#Zu klären: soll die Funktion mit Intervallangaben umgehen können?
#Dann bräuchte man entweder zwei variablen oder eine in der das intervallangaben und präzise
#d.h. intervalllänge = 0 gemeinsam gespeichert sind.
#y <- c("1300", "2342", "[1000, 2000]", "2967", "NA") etc.
#Steinbruch
#imp_roundedcont_multi <- function(y.variable.name, data.org, intervall.obs, Y_lower, Y_upper, exclude_in_tmp.data2,
# cond,
# mn,
# allowed.max.value,
# allowed.max.variable,
# allowed.min.value,
# allowed.min.variable,
# max.se = NULL, impsyn = "imp", MLestimator.output.path = NULL){
#' The function to impute rounded continuous variables
#'
#' For example the income in surveys is often reported rounded by the respondents.
#' See Drechsler, Kiesl and Speidel (2015) for more details.
#' @param y_imp_multi A Vector with the variable to impute.
#' @param X_imp_multi A data.frame with the fixed effects variables.
#' @param Z_imp_multi A data.frame with the random effects variables.
#' @param clID A vector with the cluster ID.
#' @param intercept_varname A character denoting the name of the intercept variable.
#' @param M An integer defining the number of imputations that should be made.
#' @param allowed_max_value A single numeric Value which shall not be exceeded
#' when values are imputed (e.g. the age of a person can be limited to 125).
#' @param allowed_max_variable A character naming a variable V.
#' For each Y_i the value of V_i shall not exceeded
#' (e.g. the net income shall not exceed the gross income).
#' Note that a new imputed value has to satisfy both conditions of \code{allowed_max_value}
#' and \code{allowed_max_variable} at the same time.
#' @param allowed_min_value Analog to \code{allowed_max_value}.
#' @param allowed_min_variable Analog to \code{allowed_max_variable}.
#' @return A n x M matrix. Each column is one of M imputed y-variables.
#' @return Currently a vector with the completed variable that was to be imputed
#' (so it includes the unchanged originaly observed data
#' and the values that have been missing, but now are imputed) !!!MAKE IT FIT TO THE OTHER IMPUATION ROUTINES!!!
imp_roundedcont_multi <- function(y_imp_multi, X_imp_multi, Z_imp_multi, clID,
intercept_varname, M,
allowed_max_value = Inf,
allowed_max_variable = NULL,
allowed_min_value = -Inf,
allowed_min_variable = NULL){
#######################################################################
#MS: BEGIN get starting imputation values by maximizing the likelihood#
missind <- is.na(y_imp_multi)
#MS: Einkommensvariable befuellen, damit mit ihr richtig gearbeitet werden kann...
blob <- sample_imp(y_imp_multi)
#MS: ...wie zum Beispiel eine Designmatrix erstellen.
lmstart <- lm(blob ~ 0 + . , data = X_imp_multi)
MM_0 <- model.matrix(lmstart)
#MM_0 should be different to X_imp_multi if categorical covariates are present in X_imp_multi.
#betastart <- as.vector(lmstart$coef)
#Standardise variables, that are no intercept variables
MM_1a <- MM_0[, intercept_varname, drop = FALSE]
MM_1b <- apply(MM_0[, colnames(MM_0) != intercept_varname, drop = FALSE], 2, function(x) (x - mean(x))/sd(x)) #MS: standardisieren; Hinweis x darf keine NAs beeinhalten!
MM_1 <- as.data.frame(cbind(MM_1a, MM_1b))
inc <- y_imp_multi
n <- length(y_imp_multi)
mean.inc <- mean(inc, na.rm = TRUE)
sd.inc <- sd(inc, na.rm = TRUE)
inc.std <- (inc - mean.inc)/sd.inc
log.inc <- log(inc)
mean.log.inc <- mean(log.inc, na.rm = TRUE)
sd.log.inc <- sd(log.inc, na.rm = TRUE)
log.inc.std <- (log.inc - mean.log.inc)/sd.log.inc
#MS: Standardise all incomes (precise, lower- und upper bound)
#final.data2 <- data.org
#final.data2$std.Y_lower <- (log(Y_lower) - mean.log.inc)/sd.log.inc
#final.data2$std.Y_upper <- (log(Y_upper) - mean.log.inc)/sd.log.inc
log.inc.std.tmp <- sample_imp(log.inc.std)#MS: wird nur benoetigt um die designmatrix zu kriegen (?)
#lmstart2 <- lm(log.inc.std.tmp ~ 0 + ., data = MM_1)
##MS: preparing the ml estimation
###define rounding intervals
round_base <- c(1, 5, 10, 50, 100, 500, 1000)
intervals <- round_base/2
#check if which observation are rounded
#MS: %% berechnet den Modulo. Calculate the rounding degree only for those with not an missing value in inc
#MS: New approach with a p that will be of length equal to nrow(final.data2)
p1 <- y_imp_multi %% 5 == 0 # divisable by 5
p1[is.na(p1)] <- FALSE
p2 <- y_imp_multi %% 10 == 0 # divisable by 10
p2[is.na(p2)] <- FALSE
p3 <- y_imp_multi %% 50 == 0 # etc
p3[is.na(p3)] <- FALSE
p4 <- y_imp_multi %% 100 == 0 #
p4[is.na(p4)] <- FALSE
p5 <- y_imp_multi %% 500 == 0 #
p5[is.na(p5)] <- FALSE
p6 <- y_imp_multi %% 1000 == 0 #
p6[is.na(p6)] <- FALSE
p <- factor(p1 + p2 + p3 + p4 + p5 + p6, levels = c("0", "1", "2", "3", "4", "5", "6"))
#MS: p ist Vektor der fuer jede Beobachtung (indirekt) angibt durch welchen Faktor sie ohne Rest teilbar ist.
#MS: Bspw. bedeutet ein Wert von 4, dass der Wert von HEK0600 durch den Faktor 100 teilbar ist
#MS: (weil er durch jeweils durch 5, 10, 50 und 100, teilbar ist. Also 4 mal wurde "TRUE" aufsummiert, was 4 ergbit.)
###indicator which variables need to be imputed #MS: because they are rounded (and not because they are missing)
rounded <- p != 0
#MS: !!! Dass sich rounded die Daten ohne intervall-Beobachtungen zur Grundlage hat, macht das spaetere Arbeiten etwas schwierig
#MS: Q: Warum ist length(p > 0) == 8195, aber length(which(p > 0)) == 6980?
#MS: A: Weil in which(p > 0) ja nur die Indizes der Elemente angegeben sind, die das Kriterium p > 0 erfuellen.
#MS: vergleiche 1:10 >= 7 und which(1:10 >= 7)
#####maximum likelihood estimation using starting values
####estimation of the parameters
# estimation of the starting values for eta and the thresholds on the x-axis:
# ordered probit maximum possible rounding on the rounded in income data
probitstart <- MASS::polr(as.ordered(p[!missind]) ~ inc.std[!missind],
contrasts = NULL, Hess = TRUE, model = TRUE,
method = "probit")
etastart <- as.vector(probitstart$coefficients) # the fix effect(s)
kstart <- as.vector(probitstart$zeta) # the tresholds (in the summary labeled "Intercepts")
lmstart2 <- lm(log.inc.std[!missind] ~ 0 + ., data = MM_1[!missind, , drop = FALSE])
betastart2 <- as.vector(lmstart2$coef)
sigmastart2 <- summary(lmstart2)$sigma
#####maximum likelihood estimation using the starting values
#MS: Die ML-Schaetzer sind dann die Imputationsparameter fuer die improved imputation.
function_generator <- function(para, X, y_in_negloglik, myp, mean.log.inc, sd.log.inc){
ret <- function(para){
ret_tmp <- negloglik2(para = para, X = X, y_in_negloglik = y_in_negloglik, myp = myp,
mean.log.inc = mean.log.inc, sd.log.inc = sd.log.inc)
return(ret_tmp)
}
return(ret)
}
###exclude obs below (above) the 0.5% (99.5%) income quantile before maximizing
###the likelihood. Reason: Some extrem outliers cause problems during the
###maximization
#MS: bei der Imputation sollen sie spaeter vorhanden sein, weshalb hier ein Datensatz 'data.for.imp1' "abgespalten" werden koennte.
#MS: Alternativ kann man diese Beobachtungen einfach bei der Maximierung (der Likelihood) ausschliessen,
#MS: so dass nicht jeder weitere Schritt der Designmatrix-Erzeugung separat durchgefuehrt werden muss.
#MS: Alle weiteren Schritte (vorallem die Desingmatrix-Erzeugung) werden deshalb fuer jeden Datensatz separat durchgefuehrt.
quants <- quantile(y_imp_multi, c(0.005, 0.995), na.rm = TRUE)
outliers <- which(y_imp_multi < quants[1] | y_imp_multi > quants[2])
#MS: inc.intervall brauchen wir vermutlich hier nicht mehr.
negloglik2_generated <- function_generator(para = para,
X = MM_1[-outliers, , drop = FALSE],
y_in_negloglik = y_imp_multi[-outliers],
myp = as.numeric(as.character(p[-outliers])),
mean.log.inc = mean.log.inc,
sd.log.inc = sd.log.inc)
#MS:!!!STARTWERTE NUR ZUM CHECKEN, OB TATSAECHLICH MAXIMUM GEFUNDEN, MIT 0.7 MULTIPLIZIERT!!!
a <- Sys.time()
print(paste("Starting ML-Maximization to derive imputation parameters", Sys.time()))
m2 <- optim(par = c(kstart, betastart2, etastart, sigmastart2), negloglik2_generated, method = "BFGS",
control = list(maxit = 10000), hessian = TRUE)
#MS: da optim() standardmaessig minimiert muessen wir die Likelihood-Funktion "umdrehen"
#MS: also mit -1 multiplizieren.
#MS und diese entstandene negative log-likelihood minimierem um das Maximum der Likelihood zu bekommen.
#if(!is.null(MLestimator.output.path)) save(m2, file = MLestimator.output.path)
b <- Sys.time()
print(paste("Time to find maximum likelihood estimates under improved model:",
format(difftime(b, a, units = "mins"))))
#MS: dauert bei mir ca. 58 - 82 Minuten.
par_ml2 <- m2$par
hess <- m2$hessian
#MS: Links zur nearest covariance matrix:
#MS: http://quant.stackexchange.com/questions/2074/what-is-the-best-way-to-fix-a-covariance-matrix-that-is-not-positive-semi-defi
#MS: nearPD(hess)$mat
Sigma_ml2 <- solve(hess)
#MS: END get starting imputation values by maximizing the likelihood#
#####################################################################
###set starting values equal to the observed income
###rounded income will be replaced by imputations later
inc.imp <- inc
inc.std.imp <- inc.std
log.inc.std.imp <- log.inc.std
y.imp <- array(NA, dim = c(n, M))
for(j in 1:M){
####draw new parameters #MS: because it is a Bayesian imputation
check <- TRUE
# counter <- 0
while(check){
pars <- mvtnorm::rmvnorm(1, mean = par_ml2, sigma = Sigma_ml2)
####test if drawn parameters for the thresholds are in increasing order
####and if the standard deviation of the residuals is<0
####if yes, draw again
#MS: pars entspricht c(kstart, betastart2, etastart, sigmastart2) (?)
test <- c(pars[2:6] - pars[1:5], pars[length(pars)])
#MS: pars[2:6] - pars[1:5] bewirkt, dass k1 - k0 und k2 - k1, ..., k5 - k4 gerechnet wird
#MS: und das soll nicht kleiner 0 sein, weil k1-k0 < 0 aequivalent zu k1 < k0 und das geht ja nicht.
#MS: Das letzte Element ist sigmastart2 was logischerweise positiv sein muss.
check <- any(test < 0) #MS: Es muessen alle Werte in test >= 0 sein, sonst terminiert die Schleife nicht
# counter <- counter +1
# print(counter)
}
beta_hat <- as.matrix(pars[7:(length(pars) - 2)], ncol = 1)
#MS: betastart2 hatte noch 33 Elemente, beta.hat hat nur noch 26 ?!?
#MS: es stimmt aber, dass die ersten 6 Elemente zu kstart gehoeren und die letzten 2 sind eta und sigma.
gamma1_hat <- pars[length(pars) - 1]
sigma_hat <- pars[length(pars)]
mu_g <- gamma1_hat * as.matrix(MM_1) %*% beta_hat
mu_y <- as.matrix(MM_1) %*% beta_hat
mymean <- cbind(mu_g, mu_y)
#The covariance matrix from equation (3)
Sigma <- matrix(c(1 + gamma1_hat^2 * sigma_hat^2,
gamma1_hat * sigma_hat^2, gamma1_hat * sigma_hat^2,
sigma_hat^2), nrow = 2)
###################################################################################
#MS: BEGIN IMPUTATION ONLY FOR THOSE OBSERVATION WITH NO INCOME INFORMATION AT ALL#
#MS: HERE NO UNROUNDING OR IMPUTING INTERVALL-DATA TAKES PLACE#####################
#MS: Es werden zwar zu viele Imputationswerte gezogen, da viele von den Beobachtungen die HEK0600.miss
#MS: haben auch Intervall-Angaben gemacht haben. Und diese Beobachtungen werden danach nochmals imputiert.
mytry <- rnorm(n = sum(missind),
mean = as.matrix(MM_1[missind, , drop = FALSE]) %*% beta_hat, sd = sigma_hat)
#MS: Vorschlags-Imputationswert:
imp_temp <- exp(mytry * sd.log.inc + mean.log.inc)
#MS: Einen Check, ob die gezogenen Imputierten Werte auch in dem tatsaechlich beobachteten Intervall liegen
#MS: braucht man nicht, denn schliesslich zieht man ja bereits aus der trunktierten Verteilung.
inc.imp[missind] <- imp_temp
#MS: !!!setzt aktuell vorraus, dass inc.imp kein data.frame sondern ein Vektor ist!!!
#MS: END IMPUTATION ONLY FOR THOSE OBSERVATION THAT NO INCOME INFORMATION AT ALL#
#MS: HERE NO UNROUNDING OR IMPUTING INTERVALL-DATA TAKES PLACE####################
##################################################################################
#################################
#MS: BEGIN UNROUNDING-IMPUTATION#
###define bounds for the rounding basis
bounds_hat <- c(-Inf, pars[1:6], Inf)
###define interval bounds for maximum possible rounding intervals
#MS: Needed in the following imputation lopp
#MS: but only for those observations who answered this question
#MS: I cannot write 'log.inc - log(intervalls)' etc. because we calculate log(inv - intervals)
#MS: und das kann nur nach 'log(inc) - log(1 - intervals/inc) augeloest werden.
y_lower <- (log(y_imp_multi - intervals[as.numeric(as.character(p)) + 1]) -
mean.log.inc)/sd.log.inc
y_upper <- (log(y_imp_multi + intervals[as.numeric(as.character(p)) + 1]) -
mean.log.inc)/sd.log.inc
g_lower <- bounds_hat[as.numeric(as.character(p)) + 1]
g_upper <- bounds_hat[as.numeric(as.character(p)) + 2]
###loop over all observations that need to be unrounded
for (i in which(rounded)){
# if(k %% 1000 == 0){
# print(k)
# }
test <- TRUE
while(test){
###draw from truncated multivariate normal
###drawn y must be between y_lower and y_upper
###drawn g must be smaller than g_upper (g > g_upper is not consistent with
###rounding observed in the data)
mytry <- tmvtnorm::rtmvnorm(1,
mean = mymean[i, ],
sigma = Sigma,
lower = c(-Inf, y_lower[i]),
upper = c(g_upper[i], y_upper[i]),
algorithm = "gibbs", burn.in.samples = 1000)
###draws with rejection sampling. If intervall restrictions are not fulfilled after 1 mio
###draws, NA is given back. In this case, the rounded data will stay unmodified
if(is.na(mytry[1])){
print(paste("corrected imputation not possible for record:", i))
print(paste("observed income for that record:", y_imp_multi[i]))
##generate a rounding indicater that is always consistent with the observed data
g_temp <- bounds_hat[2] - 1
mytry <- c(g.temp, log.inc.std.imp[k])
}
####get imputed rounding indicator
round_int <- sum(mytry[1] > bounds_hat)
###get imputed income on original scale
imp_temp <- exp(mytry[2] * sd.log.inc + mean.log.inc)
###test if imputed income after rounding is equal to observed rounded income given the
###imputed rounding indicator
###if not(test=TRUE), draw again
#MS: test ist ein Indikator ob der imputierte Wert zur Annahme bezueglich des Rundungsprozess passt.
test <- round(imp_temp/round_base[round_int]) * round_base[round_int] !=
y_imp_multi[i]
}
inc.imp[i] <- imp_temp
}
y.imp[, j] <- inc.imp
}
#MS: END UNROUNDING-IMPUTATION#
###############################
#MS: replace original income by imputed income
return(y.imp) #cbind(inc.imp, final.data2[, -which(names(final.data2) == y.variable.name)])
}
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