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# These functions are
# Copyright (C) 2020 S. Orso, University of Geneva
# All rights reserved.
ib.lm <- function(object, thetastart=NULL, control=list(...), extra_param = FALSE, ...){
# controls
control <- do.call("ibControl",control)
# initial estimator:
pi0 <- coef(object)
if(extra_param) pi0 <- c(pi0, sigma(object))
if(!is.null(thetastart)){
if(is.numeric(thetastart) && length(thetastart) == length(pi0)){
t0 <- thetastart
} else {
stop("`thetastart` must be a numeric vector of the same length as parameter
of interest.", call.=FALSE)
}
} else {
t0 <- pi0
}
# test diff between thetas
p <- p0 <- length(t0)
if(extra_param) p0 <- p - 1L
test_theta <- control$tol + 1
# iterator
k <- 0L
# create an environment for iterative bootstrap
env_ib <- new.env(hash=F)
# prepare data and formula for fit
cl <- getCall(object)
if(length(cl$formula)==1) cl$formula <- get(paste(cl$formula)) # get formula
intercept_only <- cl$formula[[3]] == 1 # check for intercept only models
mf <- model.frame(object)
mt <- terms(object)
if(!intercept_only){
x <- if(!is.empty.model(mt)) model.matrix(mt, mf, object$contrasts)
# check if model has an intercept
has_intercept <- attr(mt,"intercept")
if(has_intercept){
# remove intercept from design
x <- x[,!grepl("Intercept",colnames(x))]
cl$formula <- quote(y~x)
} else {
cl$formula <- quote(y~x-1)
}
assign("x",x,env_ib)
} else{
cl$formula <- quote(y~1)
}
o <- as.vector(model.offset(mf))
if(!is.null(o)) assign("o",o,env_ib)
cl$data <- NULL
# add an offset
if(!is.null(o)) cl$offset <- quote(o)
# copy the object
tmp_object <- object
# initial value
diff <- rep(NA_real_, control$maxit)
if(!extra_param) std <- NULL
# Iterative bootstrap algorithm:
while(test_theta > control$tol && k < control$maxit){
# update initial estimator
tmp_object$coefficients <- t0[1:p0]
if(extra_param) std <- t0[p]
sim <- simulation(tmp_object,control,std)
tmp_pi <- matrix(NA_real_,nrow=p,ncol=control$H)
for(h in seq_len(control$H)){
assign("y",sim[,h],env_ib)
fit_tmp <- tryCatch(error = function(cnd) NULL, {eval(cl,env_ib)})
if(is.null(fit_tmp)) next
tmp_pi[1:p0,h] <- coef(fit_tmp)
if(extra_param) tmp_pi[p,h] <- sigma(fit_tmp)
}
pi_star <- control$func(tmp_pi)
# update value
delta <- pi0 - pi_star
t1 <- t0 + delta
if(extra_param && control$constraint) t1[p] <- exp(log(t0[p]) + log(pi0[p]) - log(pi_star[p]))
# test diff between thetas
test_theta <- sum(delta^2)
if(k>0) diff[k] <- test_theta
# initialize test
if(!k) tt_old <- test_theta+1
# Alternative stopping criteria, early stop :
if(control$early_stop){
if(tt_old <= test_theta){
warning("Algorithm stopped because the objective function does not reduce")
break
}
}
# Alternative stopping criteria, "statistically flat progress curve" :
if(k > 10L){
try1 <- diff[k:(k-10)]
try2 <- k:(k-10)
if(var(try1)<=1e-3) break
mod <- lm(try1 ~ try2)
if(summary(mod)$coefficients[2,4] > 0.2) break
}
# update increment
k <- k + 1L
# Print info
if(control$verbose){
cat("Iteration:",k,"Norm between theta_k and theta_(k-1):",test_theta,"\n")
}
# update theta
t0 <- t1
}
# warning for reaching max number of iterations
if(k>=control$maxit) warning("maximum number of iteration reached")
tmp_object$fitted.values <- predict.lm(tmp_object)
tmp_object$residuals <- unname(model.frame(object))[,1] - tmp_object$fitted.values
tmp_object$call <- object$call
# additional metadata
ib_extra <- list(
iteration = k,
of = sqrt(drop(crossprod(delta))),
estimate = t0,
test_theta = test_theta,
boot = tmp_pi)
new("IbLm",
object = tmp_object,
ib_extra = ib_extra)
}
#' @rdname ib
#' @details
#' For \link[stats]{lm}, if \code{extra_param=TRUE}: the variance of the residuals is
#' also corrected. Note that using the \code{ib} is not useful as coefficients
#' are already unbiased, unless one considers different
#' data generating mechanism such as censoring, missing values
#' and outliers (see \code{\link{ibControl}}).
#' @example /inst/examples/eg_lm.R
#' @seealso \code{\link[stats]{lm}}
#' @importFrom stats lm predict.lm model.matrix
#' @export
setMethod("ib", signature = className("lm","stats"),
definition = ib.lm)
# inspired from stats::simulate.lm
#' @importFrom stats fitted sigma rnorm runif simulate
simulation.lm <- function(object, control=list(...), std=NULL, ...){
control <- do.call("ibControl",control)
set.seed(control$seed)
if(!exists(".Random.seed", envir = .GlobalEnv)) runif(1)
# user-defined simulation method
if(!is.null(control$sim)){
sim <- control$sim(object, control, std, ...)
return(sim)
}
ftd <- fitted(object)
n <- length(ftd)
ntot <- n * control$H
if(is.null(std)) std <- sigma(object)
sim <- matrix(ftd + rnorm(ntot,sd=std), ncol=control$H)
if(control$cens) sim <- censoring(sim,control$right,control$left)
if(control$mis) sim <- missing_at_random(sim, control$prop)
if(control$out) sim <- outliers(sim, control$eps, control$G)
sim
}
#' @title Simulation for linear regression
#' @description simulation method for class \linkS4class{IbLm}
#' @param object an object of class \linkS4class{IbLm}
#' @param control a \code{list} of parameters for controlling the iterative procedure
#' (see \code{\link{ibControl}}).
#' @param std \code{NULL} by default; standard deviation to pass to simulation.
#' @param ... further arguments
#' @export
setMethod("simulation", signature = className("lm","stats"),
definition = simulation.lm)
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