# R/est_msaeRBns.R In msaeRB: Ratio Benchmarking for Multivariate Small Area Estimation

#' @title EBLUPs Ratio Benchmarking for Non Sampled Area based on a Multivariate Fay Herriot (Model 1)
#'
#' @description This function gives EBLUPs ratio benchmarking for non sampled area based on multivariate Fay-Herriot (Model 1)
#'
#' @param formula an object of class list of formula describe the fitted models
#' @param vardir matrix containing sampling variances of direct estimators. The order is: \code{var1, cov12, ..., cov1r, var2, cov23, ..., cov2r, ..., cov(r-1)(r), var(r)}
#' @param weight matrix containing proportion of units in small areas. The order is: \code{w1, w2, ..., w(r)}
#' @param cluster matrix containing cluster of auxiliary variables. The order is: \code{c1, c2, ..., c(r)}
#' @param samevar logical. If \code{TRUE}, the varians is same. Default is \code{FALSE}
#' @param MAXITER maximum number of iterations for Fisher-scoring. Default is 100
#' @param PRECISION coverage tolerance limit for the Fisher Scoring algorithm. Default value is \code{1e-4}
#' @param data dataframe containing the variables named in formula, vardir, and weight
#'
#' @return This function returns a list with following objects:
#' \item{eblup}{a list containing a value of estimators}
#' \itemize{
#'   \item est.eblup : a dataframe containing EBLUP estimators
#'   \item est.eblupRB : a dataframe containing ratio benchmark estimators
#' }
#'
#' \item{fit}{a list contining following objects:}
#' \itemize{
#'   \item method : fitting method, named "REML"
#'   \item convergence : logical value of convergence of Fisher Scoring
#'   \item iterations : number of iterations of Fisher Scoring algorithm
#'   \item estcoef : a data frame containing estimated model coefficients (\code{beta, std. error, t value, p-value})
#'   \item refvar : estimated random effect variance
#' }
#' \item{random.effect}{a data frame containing values of random effect estimators}
#' \item{agregation}{a data frame containing agregation of direct, EBLUP, and ratio benchmark estimation}
#' @export est_msaeRBns
#'
#' @import abind
#' @importFrom Matrix forceSymmetric
#' @importFrom stats model.frame na.omit model.matrix median pnorm rnorm
#' @importFrom MASS mvrnorm
#'
#' @examples
#' data(datamsaeRBns)
#'
#' # Compute EBLUP and Ratio Benchmark using auxiliary variables X1 and X2 for each dependent variable
#'
#' ## Using parameter 'data'
#' Fo = list(f1 = Y1 ~ X1 + X2,
#'           f2 = Y2 ~ X1 + X2,
#'           f3 = Y3 ~ X1 + X2)
#' vardir = c("v1", "v12", "v13", "v2", "v23", "v3")
#' weight = c("w1", "w2", "w3")
#' cluster = c("c1", "c2", "c3")
#'
#' est_msae = est_msaeRBns(Fo, vardir, weight, cluster, data = datamsaeRBns)
#'
#' ## Without parameter 'data'
#' Fo = list(f1 = datamsaeRBns$Y1 ~ datamsaeRBns$X1 + datamsaeRBns$X2, #' f2 = datamsaeRBns$Y2 ~ datamsaeRBns$X1 + datamsaeRBns$X2,
#'           f3 = datamsaeRBns$Y3 ~ datamsaeRBns$X1 + datamsaeRBns$X2) #' vardir = datamsaeRBns[, c("v1", "v12", "v13", "v2", "v23", "v3")] #' weight = datamsaeRBns[, c("w1", "w2", "w3")] #' cluster = datamsaeRBns[, c("c1", "c2", "c3")] #' #' est_msae = est_msaeRBns(Fo, vardir, weight, cluster) #' #' ## Return #' est_msae$eblup$est.eblupRB # to see the Ratio Benchmark estimators #' est_msaeRBns = function (formula, vardir, weight, cluster, samevar = FALSE, MAXITER = 100, PRECISION = 1e-04, data) { r = length(formula) if (r <= 1) stop("You should use est_saeRBns() for univariate") R_function = function(vardir, n, r) { if (r == 1) { R = diag(vardir) } else { R = matrix(rep(0, times = n * r * n * r), nrow = n * r, ncol = n * r) k = 1 for (i in 1:r) { for (j in 1:r) { if (i <= j) { mat0 = matrix(rep(0, times = r * r), nrow = r, ncol = r) mat0[i, j] = 1 matVr = diag(vardir[, k], length(vardir[, k])) R_hasil = kronecker(mat0, matVr) R = R + R_hasil k = k + 1 } } } R = forceSymmetric(R) R = R } return(as.matrix(R)) } if (!missing(data)) { formuladata = lapply(formula, function(x) model.frame(x, na.action = na.omit, data)) y = unlist(lapply(formula, function(x) model.frame(x, na.action = na.omit, data)[[1]])) X = Reduce(adiag, lapply(formula, function(x) model.matrix(x, data))) W = as.matrix(data[, weight]) n = length(y)/r if (!all(vardir %in% names(data))) stop("Object vardir is not appropriate with data.") if (length(vardir) != sum(1:r)) stop("Length of vardir is not appropriate with data. The length must be ", sum(1:r)) if (any(is.na(data[, weight]))) stop("Object weight contains NA values.") if (!all(weight %in% names(data))) stop("Object weight is not appropriate with data.") if (length(weight) != r) stop("Length of weight is not appropriate with data. The length must be ", r) if (!all(cluster %in% names(data))) stop("Object cluster is not appropriate with data.") if (length(cluster) != r) stop("Length of cluster is not appropriate with data. The length must be ", r) vardir = data[, vardir] cluster = as.matrix(data[, cluster]) } else { formuladata = lapply(formula, function(x) model.frame(x, na.action = na.omit)) y = unlist(lapply(formula, function(x) model.frame(x, na.action = na.omit)[[1]])) X = Reduce(adiag, lapply(formula, function(x) model.matrix(x))) W = as.matrix(weight) n = length(y)/r if ((dim(vardir)[1] != n) || (dim(vardir)[2] != sum(1:r))) stop("Object vardir is not appropriate with data. It must be ", n ," x ", sum(1:r) ," matrix.") if (any(is.na(weight))) stop("Object weight contains NA values.") if ((dim(weight)[1] != n) || (dim(weight)[2] != r)) stop("Object weight is not appropriate with data. It must be ", n ," x ", r ," matrix.") if (any(is.na(cluster))) stop("Object cluster contains NA values.") if ((dim(cluster)[1] != n) || (dim(cluster)[2] != r)) stop("Object cluster is not appropriate with data. It must be ", n ," x ", r ," matrix.") cluster = as.matrix(cluster) } y.matrix = matrix(as.vector(y), n, r) y.matrix[y.matrix == 0] = NA indexns = unique(which(is.na(y.matrix), arr.ind = TRUE)[, 1]) indexs = c(1:n)[-indexns] n.s = length(indexs) n.ns = n - n.s y.s = y.matrix[-indexns, ] y.s.vec = as.vector(y.s) vardir.s = vardir[-indexns, ] R = R_function(vardir.s, n.s, r) W.s = W[-indexns, ] W.s = prop.table(W.s, 2) Xindexns = c() for (i in 1:r) { Xindexns = c(Xindexns, indexns + rep(n, times = n.ns)*(i - 1)) } X.s = X[-Xindexns, ] y_names = sapply(formula, "[[", 2) Ir = diag(r) In = diag(n.s) dV = list() dV1 = list() for (i in 1:r) { dV[[i]] = matrix(0, nrow = r, ncol = r) dV[[i]][i, i] = 1 dV1[[i]] = kronecker(dV[[i]], In) } convergence = TRUE if (samevar) { Vu = median(diag(R)) k = 0 diff = rep(PRECISION + 1, r) while (any(diff > PRECISION) & (k < MAXITER)) { k = k + 1 Vu1 = Vu Gr = kronecker(Vu1, Ir) Gn = kronecker(Gr, In) V = as.matrix(Gn + R) Vinv = solve(V) XstVinv = t(Vinv %*% X.s) Q = solve(XstVinv %*% X.s) P = Vinv - t(XstVinv) %*% Q %*% XstVinv Py = P %*% y.s.vec s = (-0.5) %*% sum(diag(P)) + 0.5 %*% (t(Py) %*% Py) iF = 0.5 %*% sum(diag(P %*% P)) Vu = Vu1 + solve(iF) %*% s diff = abs((Vu - Vu1)/Vu1) } Vu = as.vector((rep(max(Vu, 0), r))) names(Vu) = y_names if (k >= MAXITER && diff >= PRECISION) { convergence = FALSE } Gn = kronecker(diag(Vu), In) V = as.matrix(Gn + R) Vinv = solve(V) XstVinv = t(Vinv %*% X.s) Q = solve(XstVinv %*% X.s) P = Vinv - t(XstVinv) %*% Q %*% XstVinv Py = P %*% y.s.vec beta = Q %*% XstVinv %*% y.s.vec res = y.s.vec - X.s %*% beta random.effect = data.frame(matrix(Gn %*% Vinv %*% res, n.s, r)) names(random.effect) = y_names se.b = sqrt(diag(Q)) t.value = beta/se.b p.value = 2 * pnorm(abs(as.numeric(t.value)), lower.tail = FALSE) coef = as.matrix(cbind(beta, se.b, t.value, p.value)) colnames(coef) = c("beta", "std. error", "t value", "p-value") rownames(coef) = colnames(X) } else { Vu = apply(matrix(diag(R), nrow = n.s, ncol = r), 2, median) k = 0 diff = rep(PRECISION + 1, r) while (any(diff > rep(PRECISION, r)) & (k < MAXITER)) { k = k + 1 Vu1 = Vu if (r == 1) { Gr = Vu1 } else { Gr = diag(as.vector(Vu1)) } Gn = kronecker(Gr, In) V = as.matrix(Gn + R) Vinv = solve(V) XstVinv = t(Vinv %*% X.s) Q = solve(XstVinv %*% X.s) P = Vinv - t(XstVinv) %*% Q %*% XstVinv Py = P %*% y.s.vec s = sapply(dV1, function(x) (-0.5) * sum(diag(P %*% x)) + 0.5 * (t(Py) %*% x %*% Py)) iF = matrix(unlist(lapply(dV1, function(x) lapply(dV1, function(y) 0.5 * sum(diag(P %*% x %*% P %*% y))))), r) Vu = Vu1 + solve(iF) %*% s diff = abs((Vu - Vu1)/Vu1) } Vu = as.vector(sapply(Vu, max, 0)) if (k >= MAXITER && diff >= PRECISION){ convergence = FALSE } if (r == 1) { Gr = Vu } else { Gr = diag(as.vector(Vu)) } Gn = kronecker(Gr, In) V = as.matrix(Gn + R) Vinv = solve(V) XtVinv = t(Vinv %*% X.s) Q = as.matrix(solve(XtVinv %*% X.s)) P = Vinv - t(XtVinv) %*% Q %*% XtVinv Py = P %*% y.s.vec beta = Q %*% XtVinv %*% y.s.vec res = y.s.vec - X.s %*% beta random.effect = data.frame(matrix(Gn %*% Vinv %*% res, n.s, r)) names(random.effect) = y_names se.b = sqrt(diag(Q)) t.value = beta/se.b p.value = 2 * pnorm(abs(as.numeric(t.value)), lower.tail = FALSE) coef = as.matrix(cbind(beta, se.b, t.value, p.value)) colnames(coef) = c("beta", "std. error", "t value", "p-value") rownames(coef) = colnames(X) } random.effect = data.frame(index = indexs, random.effect) random.effect.ns = data.frame(index = indexns, matrix(NA, n.ns, r)) names(random.effect.ns) = names(random.effect) random.effect = rbind(random.effect, random.effect.ns) random.effect = random.effect[order(random.effect$index), ]
rownames(random.effect) = random.effect$index random.effect = random.effect[ ,-1] random.effect.full = matrix(NA, nrow = n, ncol = r) colnames(random.effect.full) = y_names for (i in 1:r) { df = data.frame(cluster[, i], random.effect[, i]) for (j in 1:n) { if (df[j, 2] %in% NA) { df[j, 2] = mean(df[df[, 1] == df[j,1], 2], na.rm = TRUE) } } random.effect.full[ ,i] = df[, 2] } Xbeta = X %*% beta eblup = matrix(Xbeta, nrow = n, ncol = r) + random.effect.full eblup = as.data.frame(eblup) names(eblup) = y_names random.effect.full = as.data.frame(random.effect.full) eblup.mat = as.matrix(eblup) eblup.ratio = matrix(0, nrow = n, ncol = r) alfa = c() for (i in 1:r) { eblup.ratio[, i] = eblup.mat[, i] * (sum(W.s[, i] * y.s[, i])/sum(W[, i] * eblup.mat[, i])) } eblup.ratio = as.data.frame(eblup.ratio) names(eblup.ratio) = y_names agregation.direct = diag(t(W.s) %*% y.s) agregation.eblup = diag(t(W) %*% eblup.mat) agregation.eblup.ratio = diag(t(W) %*% as.matrix(eblup.ratio)) agregation = as.matrix(rbind(agregation.direct, agregation.eblup, agregation.eblup.ratio)) colnames(agregation) = y_names result = list(eblup = list(est.eblup = NA, est.eblupRB = NA), fit = list(method = NA, convergence = NA, iteration = NA, estcoef = NA, refvar = NA), random.effect = NA, agregation = NA) result$eblup$est.eblup = eblup result$eblup$est.eblupRB = eblup.ratio result$fit$method = "REML" result$fit$convergence = convergence result$fit$iteration = k result$fit$estcoef = coef result$fit$refvar = t(Vu) result$random.effect = random.effect.full
result\$agregation = agregation
return(result)
}


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msaeRB documentation built on June 13, 2021, 1:06 a.m.