn{n_A} x \eqn{c} containing information about variable of interest from \eqn{s_A}.
#' @param ysB A numeric vector of length \eqn{n_B} or a numeric matrix or data frame of dimensions \eqn{n_B} x \eqn{c} containing information about variable of interest from \eqn{s_B}.
#' @param pi_A A numeric vector of length \eqn{n_A} or a square numeric matrix of dimension \eqn{n_A} containing first order or first and second order inclusion probabilities for units included in \eqn{s_A}.
#' @param pi_B A numeric vector of length \eqn{n_B} or a square numeric matrix of dimension \eqn{n_B} containing first order or first and second order inclusion probabilities for units included in \eqn{s_B}.
#' @param domains_A A character vector of size \eqn{n_A} indicating the domain each unit from \eqn{s_A} belongs to. Possible values are "a" and "ab".
#' @param domains_B A character vector of size \eqn{n_B} indicating the domain each unit from \eqn{s_B} belongs to. Possible values are "b" and "ba".
#' @param conf_level (Optional) A numeric value indicating the confidence level for the confidence intervals.
#' @details Hartley estimator of population total is given by
#' \deqn{\hat{Y}_H = \hat{Y}_a^A + \hat{\theta}\hat{Y}_{ab}^A + (1 - \hat{\theta})\hat{Y}_{ab}^B + \hat{Y}_b^B}
#' where \eqn{\hat{\theta} \in [0, 1]}. Optimum value for \eqn{\hat{\theta}} to minimize variance of the estimator is
#' \deqn{\hat{\theta}_{opt} = \frac{\hat{V}(\hat{Y}_{ab}^B) + \widehat{Cov}(\hat{Y}_b^B, \hat{Y}_{ab}^B) - \widehat{Cov}(\hat{Y}_a^A, \hat{Y}_{ab}^A)}{\hat{V}(\hat{Y}_{ab}^A) + \hat{V}(\hat{Y}_{ab}^B)}}
#' Taking into account the independence between \eqn{s_A} and \eqn{s_B}, an estimator for the variance of the Hartley estimator can be obtained as follows:
#' \deqn{\hat{V}(\hat{Y}_H) = \hat{V}(\hat{Y}_a^A + \hat{\theta}\hat{Y}_{ab}^A) + \hat{V}((1 - \hat{\theta})\hat{Y}_{ab}^B + \hat{Y}_b^B)}
#' If both first and second order probabilities are known, variances and covariances involved in calculation of \eqn{\hat{\theta}_{opt}} and \eqn{\hat{V}(\hat{Y}_H)} are estimated using functions \code{VarHT} and \code{CovHT}, respectively. If
#' only first order probabilities are known, variances are estimated using Deville's method and covariances are estimated using following expression
#' \deqn{\widehat{Cov}(\hat{X}, \hat{Y}) = \frac{\hat{V}(X + Y) - \hat{V}(X) - \hat{V}(Y)}{2}}
#' @return \code{Hartley} returns an object of class "EstimatorDF" which is a list with, at least, the following components:
#' \item{Call}{the matched call.}
#' \item{Est}{total and mean estimation for main variable(s).}
#' \item{VarEst}{variance estimation for main variable(s).}
#' If parameter \code{conf_level} is different from \code{NULL}, object includes component
#' \item{ConfInt}{total and mean estimation and confidence intervals for main variables(s).}
#' In addition, components \code{TotDomEst} and \code{MeanDomEst} are available when estimator is based on estimators of the domains. Component \code{Param} shows value of parameters involded in calculation of the estimator (if any).
#' By default, only \code{Est} component (or \code{ConfInt} component, if parameter \code{conf_level} is different from \code{NULL}) is shown. It is possible to access to all the components of the objects by using function \code{summary}.
#' @references Hartley, H. O. (1962)
#' \emph{Multiple Frames Surveys.}
#' Proceedings of the American Statistical Association, Social Statistics Sections, 203 - 206.
#' @references Hartley, H. O. (1974)
#' \emph{Multiple frame methodology and selected applications.}
#' Sankhya C, Vol. 36, 99 - 118.
#' @seealso \code{\link{JackHartley}}
#' @examples
#' data(DatA)
#' data(DatB)
#' data(PiklA)
#' data(PiklB)
#'
#' #Let calculate Hartley estimator for variable Feeding
#' Hartley(DatA$Feed, DatB$Feed, PiklA, PiklB, DatA$Domain, DatB$Domain)
#'
#' #Now, let calculate Hartley estimator and a 90% confidence interval
#' #for variable Leisure, considering only first order inclusion probabilities
#' Hartley(DatA$Lei, DatB$Lei, DatA$ProbA, DatB$ProbB, DatA$Domain,
#' DatB$Domain, 0.90)
#' @export
Hartley = function (ysA, ysB, pi_A, pi_B, domains_A, domains_B, conf_level = NULL)
{
cnames <- names(ysA)
ysA <- as.matrix(ysA)
ysB <- as.matrix(ysB)
pi_A <- as.matrix(pi_A)
pi_B <- as.matrix(pi_B)
if (any(is.na(ysA)))
stop("There are missing values in sample from frame A.")
if (any(is.na(ysB)))
stop("There are missing values in sample from frame B.")
if (any(is.na(pi_A)))
stop("There are missing values in inclusion probabilities from frame A.")
if (any(is.na(pi_B)))
stop("There are missing values in inclusion probabilities from frame B.")
if (any(is.na(domains_A)))
stop("There are missing values in domains from frame A.")
if (any(is.na(domains_B)))
stop("There are missing values in domains from frame B.")
if (nrow(ysA) != nrow(pi_A) | nrow(ysA) != length(domains_A) | length(domains_A) != nrow(pi_A))
stop("Arguments from frame A have different sizes.")
if (nrow(ysB) != nrow(pi_B) | nrow(ysB) != length(domains_B) | length(domains_B) != nrow(pi_B))
stop("Arguments from frame B have different sizes.")
if (ncol(ysA) != ncol(ysB))
stop("Number of variables does not match.")
if (length(which(domains_A == "a")) + length(which(domains_A == "ab")) != length(domains_A))
stop("Domains from frame A are not correct.")
if (length(which(domains_B == "b")) + length(which(domains_B == "ba")) != length(domains_B))
stop("Domains from frame B are not correct.")
cl <- match.call()
n_A <- nrow(ysA)
n_B <- nrow(ysB)
c <- ncol(ysA)
ysA <- cbind(rep(1, n_A), ysA)
ysB <- cbind(rep(1, n_B), ysB)
est <- matrix(, 2, c, dimnames = list(c("Total", "Mean"), cnames))
varest <- matrix(, 2, c, dimnames = list(c("Var. Total", "Var. Mean"), cnames))
totdom <- matrix(, 4, c, dimnames = list(c("Total dom. a", "Total dom. ab", "Total dom. b", "Total dom. ba"), cnames))
meandom <- matrix(, 4, c, dimnames = list(c("Mean dom. a", "Mean dom. ab", "Mean dom. b", "Mean dom. ba"), cnames))
par <- matrix(, 1, c, dimnames = list("theta", cnames))
if (is.null(conf_level))
interv <- NULL
else
interv <- matrix(, 6, c, dimnames = list(c("Total", "Lower Bound", "Upper Bound", "Mean", "Lower Bound", "Upper Bound"), cnames))
if (!is.null(dim(drop(pi_A))) & !is.null(dim(drop(pi_B)))) {
if (nrow(pi_A) != ncol(pi_A))
stop("Matrix of inclusion probabilities from frame A is not square.")
if (nrow(pi_B) != ncol(pi_B))
stop("Matrix of inclusion probabilities from frame B is not square.")
for (k in 1:(c+1)) {
data_a_A <- Domains(ysA[,k], domains_A, "a")
data_ab_A <- Domains(ysA[,k], domains_A, "ab")
data_b_B <- Domains(ysB[,k], domains_B, "b")
data_ab_B <- Domains(ysB[,k], domains_B, "ba")
Yhat_a_A <- HT (data_a_A, diag(pi_A))
Yhat_ab_A <- HT (data_ab_A, diag(pi_A))
Yhat_b_B <- HT (data_b_B, diag(pi_B))
Yhat_ab_B <- HT (data_ab_B, diag(pi_B))
Vhat_Yhat_a_A <- VarHT (data_a_A, pi_A)
Vhat_Yhat_ab_A <- VarHT (data_ab_A, pi_A)
Vhat_Yhat_b_B <- VarHT (data_b_B, pi_B)
Vhat_Yhat_ab_B <- VarHT (data_ab_B, pi_B)
Covhat_Yhat_a_A_Yhat_ab_A <- CovHT (data_a_A, data_ab_A, pi_A)
Covhat_Yhat_b_B_Yhat_ab_B <- CovHT (data_b_B, data_ab_B, pi_B)
theta_opt <- (Vhat_Yhat_ab_B + Covhat_Yhat_b_B_Yhat_ab_B - Covhat_Yhat_a_A_Yhat_ab_A) / (Vhat_Yhat_ab_A + Vhat_Yhat_ab_B)
if (theta_opt > 1 | theta_opt < 0) {
warning ("Optimal value of theta is smaller than 0 or greater than 1. Estimation V(Y_ab^B) / (V(Y_ab^A) + V(Y_ab^B)) has been used instead.")
theta_opt <- Vhat_Yhat_ab_B / (Vhat_Yhat_ab_A + Vhat_Yhat_ab_B)
}
if (k == 1){
domain_size_estimation <- c(Yhat_a_A, Yhat_ab_A, Yhat_b_B, Yhat_ab_B)
size_estimation <- Yhat_a_A + theta_opt * Yhat_ab_A + (1 - theta_opt) * Yhat_ab_B + Yhat_b_B
}
else
total_estimation <- Yhat_a_A + theta_opt * Yhat_ab_A + (1 - theta_opt) * Yhat_ab_B + Yhat_b_B
if (k > 1) {
totdom[,k-1] <- c(Yhat_a_A, Yhat_ab_A, Yhat_b_B, Yhat_ab_B)
meandom[,k-1] <- totdom[,k-1]/domain_size_estimation
par[,k-1] <- theta_opt
mean_estimation <- total_estimation / size_estimation
est[,k-1] <- c(total_estimation, mean_estimation)
Vhat_Yhat_Hartley <- Vhat_Yhat_a_A + theta_opt^2 * Vhat_Yhat_ab_A + (1 - theta_opt)^2 * Vhat_Yhat_ab_B + Vhat_Yhat_b_B + 2 * theta_opt * Covhat_Yhat_a_A_Yhat_ab_A + 2 * (1 - theta_opt) * Covhat_Yhat_b_B_Yhat_ab_B
Vhat_Ymeanhat_Hartley <- 1/size_estimation^2*Vhat_Yhat_Hartley
varest[,k-1] <- c(Vhat_Yhat_Hartley, Vhat_Ymeanhat_Hartley)
if (!is.null(conf_level)) {
total_upper <- total_estimation + qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Yhat_Hartley)
total_lower <- total_estimation - qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Yhat_Hartley)
mean_upper <- mean_estimation + qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Ymeanhat_Hartley)
mean_lower <- mean_estimation - qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Ymeanhat_Hartley)
interv[,k-1] <- c(total_estimation, total_lower, total_upper, mean_estimation, mean_lower, mean_upper)
}
}
}
}
else {
if (is.null(dim(drop(pi_A))) & is.null(dim(drop(pi_B)))){
for (k in 1:(c+1)) {
data_a_A <- Domains(ysA[,k], domains_A, "a")
data_ab_A <- Domains(ysA[,k], domains_A, "ab")
data_b_B <- Domains(ysB[,k], domains_B, "b")
data_ab_B <- Domains(ysB[,k], domains_B, "ba")
Yhat_a_A <- HT (data_a_A, pi_A)
Yhat_ab_A <- HT (data_ab_A, pi_A)
Yhat_b_B <- HT (data_b_B, pi_B)
Yhat_ab_B <- HT (data_ab_B, pi_B)
Vhat_Yhat_a_A <- varest (data_a_A, pik = pi_A)
Vhat_Yhat_ab_A <- varest (data_ab_A, pik = pi_A)
Vhat_Yhat_b_B <- varest (data_b_B, pik = pi_B)
Vhat_Yhat_ab_B <- varest (data_ab_B, pik = pi_B)
Covhat_Yhat_a_A_Yhat_ab_A <- (varest (Ys = ysA[,k], pik = pi_A) - Vhat_Yhat_a_A - Vhat_Yhat_ab_A)/2
Covhat_Yhat_b_B_Yhat_ab_B <- (varest (Ys = ysB[,k], pik = pi_B) - Vhat_Yhat_b_B - Vhat_Yhat_ab_B)/2
theta_opt <- (Vhat_Yhat_ab_B + Covhat_Yhat_b_B_Yhat_ab_B - Covhat_Yhat_a_A_Yhat_ab_A) / (Vhat_Yhat_ab_A + Vhat_Yhat_ab_B)
if (theta_opt > 1 | theta_opt < 0) {
warning ("Optimal value of theta is smaller than 0 or greater than 1. Estimation V(Y_ab^B) / (V(Y_ab^A) + V(Y_ab^B)) has been used instead.")
theta_opt <- Vhat_Yhat_ab_B / (Vhat_Yhat_ab_A + Vhat_Yhat_ab_B)
}
if (k == 1){
domain_size_estimation <- c(Yhat_a_A, Yhat_ab_A, Yhat_b_B, Yhat_ab_B)
size_estimation <- Yhat_a_A + theta_opt * Yhat_ab_A + (1 - theta_opt) * Yhat_ab_B + Yhat_b_B
}
else
total_estimation <- Yhat_a_A + theta_opt * Yhat_ab_A + (1 - theta_opt) * Yhat_ab_B + Yhat_b_B
if (k > 1) {
totdom[,k-1] <- c(Yhat_a_A, Yhat_ab_A, Yhat_b_B, Yhat_ab_B)
meandom[,k-1] <- totdom[,k-1]/domain_size_estimation
par[,k-1] <- theta_opt
mean_estimation <- total_estimation/size_estimation
est[,k-1] <- c(total_estimation, mean_estimation)
Vhat_Yhat_Hartley <- Vhat_Yhat_a_A + theta_opt^2 * Vhat_Yhat_ab_A + (1 - theta_opt)^2 * Vhat_Yhat_ab_B + Vhat_Yhat_b_B + 2 * theta_opt * Covhat_Yhat_a_A_Yhat_ab_A + 2 * (1 - theta_opt) * Covhat_Yhat_b_B_Yhat_ab_B
Vhat_Ymeanhat_Hartley <- 1/size_estimation^2*Vhat_Yhat_Hartley
varest[,k-1] <- c(Vhat_Yhat_Hartley, Vhat_Ymeanhat_Hartley)
if (!is.null(conf_level)) {
total_upper <- total_estimation + qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Yhat_Hartley)
total_lower <- total_estimation - qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Yhat_Hartley)
mean_upper <- mean_estimation + qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Ymeanhat_Hartley)
mean_lower <- mean_estimation - qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Ymeanhat_Hartley)
interv[,k-1] <- c(total_estimation, total_lower, total_upper, mean_estimation, mean_lower, mean_upper)
}
}
}
}
else
stop("Invalid option: Probability vector in one frame and probability matrix in the other frame. Type of probabilities structures must match.")
}
results = list(Call = cl, Est = est, VarEst = varest, TotDomEst = totdom, MeanDomEst = meandom, Param = par, ConfInt = interv)
class(results) = "EstimatorDF"
attr(results, "attributesDF") = conf_level
return(results)
}
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#' @name Hartley
#' @aliases Hartley
#' @title Hartley estimator
#'
#' @description Produces estimates for population totals and means using Hartley estimator from survey data obtained
#' from a dual frame sampling design. Confidence intervals are also computed, if required.
#'
#' @usage Hartley(ysA, ysB, pi_A, pi_B, domains_A, domains_B, conf_level = NULL)
#' @param ysA A numeric vector of length \eqn{n_A} or a numeric matrix or data frame of dimensions \eqn{n_A} x \eqn{c} containing information about variable of interest from \eqn{s_A}.
#' @param ysB A numeric vector of length \eqn{n_B} or a numeric matrix or data frame of dimensions \eqn{n_B} x \eqn{c} containing information about variable of interest from \eqn{s_B}.
#' @param pi_A A numeric vector of length \eqn{n_A} or a square numeric matrix of dimension \eqn{n_A} containing first order or first and second order inclusion probabilities for units included in \eqn{s_A}.
#' @param pi_B A numeric vector of length \eqn{n_B} or a square numeric matrix of dimension \eqn{n_B} containing first order or first and second order inclusion probabilities for units included in \eqn{s_B}.
#' @param domains_A A character vector of size \eqn{n_A} indicating the domain each unit from \eqn{s_A} belongs to. Possible values are "a" and "ab".
#' @param domains_B A character vector of size \eqn{n_B} indicating the domain each unit from \eqn{s_B} belongs to. Possible values are "b" and "ba".
#' @param conf_level (Optional) A numeric value indicating the confidence level for the confidence intervals.
#' @details Hartley estimator of population total is given by
#' \deqn{\hat{Y}_H = \hat{Y}_a^A + \hat{\theta}\hat{Y}_{ab}^A + (1 - \hat{\theta})\hat{Y}_{ab}^B + \hat{Y}_b^B}
#' where \eqn{\hat{\theta} \in [0, 1]}. Optimum value for \eqn{\hat{\theta}} to minimize variance of the estimator is
#' \deqn{\hat{\theta}_{opt} = \frac{\hat{V}(\hat{Y}_{ab}^B) + \widehat{Cov}(\hat{Y}_b^B, \hat{Y}_{ab}^B) - \widehat{Cov}(\hat{Y}_a^A, \hat{Y}_{ab}^A)}{\hat{V}(\hat{Y}_{ab}^A) + \hat{V}(\hat{Y}_{ab}^B)}}
#' Taking into account the independence between \eqn{s_A} and \eqn{s_B}, an estimator for the variance of the Hartley estimator can be obtained as follows:
#' \deqn{\hat{V}(\hat{Y}_H) = \hat{V}(\hat{Y}_a^A + \hat{\theta}\hat{Y}_{ab}^A) + \hat{V}((1 - \hat{\theta})\hat{Y}_{ab}^B + \hat{Y}_b^B)}
#' If both first and second order probabilities are known, variances and covariances involved in calculation of \eqn{\hat{\theta}_{opt}} and \eqn{\hat{V}(\hat{Y}_H)} are estimated using functions \code{VarHT} and \code{CovHT}, respectively. If
#' only first order probabilities are known, variances are estimated using Deville's method and covariances are estimated using following expression
#' \deqn{\widehat{Cov}(\hat{X}, \hat{Y}) = \frac{\hat{V}(X + Y) - \hat{V}(X) - \hat{V}(Y)}{2}}
#' @return \code{Hartley} returns an object of class "EstimatorDF" which is a list with, at least, the following components:
#' \item{Call}{the matched call.}
#' \item{Est}{total and mean estimation for main variable(s).}
#' \item{VarEst}{variance estimation for main variable(s).}
#' If parameter \code{conf_level} is different from \code{NULL}, object includes component
#' \item{ConfInt}{total and mean estimation and confidence intervals for main variables(s).}
#' In addition, components \code{TotDomEst} and \code{MeanDomEst} are available when estimator is based on estimators of the domains. Component \code{Param} shows value of parameters involded in calculation of the estimator (if any).
#' By default, only \code{Est} component (or \code{ConfInt} component, if parameter \code{conf_level} is different from \code{NULL}) is shown. It is possible to access to all the components of the objects by using function \code{summary}.
#' @references Hartley, H. O. (1962)
#' \emph{Multiple Frames Surveys.}
#' Proceedings of the American Statistical Association, Social Statistics Sections, 203 - 206.
#' @references Hartley, H. O. (1974)
#' \emph{Multiple frame methodology and selected applications.}
#' Sankhya C, Vol. 36, 99 - 118.
#' @seealso \code{\link{JackHartley}}
#' @examples
#' data(DatA)
#' data(DatB)
#' data(PiklA)
#' data(PiklB)
#'
#' #Let calculate Hartley estimator for variable Feeding
#' Hartley(DatA$Feed, DatB$Feed, PiklA, PiklB, DatA$Domain, DatB$Domain)
#'
#' #Now, let calculate Hartley estimator and a 90% confidence interval
#' #for variable Leisure, considering only first order inclusion probabilities
#' Hartley(DatA$Lei, DatB$Lei, DatA$ProbA, DatB$ProbB, DatA$Domain,
#' DatB$Domain, 0.90)
#' @export
Hartley = function (ysA, ysB, pi_A, pi_B, domains_A, domains_B, conf_level = NULL)
{
cnames <- names(ysA)
ysA <- as.matrix(ysA)
ysB <- as.matrix(ysB)
pi_A <- as.matrix(pi_A)
pi_B <- as.matrix(pi_B)
if (any(is.na(ysA)))
stop("There are missing values in sample from frame A.")
if (any(is.na(ysB)))
stop("There are missing values in sample from frame B.")
if (any(is.na(pi_A)))
stop("There are missing values in inclusion probabilities from frame A.")
if (any(is.na(pi_B)))
stop("There are missing values in inclusion probabilities from frame B.")
if (any(is.na(domains_A)))
stop("There are missing values in domains from frame A.")
if (any(is.na(domains_B)))
stop("There are missing values in domains from frame B.")
if (nrow(ysA) != nrow(pi_A) | nrow(ysA) != length(domains_A) | length(domains_A) != nrow(pi_A))
stop("Arguments from frame A have different sizes.")
if (nrow(ysB) != nrow(pi_B) | nrow(ysB) != length(domains_B) | length(domains_B) != nrow(pi_B))
stop("Arguments from frame B have different sizes.")
if (ncol(ysA) != ncol(ysB))
stop("Number of variables does not match.")
if (length(which(domains_A == "a")) + length(which(domains_A == "ab")) != length(domains_A))
stop("Domains from frame A are not correct.")
if (length(which(domains_B == "b")) + length(which(domains_B == "ba")) != length(domains_B))
stop("Domains from frame B are not correct.")
cl <- match.call()
n_A <- nrow(ysA)
n_B <- nrow(ysB)
c <- ncol(ysA)
ysA <- cbind(rep(1, n_A), ysA)
ysB <- cbind(rep(1, n_B), ysB)
est <- matrix(, 2, c, dimnames = list(c("Total", "Mean"), cnames))
varest <- matrix(, 2, c, dimnames = list(c("Var. Total", "Var. Mean"), cnames))
totdom <- matrix(, 4, c, dimnames = list(c("Total dom. a", "Total dom. ab", "Total dom. b", "Total dom. ba"), cnames))
meandom <- matrix(, 4, c, dimnames = list(c("Mean dom. a", "Mean dom. ab", "Mean dom. b", "Mean dom. ba"), cnames))
par <- matrix(, 1, c, dimnames = list("theta", cnames))
if (is.null(conf_level))
interv <- NULL
else
interv <- matrix(, 6, c, dimnames = list(c("Total", "Lower Bound", "Upper Bound", "Mean", "Lower Bound", "Upper Bound"), cnames))
if (!is.null(dim(drop(pi_A))) & !is.null(dim(drop(pi_B)))) {
if (nrow(pi_A) != ncol(pi_A))
stop("Matrix of inclusion probabilities from frame A is not square.")
if (nrow(pi_B) != ncol(pi_B))
stop("Matrix of inclusion probabilities from frame B is not square.")
for (k in 1:(c+1)) {
data_a_A <- Domains(ysA[,k], domains_A, "a")
data_ab_A <- Domains(ysA[,k], domains_A, "ab")
data_b_B <- Domains(ysB[,k], domains_B, "b")
data_ab_B <- Domains(ysB[,k], domains_B, "ba")
Yhat_a_A <- HT (data_a_A, diag(pi_A))
Yhat_ab_A <- HT (data_ab_A, diag(pi_A))
Yhat_b_B <- HT (data_b_B, diag(pi_B))
Yhat_ab_B <- HT (data_ab_B, diag(pi_B))
Vhat_Yhat_a_A <- VarHT (data_a_A, pi_A)
Vhat_Yhat_ab_A <- VarHT (data_ab_A, pi_A)
Vhat_Yhat_b_B <- VarHT (data_b_B, pi_B)
Vhat_Yhat_ab_B <- VarHT (data_ab_B, pi_B)
Covhat_Yhat_a_A_Yhat_ab_A <- CovHT (data_a_A, data_ab_A, pi_A)
Covhat_Yhat_b_B_Yhat_ab_B <- CovHT (data_b_B, data_ab_B, pi_B)
theta_opt <- (Vhat_Yhat_ab_B + Covhat_Yhat_b_B_Yhat_ab_B - Covhat_Yhat_a_A_Yhat_ab_A) / (Vhat_Yhat_ab_A + Vhat_Yhat_ab_B)
if (theta_opt > 1 | theta_opt < 0) {
warning ("Optimal value of theta is smaller than 0 or greater than 1. Estimation V(Y_ab^B) / (V(Y_ab^A) + V(Y_ab^B)) has been used instead.")
theta_opt <- Vhat_Yhat_ab_B / (Vhat_Yhat_ab_A + Vhat_Yhat_ab_B)
}
if (k == 1){
domain_size_estimation <- c(Yhat_a_A, Yhat_ab_A, Yhat_b_B, Yhat_ab_B)
size_estimation <- Yhat_a_A + theta_opt * Yhat_ab_A + (1 - theta_opt) * Yhat_ab_B + Yhat_b_B
}
else
total_estimation <- Yhat_a_A + theta_opt * Yhat_ab_A + (1 - theta_opt) * Yhat_ab_B + Yhat_b_B
if (k > 1) {
totdom[,k-1] <- c(Yhat_a_A, Yhat_ab_A, Yhat_b_B, Yhat_ab_B)
meandom[,k-1] <- totdom[,k-1]/domain_size_estimation
par[,k-1] <- theta_opt
mean_estimation <- total_estimation / size_estimation
est[,k-1] <- c(total_estimation, mean_estimation)
Vhat_Yhat_Hartley <- Vhat_Yhat_a_A + theta_opt^2 * Vhat_Yhat_ab_A + (1 - theta_opt)^2 * Vhat_Yhat_ab_B + Vhat_Yhat_b_B + 2 * theta_opt * Covhat_Yhat_a_A_Yhat_ab_A + 2 * (1 - theta_opt) * Covhat_Yhat_b_B_Yhat_ab_B
Vhat_Ymeanhat_Hartley <- 1/size_estimation^2*Vhat_Yhat_Hartley
varest[,k-1] <- c(Vhat_Yhat_Hartley, Vhat_Ymeanhat_Hartley)
if (!is.null(conf_level)) {
total_upper <- total_estimation + qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Yhat_Hartley)
total_lower <- total_estimation - qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Yhat_Hartley)
mean_upper <- mean_estimation + qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Ymeanhat_Hartley)
mean_lower <- mean_estimation - qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Ymeanhat_Hartley)
interv[,k-1] <- c(total_estimation, total_lower, total_upper, mean_estimation, mean_lower, mean_upper)
}
}
}
}
else {
if (is.null(dim(drop(pi_A))) & is.null(dim(drop(pi_B)))){
for (k in 1:(c+1)) {
data_a_A <- Domains(ysA[,k], domains_A, "a")
data_ab_A <- Domains(ysA[,k], domains_A, "ab")
data_b_B <- Domains(ysB[,k], domains_B, "b")
data_ab_B <- Domains(ysB[,k], domains_B, "ba")
Yhat_a_A <- HT (data_a_A, pi_A)
Yhat_ab_A <- HT (data_ab_A, pi_A)
Yhat_b_B <- HT (data_b_B, pi_B)
Yhat_ab_B <- HT (data_ab_B, pi_B)
Vhat_Yhat_a_A <- varest (data_a_A, pik = pi_A)
Vhat_Yhat_ab_A <- varest (data_ab_A, pik = pi_A)
Vhat_Yhat_b_B <- varest (data_b_B, pik = pi_B)
Vhat_Yhat_ab_B <- varest (data_ab_B, pik = pi_B)
Covhat_Yhat_a_A_Yhat_ab_A <- (varest (Ys = ysA[,k], pik = pi_A) - Vhat_Yhat_a_A - Vhat_Yhat_ab_A)/2
Covhat_Yhat_b_B_Yhat_ab_B <- (varest (Ys = ysB[,k], pik = pi_B) - Vhat_Yhat_b_B - Vhat_Yhat_ab_B)/2
theta_opt <- (Vhat_Yhat_ab_B + Covhat_Yhat_b_B_Yhat_ab_B - Covhat_Yhat_a_A_Yhat_ab_A) / (Vhat_Yhat_ab_A + Vhat_Yhat_ab_B)
if (theta_opt > 1 | theta_opt < 0) {
warning ("Optimal value of theta is smaller than 0 or greater than 1. Estimation V(Y_ab^B) / (V(Y_ab^A) + V(Y_ab^B)) has been used instead.")
theta_opt <- Vhat_Yhat_ab_B / (Vhat_Yhat_ab_A + Vhat_Yhat_ab_B)
}
if (k == 1){
domain_size_estimation <- c(Yhat_a_A, Yhat_ab_A, Yhat_b_B, Yhat_ab_B)
size_estimation <- Yhat_a_A + theta_opt * Yhat_ab_A + (1 - theta_opt) * Yhat_ab_B + Yhat_b_B
}
else
total_estimation <- Yhat_a_A + theta_opt * Yhat_ab_A + (1 - theta_opt) * Yhat_ab_B + Yhat_b_B
if (k > 1) {
totdom[,k-1] <- c(Yhat_a_A, Yhat_ab_A, Yhat_b_B, Yhat_ab_B)
meandom[,k-1] <- totdom[,k-1]/domain_size_estimation
par[,k-1] <- theta_opt
mean_estimation <- total_estimation/size_estimation
est[,k-1] <- c(total_estimation, mean_estimation)
Vhat_Yhat_Hartley <- Vhat_Yhat_a_A + theta_opt^2 * Vhat_Yhat_ab_A + (1 - theta_opt)^2 * Vhat_Yhat_ab_B + Vhat_Yhat_b_B + 2 * theta_opt * Covhat_Yhat_a_A_Yhat_ab_A + 2 * (1 - theta_opt) * Covhat_Yhat_b_B_Yhat_ab_B
Vhat_Ymeanhat_Hartley <- 1/size_estimation^2*Vhat_Yhat_Hartley
varest[,k-1] <- c(Vhat_Yhat_Hartley, Vhat_Ymeanhat_Hartley)
if (!is.null(conf_level)) {
total_upper <- total_estimation + qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Yhat_Hartley)
total_lower <- total_estimation - qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Yhat_Hartley)
mean_upper <- mean_estimation + qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Ymeanhat_Hartley)
mean_lower <- mean_estimation - qnorm(1 - (1 - conf_level) / 2) * sqrt(Vhat_Ymeanhat_Hartley)
interv[,k-1] <- c(total_estimation, total_lower, total_upper, mean_estimation, mean_lower, mean_upper)
}
}
}
}
else
stop("Invalid option: Probability vector in one frame and probability matrix in the other frame. Type of probabilities structures must match.")
}
results = list(Call = cl, Est = est, VarEst = varest, TotDomEst = totdom, MeanDomEst = meandom, Param = par, ConfInt = interv)
class(results) = "EstimatorDF"
attr(results, "attributesDF") = conf_level
return(results)
}
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