R/estimate_nonadaptive.R

In huangrh/relvm: Random Effect Laten Variable Model For Hospital Compare

# Copyright (C) 2016-2017 Ren-Huai Huang <huangrenhuai@gmail.com>
#
# This file is part of relvm.
#
# relvm is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# relvm is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with relvm.  If not, see <http://www.gnu.org/licenses/>.


#' Random Effect Latent Variable Model By Non Adaptive Quadrature Approximation
#'
#' Estimate multiple groups of the random effect latent variable model by gauss
#' hermite quadrature.
#'
#'
#' @param object A mstbl object.
#' @param groups A vector of measure group names. The default is NULL, in which
#'   case a vector of all groups will be generated accordingly.
#' @param fit A list of fitting parameters. \itemize{ \item qpoints: The numbe
#'   of the quadrature points. \item init: Initial values for mu, fl, and err
#'   term in a list. fl is the factor loading. They will be initialized
#'   generally if it is null. The default is a list with for all mu and one for
#'   others. \item predict: The default is TRUE. \item adaptive: noad, no
#'   adaptive or ad, use adaptive.}
#'
#' @return An list of S3 object of class "relvm" with estimated parametes.
#' @seealso \code{\link{mstbl}}
#' @importFrom pracma hessian
#'
#' @export
#'
relvm_noad <- function(object,groups=NULL,fit=list(qpoints=30,init=NULL,predict=TRUE),file = NULL) {

    if (!is.null(file) && file.exists(file)) {
        # if the cached file exists
        allout <- readRDS(file)
    } else {

        # -------------------------------------------------------
        # Merge both tables of the measure score and weights.
        alldf  <- merge(x=object$mstbl_std, y=object$wtbl, by="ccnid", all=TRUE)

        # Check & update "groups"
        mtbl       <- create_measure_tbl(alldf)
        all_groups <- unique(mtbl$group)
        if (is.null(groups)) {
            groups <- all_groups
        } else if (any(groups %in% all_groups)) {
            groups <- groups[groups %in% all_groups]
        } else stop("The group name do not match.")

        # Fit control
        fit_default   <- list(qpoints = 30,init=NULL,predict=TRUE,adaptive=c("noad","ad"))
        extra_default <- fit_default[!(names(fit_default) %in% names(fit))]
        fit[names(extra_default)] <- extra_default

        qpoints = fit[["qpoints"]]
        init    = fit[["init"]]
        predict = fit[["predict"]]
        adaptive= fit[["adaptive"]][1]

        # ------------------------------------------------------------------#
        start_time = Sys.time()
        cat(sprintf("Fitting started at: %-15s\n",start_time))

        # Call relvm_single
        # snowfall::sfInit(parallel=TRUE,cpus=2);snowfall::sfExportAll()
        # snowfall::sfExport(create_measure_tbl)

        allout <- sapply(groups, relvm_single_noad, df=alldf, qpoints=qpoints,
                         init = init, predict = predict, adaptive=adaptive,simplify = FALSE)

        # snowfall::sfRemoveAll()
        # snowfall::sfStop()
        cat("\n","Total time: ", as.character.Date(Sys.time() - start_time),"\n")
        # ------------------------------------------------------------------#
        # After Relvm:
        # Merge the predicted group score if there is multiple group.
        preds <- alldf[,1,drop=FALSE] # take the column "ccnid"
        for (group in allout) {preds <- merge(x=preds,y=group$pred,all=TRUE)}
        colnames(preds) <- gsub("pred_","",colnames(preds))

        # Calculate the summary score.
        hospital_score <- rstarating::sum_score(preds)
        hospital_score <- merge.data.frame(x=hospital_score,y=object$report_indicator,
                                           by='ccnid',all.x=TRUE)
        # ************
        # Oct. 2016 used all hospitals to run the clustering
        # Dec. 2017 used only the valid hospitals (report_indicator == 1) to run the clustering.
        # hospital_score <- subset(hospital_score, report_indicator == 1)

        # Merge factor loadings and other parametes.
        pars <- data.frame()
        for (group in allout) {pars = rbind(pars,group$par)}

        # convergence
        convergence<- data.frame(convergence=vapply(allout,function(x) {x$convergence},c(0)))
        value      <- data.frame(value=vapply(allout,  function(x) x$value,c(0)))
        message    <- data.frame(message=vapply(allout,function(x) x$message,"0"),stringsAsFactors = FALSE)
        counts     <- t(as.data.frame(vapply(allout,   function(x) x$counts,c(0L,0L))))

        #output
        allout$groups <- structure(list(preds=preds,pars=pars,
                                        summary_score=hospital_score,
                                        counts= as.matrix(counts),
                                        value = as.matrix(value),
                                        message=as.matrix(message),
                                        convergence = as.matrix(convergence)),class="relvm")

        # save the data
        if (!is.null(file)) {
            # check if the file directory exists. Create one if not.
            file_dir <- dirname(file)
            if (!dir.exists(file_dir)) file_dir_created <- dir.create(file_dir,recursive =TRUE)
            saveRDS(allout,file=file)
        }
    }

    # output
    structure(allout, class='relvms')
}

# Simplified normal density function.
dnorm2 <- function(x,mean=0,sd=1) -(log(2 * pi) +2*log(sd)+((x-mean)/sd)^2)/2

#

#' Estimation Of The Random Effect Latent Variable Model Parameters
#'
#' Estimate the random effect latent variable model
#'
#' @param mstbl_std The standized measure score table.
#' @param wts_tbl The measure score weight table.
#' @param qpoints The numbe of the quadrature points.
#' @param init Initial values for mu, fl, and err term in a list. fl is the
#'   factor loading. They will be initialized generally if it is null. The
#'   default is a list with for all mu and one for others.
#' @param predict The default is TRUE.
#'
#' @return An object of S3 class "relvm" with estimated parametes.
#'
relvm_single_noad <- function(group, df, qpoints,init,predict,adaptive) {
    # -------------------------------------------------------#
    # Prepare to fit
    # start of the cycle
    start_time = Sys.time()
    cat(adaptive,"-",qpoints,"qpts",": ")
    cat(sprintf("Fitting: %-15s =>",group))

    # data table & weight table
    subdat    <- sub1group(group,df)
    mstbl_std <- as.matrix(subdat$mstbl_std)
    wts_tbl   <- as.matrix(subdat$wtbl)

    # Setup and initialize the parameters
    nc <- ncol(mstbl_std);
    if (is.null(init)) {
        init <- unlist(list(mu  = rep(0.5, nc),
                            fl  = rep(0.5, nc),
                            err = rep(0.5, nc)))}
    # cc$x & cc$w
    cc <- pracma::gaussHermite(qpoints);
    ccidx <- cc$w>1e-36;
    cc$w = cc$w[ccidx];
    cc$x = cc$x[ccidx];
    cc_len=length(cc$x);


    #--------------------------------------------------------#
    # Fit the function
    fit <- optim(par     = init,      # Model parameter
                 fn      = venll11m,  # venll11m,   # Estimation function
                 gr      = NULL,
                 method  = "L-BFGS-B",
                 control = list(maxit=1000), # set factr=1e-8
                 hessian = FALSE,
                 score   = mstbl_std,
                 wts     = wts_tbl,
                 cc      = cc,
                 qpoints = cc_len)

    #--------------------------------------------------------#
    # Output the fitting
    #
    # Format fit$par
    theta_names <- names(fit$par);
    fit$par     <- data.frame(name = names(subdat$mstbl_std),
                              fl = fit$par[grepl("fl", theta_names)],
                              mu = fit$par[grepl("mu", theta_names)],
                              err= fit$par[grepl("err",theta_names)],
                              row.names=NULL)
    # Prediction
    if (identical(predict, TRUE)) {
        pred_out          <- relvm:::pred(mstbl_std,wts_tbl,pms=fit$par);

        colnames(pred_out)<- paste(colnames(pred_out),group,sep="_")
        pred_out          <- cbind(subdat$ccnid,pred_out)
        fit$pred          <- pred_out[,1:2]

        #
        fit$stderr        <- pred_out[,c(1,3)]
    }

    # Add three fields to the output
    init_names  <- names(init);
    fit$init    <- data.frame(name = names(subdat$mstbl_std),
                              fl = init[grepl("fl", init_names)],
                              mu = init[grepl("mu", init_names)],
                              err= init[grepl("err",init_names)], row.names=NULL)

    fit$mstbl_std = cbind(subdat$ccnid,mstbl_std)
    fit$wtbl      = cbind(subdat$ccnid,wts_tbl)

    # Output
    cat(" : ", as.character.Date(Sys.time() - start_time))
    cat(", ",fit$message,       "\n")

    structure(fit,class="relvm")
}


# object function
venll12 <- function(par,score,wts,cc,qpoints) {

    # Reconstruction of the parameters
    nr <- nrow(score); nc <- ncol(score)
    mu    <- par[grepl("mu", names(par))]         #
    fl    <- par[grepl("fl", names(par))]         # factor loading
    err   <- par[grepl("err", names(par))]

    # fv matrix
    fv  <- 1.4142135623730951 * cc$x

    # Weighted log likelyhood
    # 3D array:
    wts_arr   <- aperm(array(wts,  dim=c(nr,nc,qpoints)),c(2,3,1))
    score_arr <- aperm(array(score,dim=c(nr,nc,qpoints)),c(2,3,1))
    means_arr <-array(mu+c(fl %o% fv),   dim=c(nc,qpoints,nr))
    wll_mtx   <- colSums(wts_arr * dnorm2(score_arr, mean=means_arr, sd = err),na.rm=TRUE)

    # Gaussian quadrature integral approximation
    # gqi <- log(sum(exp(joint_mtx + log(cc$w) +(cc$x)^2),na.rm=TRUE))
    # log(2*pi)/2 = 0.91893853320467267=dnorm_cpp(cc$x * sqrt(2), mean=0,sd=1) +(cc$x)^2;
    # log(sqrt(2))=0.3465735902799727
    gqi <- matrixStats::colLogSumExps(log(cc$w) + wll_mtx - 0.91893853320467267,na.rm=TRUE)
    -sum(gqi +0.3465735902799727, na.rm=TRUE)
}



venll11m <- function(par,score,wts,cc,qpoints) {
    # Reconstruction of the parameters
    nr <- nrow(score); nc <- ncol(score)
    mu    <- par[grepl("mu", names(par))]         #
    fl    <- par[grepl("fl", names(par))]         # factor loading
    err   <- par[grepl("err", names(par))]
    err   <- abs(err)

    # 2nd derivative
    # coefs <- sqrt(2/(rowSums((fl^2 * wts/err^2), na.rm = TRUE) + 1))
    coefs <- rep(sqrt(2),nr)

    # fv matrix
    fv_mtx  <- cc$x %o% coefs

    # 3D array:
    wts_arr   <- aperm(array(wts,  dim=c(nr,nc,qpoints)),c(2,3,1))
    score_arr <- aperm(array(score,dim=c(nr,nc,qpoints)),c(2,3,1))
    means_arr <- array(mu,         dim=c(nc,qpoints,nr)) + fl %o% fv_mtx

    # Weighted log likelyhood
    wll_mtx   <- colSums(wts_arr * dnorm2(score_arr, mean=means_arr, sd = err),na.rm=TRUE)

    # Joint probability
    joint_mtx <- wll_mtx +  dnorm2(fv_mtx, mean=0,sd=1)

    # Gaussian quadrature integral approximation
    gqi <- matrixStats::colLogSumExps(joint_mtx + log(cc$w) +(cc$x)^2,na.rm=TRUE)
    -sum(log(coefs)+gqi, na.rm=TRUE)
}