R/mgedist.R

In fitdistrplus: Help to Fit of a Parametric Distribution to Non-Censored or Censored Data

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#   Copyright (c) 2009 Marie Laure Delignette-Muller                                                                                                  
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#   This program is free software; you can redistribute it and/or modify                                               
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### maximum goodness-of-fit estimation for censored or non-censored data
### and continuous distributions
### (at this time only available for non censored data)
###
###         R functions
### 

mgedist <- function (data, distr, gof = "CvM", start=NULL, fix.arg=NULL, optim.method="default",
    lower=-Inf, upper=Inf, custom.optim=NULL, silent=TRUE, gradient=NULL, 
    checkstartfix=FALSE, ...)
    # data may correspond to a vector for non censored data or to
    # a dataframe of two columns named left and right for censored data 
{
    if (!is.character(distr)) 
        stop("distr must be a character string naming a distribution")
    else 
        distname <- distr
        
    if (is.element(distname,c("binom","nbinom","geom","hyper","pois"))) 
        stop("Maximum goodness-of-fit estimation method is not intended to fit discrete distributions")

    pdistname <- paste("p",distname,sep="")
    if (!exists(pdistname, mode="function"))
        stop(paste("The ", pdistname, " function must be defined"))

    ddistname <- paste("d",distname,sep="")    
    if (!exists(ddistname, mode="function"))
        stop(paste("The ", ddistname, " function must be defined"))
    argddistname <- names(formals(ddistname))

    if(is.null(custom.optim))
      optim.method <- match.arg(optim.method, c("default", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent"))
    
    gof <- match.arg(gof, c("CvM", "KS", "AD", "ADR", "ADL", "AD2R", "AD2L", "AD2"))
   
    start.arg <- start #to avoid confusion with the start() function of stats pkg (check is done lines 87-100)
    if(is.vector(start.arg)) #backward compatibility
      start.arg <- as.list(start.arg)
    
    my3dots <- list(...)
    if ("weights" %in% names(my3dots))
      stop("Weights is not allowed for maximum GOF estimation")
    
    if (is.vector(data)) {
        cens <- FALSE
        if (!(is.numeric(data) & length(data)>1)) 
            stop("data must be a numeric vector of length greater than 1 for non censored data
            or a dataframe with two columns named left and right and more than one line for censored data")
    }
    else {
        cens <- TRUE
        censdata <- data
        if (!(is.vector(censdata$left) & is.vector(censdata$right) & length(censdata[,1])>1))
        stop("data must be a numeric vector of length greater than 1 for non censored data
        or a dataframe with two columns named left and right and more than one line for censored data")
        pdistname<-paste("p",distname,sep="")
        if (!exists(pdistname,mode="function"))
            stop(paste("The ",pdistname," function must be defined to apply maximum likelihood to censored data"))

    }
    
    if (cens) {
        # Definition of datasets lcens (left censored)=vector, rcens (right censored)= vector,
        #   icens (interval censored) = dataframe with left and right 
        # and ncens (not censored) = vector
        lcens<-censdata[is.na(censdata$left),]$right
        if (any(is.na(lcens)) )
            stop("An observation cannot be both right and left censored, coded with two NA values")
        rcens<-censdata[is.na(censdata$right),]$left
        ncens<-censdata[censdata$left==censdata$right & !is.na(censdata$left) & 
            !is.na(censdata$right),]$left
        icens<-censdata[censdata$left!=censdata$right & !is.na(censdata$left) & 
            !is.na(censdata$right),]
        # Definition of a data set for calculation of starting values
        data<-c(rcens,lcens,ncens,(icens$left+icens$right)/2)
    }
    
    if(!checkstartfix) #pre-check has not been done by fitdist() or bootdist()
    {
      # manage starting/fixed values: may raise errors or return two named list
      arg_startfix <- manageparam(start.arg=start, fix.arg=fix.arg, obs=data, 
                                  distname=distname)
      
      #check inconsistent parameters
      hasnodefaultval <- sapply(formals(ddistname), is.name)
      arg_startfix <- checkparamlist(arg_startfix$start.arg, arg_startfix$fix.arg, 
                                     argddistname, hasnodefaultval)
      #arg_startfix contains two names list (no longer NULL nor function)  
      
      #set fix.arg.fun
      if(is.function(fix.arg))
        fix.arg.fun <- fix.arg
      else
        fix.arg.fun <- NULL
    }else #pre-check has been done by fitdist() or bootdist()
    {
      arg_startfix <- list(start.arg=start, fix.arg=fix.arg)
      fix.arg.fun <- NULL
    }
    
    #unlist starting values as needed in optim()
    vstart <- unlist(arg_startfix$start.arg)
    #sanity check
    if(is.null(vstart))
      stop("Starting values could not be NULL with checkstartfix=TRUE")
    
    #erase user value
    #(cannot coerce to vector as there might be different modes: numeric, character...)
    fix.arg <- arg_startfix$fix.arg
    
   ############# MGE fit using optim or custom.optim ##########

    # definition of the function to minimize depending on the argument gof
    # for non censored data
    if (!cens) 
    {
        # the argument names are:
        # - par for parameters (like in optim function)
        # - fix.arg for optional fixed parameters
        # - obs for observations (previously dat but conflicts with genoud data.type.int argument)
        # - pdistnam for distribution name
        if (gof == "CvM")
            fnobj <- function(par, fix.arg, obs, pdistnam)
            { 
                n <- length(obs)
                s <- sort(obs)
                theop <- do.call(pdistnam,c(list(s),as.list(par),as.list(fix.arg)))
                1/(12*n) + sum( ( theop - (2 * 1:n - 1)/(2 * n) )^2 )
            }
        else     
        if (gof == "KS")
            fnobj <- function(par, fix.arg, obs, pdistnam) 
            {
                n <- length(obs)
                s <- sort(obs)
                obspu <- seq(1,n)/n
                obspl <- seq(0,n-1)/n
                theop <- do.call(pdistnam,c(list(s),as.list(par),as.list(fix.arg)))
                max(pmax(abs(theop-obspu),abs(theop-obspl)))
            }
        else
        if (gof == "AD")
            fnobj <- function(par, fix.arg, obs, pdistnam)
            { 
                n <- length(obs)
                s <- sort(obs)
                theop <- do.call(pdistnam,c(list(s),as.list(par),as.list(fix.arg)))
                - n - mean( (2 * 1:n - 1) * (log(theop) + log(1 - rev(theop))) ) 
            }
        else
        if (gof == "ADR")
            fnobj <- function(par, fix.arg, obs, pdistnam)
            { 
                n <- length(obs)
                s <- sort(obs)
                theop <- do.call(pdistnam,c(list(s),as.list(par),as.list(fix.arg)))
                n/2 - 2 * sum(theop) - mean ( (2 * 1:n - 1) * log(1 - rev(theop)) )
            }
        else
        if (gof == "ADL")
            fnobj <- function(par, fix.arg, obs, pdistnam)
            { 
                n <- length(obs)
                s <- sort(obs)
                theop <- do.call(pdistnam,c(list(s),as.list(par),as.list(fix.arg)))
                -3*n/2 + 2 * sum(theop) - mean ( (2 * 1:n - 1) * log(theop) )
            }
        else  
        if (gof == "AD2R")
            fnobj <- function(par, fix.arg, obs, pdistnam)
            { 
                n <- length(obs)
                s <- sort(obs)
                theop <- do.call(pdistnam,c(list(s),as.list(par),as.list(fix.arg)))
                2 * sum(log(1 - theop)) + mean ( (2 * 1:n - 1) / (1 - rev(theop)) )
            }
        else  
        if (gof == "AD2L")
            fnobj <- function(par, fix.arg, obs, pdistnam)
            { 
                n <- length(obs)
                s <- sort(obs)
                theop <- do.call(pdistnam,c(list(s),as.list(par),as.list(fix.arg)))
                2 * sum(log(theop)) + mean ( (2 * 1:n - 1) / theop )
            }
         else  
        if (gof == "AD2")
            fnobj <- function(par, fix.arg, obs, pdistnam)
            { 
                n <- length(obs)
                s <- sort(obs)
                theop <- do.call(pdistnam,c(list(s),as.list(par),as.list(fix.arg)))
                2 * sum(log(theop) + log(1 - theop) ) + 
                mean ( ((2 * 1:n - 1) / theop) + ((2 * 1:n - 1) / (1 - rev(theop))) )
            }
    }
    else # if (!cens) 
        stop("Maximum goodness-of-fit estimation is not yet available for censored data.")
        
    # Function to calculate the loglikelihood to return
    loglik <- function(par, fix.arg, obs, ddistnam) {
        sum(log(do.call(ddistnam, c(list(obs), as.list(par), as.list(fix.arg)) ) ) )
    }
    
    owarn <- getOption("warn")        
   
    # Try to minimize the gof distance using the base R optim function
    if(is.null(custom.optim))
    {
        hasbound <- any(is.finite(lower) | is.finite(upper))
      
        # Choice of the optimization method  
        if (optim.method == "default")
        {
          meth <- ifelse(length(vstart) > 1, "Nelder-Mead", "BFGS") 
        }else
          meth <- optim.method
      
        if(meth == "BFGS" && hasbound && is.null(gradient))
        {
          meth <- "L-BFGS-B"
          txt1 <- "The BFGS method cannot be used with bounds without provided the gradient."
          txt2 <- "The method is changed to L-BFGS-B."
          warning(paste(txt1, txt2))
        }
      
        options(warn=ifelse(silent, -1, 0))
        #select optim or constrOptim
        if(hasbound) #finite bounds are provided
        {
          if(!is.null(gradient))
          {
            opt.fun <- "constrOptim"
          }else #gradient == NULL
          {
            if(meth == "Nelder-Mead")
              opt.fun <- "constrOptim"
            else if(meth %in% c("L-BFGS-B", "Brent"))
              opt.fun <- "optim"
            else
            {
              txt1 <- paste("The method", meth, "cannot be used by constrOptim() nor optim() without gradient and bounds.")
              txt2 <- "Only optimization methods L-BFGS-B, Brent and Nelder-Mead can be used in such case."
              stop(paste(txt1, txt2))
            }
          }
          if(opt.fun == "constrOptim")
          {
            #recycle parameters
            npar <- length(vstart) #as in optim() line 34
            lower <- as.double(rep_len(lower, npar)) #as in optim() line 64
            upper <- as.double(rep_len(upper, npar))
            
            # constraints are : Mat %*% theta >= Bnd, i.e. 
            # +1 * theta[i] >= lower[i]; 
            # -1 * theta[i] >= -upper[i]
            
            #select rows from the identity matrix
            haslow <- is.finite(lower)
            Mat <- diag(npar)[haslow, ]
            #select rows from the opposite of the identity matrix
            hasupp <- is.finite(upper)
            Mat <- rbind(Mat, -diag(npar)[hasupp, ])
            colnames(Mat) <- names(vstart)
            rownames(Mat) <- paste0("constr", 1:NROW(Mat))
            
            #select the bounds
            Bnd <- c(lower[is.finite(lower)], -upper[is.finite(upper)])
            names(Bnd) <- paste0("constr", 1:length(Bnd))
            
            initconstr <- Mat %*% vstart - Bnd
            if(any(initconstr < 0))
              stop("Starting values must be in the feasible region.")
            
            opttryerror <- try(opt <- constrOptim(theta=vstart, f=fnobj, ui=Mat, ci=Bnd, grad=gradient,
                                                  fix.arg=fix.arg, obs=data, pdistnam=pdistname, hessian=!is.null(gradient), method=meth, 
                                                    ...), silent=TRUE)
            if(!inherits(opttryerror, "try-error"))
              if(length(opt$counts) == 1) #appears when the initial point is a solution
                opt$counts <- c(opt$counts, NA)
            
            
          }else #opt.fun == "optim"
          {
            opttryerror <- try(opt <- optim(par=vstart, fn=fnobj, fix.arg=fix.arg, obs=data, gr=gradient,
                                            pdistnam=pdistname, hessian=TRUE, method=meth, lower=lower, upper=upper, 
                                              ...), silent=TRUE)       
          }
          
        }else #hasbound == FALSE
        {
          opt.fun <- "optim"
          opttryerror <- try(opt <- optim(par=vstart, fn=fnobj, fix.arg=fix.arg, obs=data, gr=gradient,
                                          pdistnam=pdistname, hessian=TRUE, method=meth, lower=lower, upper=upper, 
                                            ...), silent=TRUE)       
        }
        options(warn=owarn)
                
        if (inherits(opttryerror,"try-error"))
        {
            warnings("The function optim encountered an error and stopped.")
            if(getOption("show.error.messages")) print(attr(opttryerror, "condition"))          
            return(list(estimate = rep(NA,length(vstart)), convergence = 100, loglik = NA, 
                        hessian = NA))
        }
        
        if (opt$convergence>0) {
            warnings("The function optim failed to converge, with the error code ",
                     opt$convergence)
        }
        if(is.null(names(opt$par)))
          names(opt$par) <- names(vstart)
        res <- list(estimate = opt$par, convergence = opt$convergence, value = opt$value, 
                    hessian = opt$hessian, optim.function=opt.fun, optim.method=meth, 
                    fix.arg = fix.arg, fix.arg.fun = fix.arg.fun, weights=NULL,
                    counts=opt$counts, optim.message=opt$message,
                    loglik=loglik(opt$par, fix.arg, data, ddistname), gof=gof)
    }
    else # Try to minimize the gof distance using a user-supplied optim function 
    {
        options(warn=ifelse(silent, -1, 0))
        if (!cens)
            opttryerror <- try(opt <- custom.optim(fn=fnobj, fix.arg=fix.arg, obs=data, pdistnam=pdistname, par=vstart, ...),
            silent=TRUE)
        else
            stop("Maximum goodness-of-fit estimation is not yet available for censored data.")
        options(warn=owarn)
        
        if (inherits(opttryerror,"try-error"))
        {
            warnings("The customized optimization function encountered an error and stopped.")
            if(getOption("show.error.messages")) print(attr(opttryerror, "condition"))          
            return(list(estimate = rep(NA,length(vstart)), convergence = 100, value = NA, 
                        hessian = NA))
        }
        
        if (opt$convergence>0) {
            warnings("The customized optimization function failed to converge, with the error code ",
                     opt$convergence)
        }
        if(is.null(names(opt$par)))
          names(opt$par) <- names(vstart)
        argdot <- list(...)
        method.cust <- argdot$method
        res <- list(estimate = opt$par, convergence = opt$convergence, value = opt$value, 
                    hessian = opt$hessian, optim.function=custom.optim, optim.method=method.cust,
                    fix.arg = fix.arg, fix.arg.fun = fix.arg.fun, weights=NULL,
                    counts=opt$counts, optim.message=opt$message,
                    loglik=loglik(opt$par, fix.arg, data, ddistname), gof=gof)
    }   
   
    return(res)                
}