R/WaldMult.R

In lcmm: Extended Mixed Models Using Latent Classes and Latent Processes

#' Multivariate Wald Test
#' 
#' This function provides multivariate and univariate Wald tests for
#' combinations of parameters from \code{hlme}, \code{lcmm}, \code{multlcmm},
#' \code{Jointlcmm} or \code{mpjlcmm} models.
#' 
#' 
#' @param Mod an object of class \code{hlme}, \code{lcmm}, \code{multlcmm},
#' \code{Jointlcmm} or \code{mpjlcmm}
#' @param pos a vector containing the indices in \code{Mod$best} of the parameters to
#' test
#' @param contrasts a numeric vector of same length as pos.  If NULL (the
#' default), a simultaneous test of the appropriate parameters is realised.  If
#' contrasts is specified, the quantity to test is the dot product of pos and
#' contrasts.
#' @param name a character containing the name the user wants to give to the
#' test. By default, the name's test is the null hypothesis.
#' @param value the value(s) to test against. By default, test against 0.
#' @return If contrasts is NULL, the function returns a matrix with 1 row and 2
#' columns containing the value of the Wald test's statistic and the associated
#' p-value.
#' 
#' If contrasts is not NULL, the function returns a matrix with 1 row and 4
#' columns containing the value of the coefficient (dot product of pos and
#' contrasts), his standard deviation, the value of the Wald test's statistic
#' and the associated p-value.
#' @author Cecile Proust-Lima, Lionelle Nkam and Viviane Philipps
#' 
#' @export
#' 
WaldMult <- function(Mod,pos=NULL,contrasts=NULL,name=NULL,value=NULL)
{ 
    #if (!(class(Mod) %in% c("hlme","lcmm","multlcmm","Jointlcmm","mpjlcmm"))) stop("applies to \"hlme\" or \"lcmm\" or \"multlcmm\" or \"Jointlcmm\" or \"mpjlcmm\" objects only")
    if(!inherits(Mod, c("hlme","lcmm","multlcmm","Jointlcmm","mpjlcmm", "externX", "externSurv"))) stop("applies to \"hlme\" or \"lcmm\" or \"multlcmm\" or \"Jointlcmm\" or \"mpjlcmm\" or \"externX\" or \"externSurv\" objects only")

    ## prm estimes et leur variance
    Mod$best <- estimates(Mod)
    V <- VarCov(Mod)
    
    
    ## On teste si pos est un vecteur
    if (is.null(pos))
        {
            stop("pos must be specified")
        }
    else
        {
            if (!is.vector(pos)) stop("Error : pos must be a numeric vector")
            
            ## On cree la matrice qui recevra les varcov des parametres de pos
            Mat <- matrix(0,nrow=length(pos),ncol=length(pos))
            
            ## Remplissage de Mat sans boucles
            Mat <- V[pos,pos]
            
            ## Wald Multivarie, sans le vecteur contrasts
            Vect <- Mod$best[pos]
            
            
            if (is.null(contrasts))
                { 
                    
                    if (!is.null(value))
                        {
                            if (!is.vector(value)) stop("Error : value must be a numeric vector")
                            if (length(value)!=length(pos)) stop("value must have the same length as the vector pos")
                          
                            Vect <- Mod$best[pos]-value
                        }
                    
                    
                    Wald <- t(Vect)%*%solve(Mat)%*%Vect
                    
                    ## Nombre de degre de liberte
                    ddl <- length(pos)
                    ## Pvalue
                    p_value <- 1-pchisq(Wald,df=ddl)
                    ##cat("pvalue",p_value1,"\n")
                    
                    Results <- matrix(NA,nrow=1,ncol=2)
                    colnames(Results)<-c("Wald Test","p_value")
                    if (is.null(name)) 
                        {
                            if (!is.null(value))
                                {
                                    rownames(Results)<-paste(names(Mod$best[pos])," = ",value,collapse=" and ",sep="")
                                }
                            else
                                {
                                    rownames(Results)<-paste(paste(names(Mod$best[pos]),collapse=" = "),"= 0")
                                }
                        }
                    ## paste(names(Mod$best[pos])," = 0 ",collapse=" and ",sep="")} 
                    else
                        {
                            rownames(Results)<-name
                        }
                    
                    Results[,1] <- round(Wald,5)
                    Results[,2] <- round(p_value,5)
                }
            
            ## Wald Univarie avec le vecteur contrasts
            else
                {
                    ## Conditions d'application
                    if (length(contrasts)!=length(pos))
                        {
                            stop("contrasts must have the same length as the vector pos")
                        } 
                    if (sum(abs(contrasts))==0) 
                        {
                            stop("The absolute value of the sum of contratsts components must be different from 0")
                        }
                
                

                    Scalaire <- sum(Vect*contrasts)
                    
                    ## Utilisation de value
                    if (!is.null(value))
                        {
                            if (!is.vector(value)) stop("value must be a numeric vector")
                            if (length(value)!=1) stop("value must be a vector with a unique argument")
                        
                            Scalaire <- sum(Vect*contrasts)-value
                        }
                
                    ## Calcul de la variance de scalaire sans boucle
                    Var <- t(contrasts)%*%Mat%*%contrasts
                

                    Wald <- Scalaire/sqrt(Var)
                    p_value <- 2*(1-pnorm(abs(Wald)))
                    
                    Results <- matrix(NA,nrow=1,ncol=4)
                    colnames(Results)<-c("coef","Se","Wald Test","p_value")
                    if (is.null(name)) 
                    {
                        if(is.null(value)) value <- 0
                        rownames(Results)<-paste(paste(names(Mod$best[pos]),"*",contrasts,collapse=" + "),"= ",value)
                    } 
                    else
                        {
                            rownames(Results)<-name
                        }
                
                
                    Results[,1] <- round(sum(Vect*contrasts),5)
                    Results[,2] <- round(sqrt(Var),5)
                    Results[,3] <- round(Wald,5)
                    Results[,4] <- round(p_value,5)
                }
            
            return(Results)
            
        }  
}