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### leverage2.R ---
##----------------------------------------------------------------------
## Author: Brice Ozenne
## Created: feb 19 2018 (17:58)
## Version:
## Last-Updated: jan 23 2024 (10:25)
## By: Brice Ozenne
## Update #: 178
##----------------------------------------------------------------------
##
### Commentary:
##
### Change Log:
##----------------------------------------------------------------------
##
### Code:
## * documentation - leverage2
#' @title Leverage With Small Sample Correction.
#' @description Extract leverage values from a latent variable model, with small sample correction.
#' @name leverage2
#'
#' @param object a \code{lvmfit} or \code{lvmfit2} object (i.e. output of \code{lava::estimate} or \code{lavaSearch2::estimate2}).
#' @param format [character] Use \code{"wide"} to return the residuals in the wide format (one row relative to each sample).
#' Otherwise use \code{"long"} to return the residuals in the long format.
#' @param ssc [character] method used to correct the small sample bias of the variance coefficients: no correction (\code{"none"}/\code{FALSE}/\code{NA}),
#' correct the first order bias in the residual variance (\code{"residual"}), or correct the first order bias in the estimated coefficients \code{"cox"}).
#' Only relevant when using a \code{lvmfit} object.
#' @param ... additional argument passed to \code{estimate2} when using a \code{lvmfit} object.
#'
#' @details The leverage are defined as the partial derivative of the fitted values with respect to the observations.
#' \deqn{
#' leverage_i = \frac{\partial \hat{Y}_i}{\partial Y_i}
#' }
#' See Wei et al. (1998). \cr \cr
#'
#' When argument object is a \code{lvmfit} object, the method first calls \code{estimate2} and then extract the leverage.
#'
#' @seealso \code{\link{estimate2}} to obtain \code{lvmfit2} objects.
#'
#' @return a matrix containing the leverage relative to each sample (in rows)
#' and each endogenous variable (in column).
#'
#' @references Bo-Cheng Wei et al., Generalized Leverage and its applications (1998), Scandinavian Journal of Statistics 25:1:25-37.
#'
#' @examples
#' #### simulate data ####
#' set.seed(10)
#' m <- lvm(Y1~eta,Y2~eta,Y3~eta)
#' latent(m) <- ~eta
#' d <- lava::sim(m,20, latent = FALSE)
#'
#' #### latent variable models ####
#' e.lvm <- estimate(m, data = d)
#' leverage2(e.lvm)
#'
#' @concept estimator
#' @keywords smallSampleCorrection
#'
#' @export
`leverage2` <-
function(object, format, ssc, ...) UseMethod("leverage2")
## * leverage2.lvmfit
#' @rdname leverage2
#' @export
leverage2.lvmfit <- function(object, format = "wide", ssc = lava.options()$ssc, ...){
return(leverage2(estimate2(object, ssc = ssc, ...), format = format))
}
## * leverage2.lvmfit2
#' @rdname leverage2
#' @export
leverage2.lvmfit2 <- function(object, format = "wide", ...){
dots <- list(...)
if(length(dots)>0){
warning("Argument(s) \'",paste(names(dots),collapse="\' \'"),"\' not used by ",match.call()[1],". \n")
}
format <- match.arg(format, choices = c("long","wide"))
if(format == "wide"){
return(object$sCorrect$leverage)
}else if(format == "long"){
endogenous <- colnames(object$sCorrect$leverage)
n.endogenous <- length(endogenous)
outW <- data.frame(cluster = 1:NROW(object$sCorrect$leverage), object$sCorrect$leverage)
outL <- stats::na.omit(stats::reshape(outW,
idvar = "id",
direction = "long",
varying = list(endogenous),
timevar = "endogenous",
v.names = "leverage"))
rownames(outL) <- NULL
outL$endogenous <- factor(outL$endogenous, levels = 1:n.endogenous, labels = endogenous)
reorder <- match(interaction(object$sCorrect$old2new.order$XXclusterXX.old,object$sCorrect$old2new.order$XXendogenousXX.old),
interaction(outL$cluster,outL$endogenous))
return(outL[reorder,])
}
}
## * .leverage2
.leverage2 <- function(Omega, epsilon, dmu, dOmega, vcov.param,
name.pattern, missing.pattern, unique.pattern,
endogenous, n.endogenous, param, param.mean, param.var, n.cluster){
n.pattern <- NROW(unique.pattern)
n.param <- length(param)
leverage <- matrix(NA, nrow = n.cluster, ncol = n.endogenous,
dimnames = list(NULL, endogenous))
if(length(param.mean)==0){
leverage[] <- 0
return(leverage)
}
if(is.null(vcov.param)){
stop("Cannot compute the leverage values without the variance-covariance matrix of the coefficients. \n")
}
scoreY <- array(0, dim = c(n.cluster, n.endogenous, n.param),
dimnames = list(NULL, endogenous, param))
for(iP in 1:n.pattern){ ## iP <- 1
iIndex <- missing.pattern[[iP]]
iY <- which(unique.pattern[iP,]==1)
iOmega <- Omega[iY,iY,drop=FALSE]
iOmegaM1 <- chol2inv(chol(iOmega))
iOmegaM1.epsilon <- epsilon[iIndex,iY,drop=FALSE] %*% iOmegaM1
## derivative of the score regarding Y
for(iParam in param){
if(iParam %in% param.mean){
if(length(iY)>1){
scoreY[iIndex,iY,iParam] <- scoreY[iIndex,iY,iParam] + t(dmu[iParam,iY,iIndex]) %*% iOmegaM1
}else{
scoreY[iIndex,iY,iParam] <- scoreY[iIndex,iY,iParam] + dmu[iParam,iY,iIndex] * iOmegaM1[1,1]
}
}
if(iParam %in% param.var){
scoreY[iIndex,iY,iParam] <- scoreY[iIndex,iY,iParam] + 2 * iOmegaM1.epsilon %*% dOmega[[iParam]][iY,iY,drop=FALSE] %*% iOmegaM1
}
}
## leverage
for(iiY in iY){ ## iiY <- iY[2]
if(length(param.mean)==1){
leverage[iIndex,iiY] <- dmu[param.mean,iiY,iIndex] * (scoreY[iIndex,iiY,] %*% vcov.param)[,param.mean]
}else if(n.param==1){
leverage[iIndex,iiY] <- dmu[param.mean,iiY,iIndex] * vcov.param * scoreY[iIndex,iiY,]
} else{
leverage[iIndex,iiY] <- rowSums(t(dmu[param.mean,iiY,iIndex]) * (scoreY[iIndex,iiY,] %*% vcov.param)[,param.mean,drop=FALSE] )
}
## dmu2 <- matrix(0, nrow = n.param, ncol = length(iIndex), dimnames = list(param,NULL))
## dmu2[param.mean,] <- dmu[param.mean,iiY,iIndex]
## diag( t(dmu2) %*% vcov.param %*% t(scoreY[iIndex,iiY,]) )
}
}
return(leverage)
}
##----------------------------------------------------------------------
### leverage2.R ends here
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