R/ordFusion.R

In ordPens: Selection, Fusion, Smoothing and Principal Components Analysis for Ordinal Variables

ordFusion <- function(x, y, u = NULL, z = NULL, offset = rep(0,length(y)), lambda, 
                      model = c("linear", "logit", "poisson", "cumulative"), restriction = c("refcat", "effect"), 
                      scalex = TRUE, nonpenx = NULL, frac.arclength = NULL, ...)
{
  model <- match.arg(model)
  model <- switch(model, linear="linear", logit="logit", poisson="poisson", cumulative="cumulative")
  restriction <- match.arg(restriction) 
  
  ## Check the x matrix
  if(!(is.matrix(x) | is.numeric(x) | is.data.frame(x)))
    stop("x has to be a matrix, numeric vector or data.frame")
  
  if(any(is.na(x)))
    stop("Missing values in x are not allowed")
  
  
  ## Check the response
  if(!is.numeric(y))
    stop("y has to be numeric")
  
  if(model == "logit" & any(!is.element(y[!is.na(y)], c(0,1))))
    stop("y has to be 0/1 coded")
  
  tol <- .Machine$double.eps^0.5 
  if((model == "poisson" | model == "cumulative") & 
     (any(abs(y[!is.na(y)] - round(y[!is.na(y)])) > tol) | any(y[!is.na(y)] < 0)))
    stop("y has to contain nonnegative integers")
  
  
  ## Check the other arguments
  if(length(offset) != length(y))
    stop("length(offset) not equal length(y)")  
  
  if(!is.null(nonpenx))
  {if(max(nonpenx) > ncol(as.matrix(x)))
    stop("max(nonpenx) > ncol(x)")}
  
  ## ordinal predictors  
  x <- xord <- as.matrix(x)
  px <- ncol(x)
  kx <- apply(x,2,max)
  xnames <- colnames(x)
  grp <- rep(1:px,kx-1)
  x <- coding(x, constant=FALSE)
  x <- x[!is.na(y),]

  lmbd <- lmbs <- sort(lambda, decreasing = TRUE)
  
  ## nominal predictors
  if (length(u) > 0)
  {
    if(!(is.matrix(u) | is.numeric(u) | is.data.frame(u)))
      stop("u has to be a matrix, numeric vector or data.frame")
    if(any(is.na(u)))
      stop("Missing values in u are not allowed")
    
    u <- as.matrix(u)
    if(nrow(u) != length(y))
      stop("u and y do not have correct dimensions")
    if(any(!apply(u,2,is.numeric)))
      stop("Entries of u have to be of type 'numeric'")
    if(any(abs(u - round(u)) > tol) | any(u < 1))
      stop("u has to contain positive integers")
    pu <- ncol(u)
    ku <- apply(u,2,max)
    unames <- colnames(u)
    grp <- c(grp,rep(max(grp)+(1:pu),ku-1))
    u <- coding(u, constant=FALSE, splitcod=FALSE)
    u <- u[!is.na(y),]
    nonpenu <- 1:pu
  }
  else
  {
    pu <- NULL
    nonpenu <- NULL
    ku <- NULL
  }
  
  ## metric predictors
  if (length(z) > 0)
  {
    if(!(is.matrix(z) | is.numeric(z) | is.data.frame(z)))
      stop("z has to be a matrix, numeric vector or data.frame")
    if(any(is.na(z)))
      stop("Missing values in z are not allowed")
    
    z <- as.matrix(z)
    if(nrow(z) != length(y))
      stop("z and y do not have correct dimensions")
    if(any(!apply(z,2,is.numeric)))
      stop("Entries of z have to be of type 'numeric'")
    pz <- ncol(z)
    znames <- colnames(z)
    grp <- c(grp,max(grp)+(1:pz))
    z <- z[!is.na(y),]
    nonpenz <- 1:pz
  }
  else
  {
    pz <- NULL
    nonpenz <- NULL
  }
  
  xuz <- cbind(x,u,z)    
  offset <- offset[!is.na(y)]
  y <- y[!is.na(y)]
  
  ## fitting
  nonpen <- c(nonpenx, px+nonpenu, px+ifelse(length(pu)>0,pu,0)+nonpenz)
  if (length(nonpen) > 0)
  {
    nonpen2 <- 1:ncol(xuz)
    nonpen2[!is.element(grp,nonpen)] <- -1
    nonpen2 <- nonpen2[nonpen2 > 0]
  }
  else
  {
    nonpen2 <- NULL
  }
  
  if (model == "linear")
  {
    if (is.null(frac.arclength))
      frac.arclength <- 1
    
    flmodel <- glmpath(xuz, y, nopenalty.subset = nonpen2,
                       family = gaussian, standardize = scalex,
                       frac.arclength = frac.arclength, ...)
  }
  else if (model == "logit")
  {
    if (is.null(frac.arclength))
      frac.arclength <- 0.1
    
    flmodel <- glmpath(xuz, y, nopenalty.subset = nonpen2,
                       family = binomial, standardize = scalex,
                       frac.arclength = frac.arclength, ...)
  }
  else if (model == "poisson")
  {
    if (is.null(frac.arclength))
      frac.arclength <- 0.1
    
    flmodel <- glmpath(xuz, y, nopenalty.subset = nonpen2,
                       family = poisson, standardize = scalex,
                       frac.arclength = frac.arclength, ...)
  }

  
  xgrp <- grp[1:ncol(x)]
  
  if(model == "cumulative")
  {
    q <- length(levels(factor(y))) - 1
    flmodel <- ordinalNet(x=x, y=factor(y), lambdaVals = lmbd/length(y), 
                          family="cumulative", link="logit", ...) 
    nloglik <- - flmodel$loglik
    
    constant <- constrefcat <- t(flmodel$coefs[,1:q, drop=F])  
    xc <- - t(flmodel$coefs[,-(1:q), drop=F])  
  }
  else
  {
    lmbd <- c(max(flmodel$lambda),lmbd[lmbd < max(flmodel$lambda)])
    
    flx <- predict(flmodel, s = lmbd, type = "coefficients",
                   mode = "lambda")
    constant <- flx[,1]
    xuzc <- t(flx[,-1,drop=F])
    xc <- cbind(xuzc[1:ncol(x),])
  }
  
  for (j in 1:max(xgrp))
  {
    xc[xgrp==j,] <- apply(xc[xgrp==j, ,drop=FALSE],2,cumsum)
  }
  if (length(xnames)==0)
    xnames <- paste("x",1:px,sep="")
  
  xnames <- rep(xnames,kx)
  xnames <- paste(xnames,":",sequence(kx),sep="")
  
  xcoefs <- matrix(0,length(xnames),ncol(xc))
  xcoefs[sequence(kx)>1,] <- xc
  xcrefcat <- xcoefs  
  
  if (length(u) > 0)
  {
    if (ncol(u) > 1)
      uc <- cbind(xuzc[ncol(x)+(1:ncol(u)),])
    else
      uc <- rbind(xuzc[ncol(x)+1,])
    
    if (length(unames)==0)
      unames <- paste("u",1:pu,sep="")
    
    unames <- rep(unames,ku)
    unames <- paste(unames,":",sequence(ku),sep="")
    
    ucoefs <- matrix(0,length(unames),ncol(uc))
    ucoefs[sequence(ku)>1,] <- uc
  }
  else
  {
    ucoefs <- NULL
    unames <- NULL
  }
  
  if (length(z) > 0)
  {
    if (ncol(z) > 1)
      zcoefs <- cbind(xuzc[length(grp)+2-(ncol(z):1),])
    else
      zcoefs <- rbind(xuzc[length(grp)+1,])
    
    if (length(znames)==0)
      znames <- paste("z",1:pz,sep="")
  }
  else
  {
    zcoefs <- NULL
    znames <- NULL
  }
  
   
  ## Effect coding / sum to zero restriction
  if(restriction == "effect")
  {
    modelbjk <-  xc[1:ncol(x), ,drop=F]  
    transcoef <- matrix(NA, ncol(x), ncol(xc)) 
    transb1 <- matrix(NA, px, ncol(xc)) 
    for(j in 1:px){ 
      means <- drop(apply(modelbjk[grp==j,,drop=F], 2, function(x) mean(c(0,x))) )
      for(i in 1:ncol(xc)){
        transcoef[grp==j,i] <- beffcjk <- modelbjk[grp==j,i] - means[i]
        transb1[j,i] <- - sum(beffcjk)
      }   
    }
    xcoefs[sequence(kx)>1,] <- transcoef 
    xcoefs[sequence(kx)==1,] <- transb1 
    if(model == "cumulative") constant <- sweep(constant, 2, apply(transb1,2,sum), "+")
  }
  
  if(model == "cumulative")
  {
    coefs <- rbind(xcoefs, constant)
    
    thetanames <- paste("intercept:", sequence(q), sep="")
    rownames(coefs) <- c(xnames, thetanames)
    
    flmodel$lambda <- flmodel$lambdaVals*length(y); flmodel$model <- "cumulative"; flmodel$xlevels <- kx; flmodel$zcovars <- 0; class(flmodel) <- "ordPen"; flmodel$restriction <- "refcat"
    flmodel$coefficients <- rbind(xcrefcat, constrefcat)  
    fits <- predict(flmodel, newx = xord, type = "response", ...) 
    colnames(coefs) <- lmbd
 
  }
  else
  {
    coefs <-  rbind(constant,xcoefs,ucoefs,zcoefs)
    
    rownames(coefs) <- c("intercept",xnames,unames,znames)
    fits <- predict(flmodel, newx = xuz, s = lmbd, type = "response",
                    mode = "lambda")                     
    colnames(fits) <- lmbd
    colnames(coefs) <- lmbd
    rownames(fits) <- NULL
    
    ladd <- sum(lmbs > max(flmodel$lambda)) 
    if (ladd > 0)
    {
      cadd <- matrix(coefs[,1],nrow(coefs),ladd, byrow = FALSE)
      fadd <- matrix(fits[,1],nrow(fits),ladd, byrow = FALSE)
      coefs <- cbind(cadd,coefs[,-1])
      fits <- cbind(fadd,fits[,-1])
    }
    else
    {
      coefs <- cbind(coefs[,-1])
      fits <- cbind(fits[,-1])
    }
    colnames(coefs) <- colnames(fits) <- lmbs
    rownames(fits) <- NULL

    nloglik <- NULL  
  }  
 
  out <- list(fitted = fits,
              coefficients = coefs, 
              model = model,
              restriction = restriction,
              lambda = lmbs,
              xlevels = kx,
              ulevels = ku,
              zcovars = length(znames))
  structure(out, class = "ordPen")
}