R/mquantreg.R

In expectreg: Expectile and Quantile Regression

Mqreg <- function(formula,data=NULL,smooth=c("schall","acv","fixed"),estimate=c("iprls","restricted"),lambda=1,tau=NA, robust = 1.345,adaptive=FALSE,ci=FALSE, LSMaxCores = 1)
{  
  smooth = match.arg(smooth)
  estimate = match.arg(estimate)

  if(!is.na(charmatch(tau[1],"density")) && charmatch(tau[1],"density") > 0)
  {
    pp <- seq(0.01, 0.99, by=0.01)
  }
  else if(any(is.na(tau)) || !is.vector(tau) || any(tau > 1) || any(tau < 0))
  {
    pp <- c(0.01,0.02,0.05,0.1,0.2,0.5,0.8,0.9,0.95,0.98, 0.99)
  }
  else
  {
    pp <- tau
  }
  np <- length(pp)

  yy = eval(as.expression(formula[[2]]),envir=data,enclos=environment(formula))
  attr(yy,"name") = deparse(formula[[2]])
  m = length(yy)

  design = list()
  x = list()
  types = list()
  bnd = list()
  Zspathelp = list()
  nb = vector()
  krig.phi = list()
  center = TRUE
  varying = list()
  Blist = list()
  Plist = list()
  
  if (formula[[3]] == "1")
  {
      design[[1]] = rb(matrix(1,nrow=m,ncol=1),"parametric",center=F)
      smooth = "fixed"
  }
  else if(formula[[3]] == ".")
  {
      design[[1]] = rb(data[,names(data) != all.vars(formula[[2]])],"parametric")
      smooth = "fixed"
  }
  else
    for(i in 1:length(labels(terms(formula))))
    {
      types[[i]] = strsplit(labels(terms(formula))[i],"(",fixed=TRUE)[[1]][1]
      
      if(types[[i]] == labels(terms(formula))[i])
      {
        design[[i]] = rb(matrix(eval(parse(text=labels(terms(formula))[i]),envir=data,enclos=environment(formula)),nrow=m),"parametric")
        #formula = eval(substitute(update(formula, . ~ variable2 + . - variable1),
        #               list(variable1 = as.name(types[[i]]),variable2 = as.name(paste("rb(",types[[i]],",'parametric')",sep="")))))
        types[[i]] = "parametric"
      }
      else  
        design[[i]] = eval(parse(text=labels(terms(formula))[i]),envir=data,enclos=environment(formula))
    }
  nterms = length(design)

  varying[[1]] = design[[1]][[9]]
  if(any(!is.na(varying[[1]])))
  {
    B = design[[1]][[1]] * varying[[1]]
    Blist[[1]] = design[[1]][[1]] * varying[[1]]
  }
  else
  {
    B = design[[1]][[1]]
    Blist[[1]] = design[[1]][[1]]
  }

  DD = as.matrix(design[[1]][[2]])
  Plist[[1]] = DD
  x[[1]] = design[[1]][[3]]
  names(x)[1] = design[[1]]$xname
  types[[1]] = design[[1]][[4]]
  bnd[[1]] = design[[1]][[5]]
  Zspathelp[[1]] = design[[1]][[6]]
  nb[1] = ncol(design[[1]][[1]])
  krig.phi[[1]] = design[[1]][[7]]
  center = center && design[[1]][[8]]
  constmat = as.matrix(design[[1]]$constraint)

  if(length(design) > 1)
  for(i in 2:length(labels(terms(formula))))
  {
    varying[[i]] = design[[i]][[9]]
    if(any(!is.na(varying[[i]])))
    {
      B = design[[i]][[1]] * varying[[i]]
      Blist[[i]] = design[[i]][[1]] * varying[[i]]
    }
    else
    {
      B = cbind(B,design[[i]][[1]])
      Blist[[i]] = design[[i]][[1]]
    }
    
    design[[i]][[2]] = as.matrix(design[[i]][[2]])
    Plist[[i]] = design[[i]][[2]]
    DD = rbind(cbind(DD,matrix(0,nrow=nrow(DD),ncol=ncol(design[[i]][[2]]))),
               cbind(matrix(0,nrow=nrow(design[[i]][[2]]),ncol=ncol(DD)),design[[i]][[2]]))
    constmat = rbind(cbind(constmat,matrix(0,nrow=nrow(constmat),ncol=ncol(design[[i]]$constraint))),
               cbind(matrix(0,nrow=nrow(design[[i]]$constraint),ncol=ncol(constmat)),design[[i]]$constraint))
    x[[i]] = design[[i]][[3]]
    names(x)[i] = design[[i]]$xname
    types[[i]] = design[[i]][[4]]
    bnd[[i]] = design[[i]][[5]]
    Zspathelp[[i]] = design[[i]][[6]]
    nb[i] = ncol(design[[i]][[1]])
    krig.phi[[i]] = design[[i]][[7]]
    center = center && design[[i]][[8]]
  }

  if(center)
  {
    B = cbind(1,B)
    DD = rbind(0,cbind(0,DD))
    constmat = rbind(0,cbind(0,constmat))
  }
  
  amplitude = NULL

  if(estimate == "iprls")
  {
    coef.vector = iprls(B,DD,yy,pp,lambda,smooth,nb,center,constmat,robust,adaptive, LSMaxCores)
    amplitude = coef.vector[[3]]
  }
  else if(estimate == "restricted")
    coef.vector = restricted(B,DD,yy,pp,lambda,smooth,nb,center,constmat,robust)

  vector.a.ma.schall = coef.vector[[1]]
  lala = coef.vector[[2]]
  ww = coef.vector[[4]]
  diag.hat = coef.vector[[5]]

  fitted = B %*% vector.a.ma.schall

  covariance = NULL

##############################
if(ci)
{
  #W = list()
  covariance = list()

  for(i in 1:np)
  {
  	res = yy - fitted[,i,drop=F]
  
  	s.tmp = median(abs(res-median(res)))/0.6745 

  	if(adaptive)
  	{
  	  s = s.tmp #* sqrt(amplitude[1:m])
  	  cc = robust * abs(amplitude)
  	}
  	else
  	{
      s = s.tmp 
      cc = robust
    }
  	resid = res/s
  	W=diag(2*c(pp[i]*(0<=resid & resid<=cc)+(1-pp[i])*(-cc<=resid & resid<0)),m,m)
    V=diag(c((ww[,i]^2)*(resid^2)),m,m)	

    lahmda = rep(lala[,i],times=nb)
    if(center)
      lahmda = c(0,lahmda)
    K = lahmda * t(DD) %*% DD
    helpmat = solve(t(B)%*%diag((1/s),m)%*%W%*%B + K) 


Epsi2=sum((ww[,i]*resid)^2)/(m-ncol(B))
Epsi=(sum(2/s*(pp[i]*(0<=resid & resid<=cc)+(1-pp[i])*(-cc<=resid & resid<0)))/m)

 
  psi = abs(-(1-pp[i])*cc*(resid< -cc)+(1-pp[i])* resid*(resid <0 & resid>=-cc)+pp[i]* resid*(resid>=0 & resid <cc)+pp[i]*cc*(resid>=cc))
 
  
covariance[[i]] = (m/(m-ncol(B))) * helpmat %*% (t(B) %*% diag(psi[,1])^2 %*% diag(1/(1-diag.hat[,i]))  %*% B) %*% helpmat

  }

}
##############################


  Z <- list()
  coefficients <- list()
  final.lambdas <- list()
  helper <- list()
  
  
  
  if(center)
  {
    intercept = vector.a.ma.schall[1,]
    B = B[,-1,drop=FALSE]
    vector.a.ma.schall = vector.a.ma.schall[-1,,drop=FALSE]
  }
  else
    intercept = rep(0,np)

  for(k in 1:length(design))
  {
    final.lambdas[[k]] = lala[k,]
    names(final.lambdas)[k] = design[[k]]$xname
  
    partbasis = (sum(nb[0:(k-1)])+1):(sum(nb[0:k]))
  
    if(types[[k]] == "pspline")
    {
      Z[[k]] <- matrix(NA, m, np)
      coefficients[[k]] = matrix(NA,nrow=nb[k],ncol=np)
      helper[[k]] = NA
      for(i in 1:np)
      {
        Z[[k]][,i] <- design[[k]][[1]] %*% vector.a.ma.schall[partbasis,i,drop=FALSE] + intercept[i]
        coefficients[[k]][,i] = vector.a.ma.schall[partbasis,i,drop=FALSE]
      }
    }
    else if(types[[k]] == "markov")
    {
      Z[[k]] <- matrix(NA, m, np)
      coefficients[[k]] = matrix(NA,nrow=nb[k],ncol=np)
      helper[[k]] = list(bnd[[k]],Zspathelp[[k]])
      for(i in 1:np)
      {
        Z[[k]][,i] = design[[k]][[1]] %*% vector.a.ma.schall[partbasis,i,drop=FALSE] + intercept[i]
        coefficients[[k]][,i] = vector.a.ma.schall[partbasis,i,drop=FALSE]
      }
    }
    else if(types[[k]] == "2dspline")
    {
      Z[[k]] <- matrix(NA, m, np)
      coefficients[[k]] = matrix(NA,nrow=nb[k],ncol=np)
      helper[[k]] = NA
      for(i in 1:np)
      {
        Z[[k]][,i] = design[[k]][[1]] %*% vector.a.ma.schall[partbasis,i,drop=FALSE] + intercept[i]
        coefficients[[k]][,i] = vector.a.ma.schall[partbasis,i,drop=FALSE]
      }
      
    }
    else if(types[[k]] == "radial")
    {
      Z[[k]] <- matrix(NA, m, np)
      coefficients[[k]] = matrix(NA,nrow=nb[k],ncol=np)
      helper[[k]] = NA
      for(i in 1:np)
      {
        Z[[k]][,i] = design[[k]][[1]] %*% vector.a.ma.schall[partbasis,i,drop=FALSE] + intercept[i]
        coefficients[[k]][,i] = vector.a.ma.schall[partbasis,i,drop=FALSE]
      }
    }
    else if(types[[k]] == "krig")
    {
      Z[[k]] <- matrix(NA, m, np)
      coefficients[[k]] = matrix(NA,nrow=nb[k],ncol=np)
      helper[[k]] = krig.phi[[k]]
      for(i in 1:np)
      {
        Z[[k]][,i] = design[[k]][[1]] %*% vector.a.ma.schall[partbasis,i,drop=FALSE] + intercept[i]
        coefficients[[k]][,i] = vector.a.ma.schall[partbasis,i,drop=FALSE]
      }
    }
    else if(types[[k]] == "random")
    {
      Z[[k]] <- matrix(NA, m, np)
      coefficients[[k]] = matrix(NA,nrow=nb[k],ncol=np)
      helper[[k]] = NA
      for(i in 1:np)
      {
        Z[[k]][,i] <- design[[k]][[1]] %*% vector.a.ma.schall[partbasis,i,drop=FALSE] + intercept[i]
        coefficients[[k]][,i] = vector.a.ma.schall[partbasis,i,drop=FALSE]
      }

    }
    else if(types[[k]] == "ridge")
    {
      Z[[k]] <- matrix(NA, m, np)
      coefficients[[k]] = matrix(NA,nrow=nb[k],ncol=np)
      helper[[k]] = NA
      for(i in 1:np)
      {
        Z[[k]][,i] <- design[[k]][[1]] %*% vector.a.ma.schall[partbasis,i,drop=FALSE] + intercept[i]
        coefficients[[k]][,i] = vector.a.ma.schall[partbasis,i,drop=FALSE]
      }
    }
    else if(types[[k]] == "parametric")
    {    
      Z[[k]] <- matrix(NA, m, np)
      coefficients[[k]] = matrix(NA,nrow=nb[k],ncol=np)
      helper[[k]] = NA
      for(i in 1:np)
      {
        Z[[k]][,i] <- design[[k]][[1]] %*% vector.a.ma.schall[partbasis,i,drop=FALSE] + intercept[i]
        coefficients[[k]][,i] = vector.a.ma.schall[partbasis,i,drop=FALSE]
      }
    }
    else if(types[[k]] == "special")
    {    
      Z[[k]] <- matrix(NA, m, np)
      coefficients[[k]] = matrix(NA,nrow=nb[k],ncol=np)
      helper[[k]] = NA
      for(i in 1:np)
      {
        Z[[k]][,i] <- design[[k]][[1]] %*% vector.a.ma.schall[partbasis,i,drop=FALSE] + intercept[i]
        coefficients[[k]][,i] = vector.a.ma.schall[partbasis,i,drop=FALSE]
      }
    }
    names(Z)[k] = design[[k]]$xname
    names(coefficients)[k] = design[[k]]$xname
  }

  desmat = B
  if(center)
    desmat = cbind(1,B)

  result = list("lambda"=final.lambdas,"intercepts"=intercept,"coefficients"=coefficients,"values"=Z,"response"=yy,"covariates"=x,
                "formula"=formula,"asymmetries"=pp,"effects"=types,"helper"=helper,"design"=desmat,"bases"=design,"fitted"=fitted,"amplitude"=amplitude,"covmat"=covariance)

             
  result$predict <- function(newdata=NULL)
         {
           BB = list()
           values = list()
           bmat = NULL
           for(k in 1:length(coefficients))
           {
             BB[[k]] = predict(design[[k]],newdata)
             values[[k]]  <- BB[[k]] %*% coefficients[[k]]
             values[[k]] = t(apply(values[[k]],1,function(x) { x + intercept } ))
             bmat = cbind(bmat,BB[[k]])
           }
           if(center)
           {
             bmat = cbind(1,bmat)
             vector.a.ma.schall = rbind(intercept,vector.a.ma.schall)
           }
           fitted = bmat %*% vector.a.ma.schall
           names(values) = names(coefficients)
           
           list("fitted"=fitted,"values"=values)
         }
  
  class(result) = c("expectreg",estimate)
  
  result
}