R/phylolm.R

In phylolm: Phylogenetic Linear Regression

phylolm <- function(formula, data=list(), phy, 
	model=c("BM","OUrandomRoot","OUfixedRoot","lambda","kappa","delta","EB","trend"),
	lower.bound=NULL, upper.bound=NULL, starting.value=NULL, measurement_error = FALSE,
	boot=0,full.matrix = TRUE, ...)
{

  ## initialize	
  if (!inherits(phy, "phylo")) stop("object \"phy\" is not of class \"phylo\".")
  model = match.arg(model)	
  if ((model=="trend")&(is.ultrametric(phy)))
   stop("the trend is unidentifiable for ultrametric trees.")
  if ((model=="lambda") && measurement_error)
    stop("the lambda transformation and measurement error cannot be used together: they are not distinguishable")
  if (is.null(phy$edge.length)) stop("the tree has no branch lengths.")
  if (is.null(phy$tip.label)) stop("the tree has no tip labels.")	
  tol = 1e-10	

  mf = model.frame(formula=formula,data=data)
  
  
  if (is.null(rownames(mf))) {
   if (nrow(mf)!=length(phy$tip.label))
      stop("number of rows in the data does not match the number of tips in the tree.")
   warning("the data has no names, order assumed to be the same as tip labels in the tree.\n")
  }
  else { # the data frame has row names
    taxa_without_data = setdiff(phy$tip.label, rownames(mf))
    if (length(taxa_without_data)>0){
      warning("will drop from the tree ", length(taxa_without_data), " taxa with missing data")
      phy = drop.tip(phy, taxa_without_data)
    }
    if (length(phy$tip.label)<2)
      stop("names of the data do not match with tip labels.")
    taxa_notin_tree = setdiff(rownames(mf), phy$tip.label)
    if (length(taxa_notin_tree)>0){
      warning(length(taxa_notin_tree), " taxa not in the tree: their data will be ignored")
      mf = mf[-which(rownames(mf) %in% taxa_notin_tree),,drop=F]
    }
    # now we should have that: nrow(mf)==length(phy$tip.label)
    ordr = match(phy$tip.label, rownames(mf))
    if (any(is.na(ordr))) # should never happen given earlier checks
      stop("data names do not match with the tip labels.\n")
    mf = mf[ordr,,drop=F]
  }
  X = model.matrix(attr(mf, "terms"), data=mf)
  y = model.response(mf)
  d = ncol(X)

  phy = reorder(phy,"pruningwise")
  n <- length(phy$tip.label)
  N <- dim(phy$edge)[1]
  ROOT <- n + 1L
  anc <- phy$edge[, 1]
  des <- phy$edge[, 2]
  externalEdge <- des<=n

  OU = c("OUrandomRoot","OUfixedRoot")
  flag = 0 # flag and D are used for OU model if tree is not ultrametric:
  D = NULL #            for the generalized 3-point structure

  ## preparing for OU model
  if (model %in% OU) {
    D = numeric(n)
    if (!is.ultrametric(phy)) {
      flag = 1
      dis = pruningwise.distFromRoot(phy)
      Tmax = max(dis[1:n])
      D = Tmax - dis[1:n]
      D = D - mean(D)
      phy$edge.length[externalEdge] <- phy$edge.length[externalEdge] + D[des[externalEdge]]
      ## phy is now ultrametric, with height Tmax:
      Tmax = Tmax + min(D)
    }
  }
	
  ## preparing for trend model
  if (model == "trend") {
    trend = pruningwise.distFromRoot(phy)[1:n]
    X = cbind(X,trend)
    d = d+1
  }

  ## calculate Tmax = average distance from root to tips,
  ## to choose appropriate starting values later # fixit
  dis = pruningwise.distFromRoot(phy)[1:n]
  Tmax = mean(dis)

  ## Default bounds
  bounds.default = matrix(c(1e-7/Tmax,50/Tmax,1e-7,1,1e-6,1,1e-5,3,-3/Tmax,0,1e-16,1e16), ncol=2, byrow=TRUE)
  rownames(bounds.default) = c("alpha","lambda","kappa","delta","rate","sigma2_error")
  colnames(bounds.default) = c("min","max")

  ## Default starting values
  starting.values.default = c(0.5/Tmax,0.5,0.5,0.5,-1/Tmax,1) 
  names(starting.values.default) = c("alpha","lambda","kappa","delta","rate","sigma2_error")

  ## User defined bounds and starting values
  if (is.null(lower.bound)) {
    if (model %in% OU) 
      lower.bound = bounds.default[1,1]
    if (model=="lambda") lower.bound = bounds.default[2,1]
    if (model=="kappa") lower.bound = bounds.default[3,1]
    if (model=="delta") lower.bound = bounds.default[4,1]
    if (model=="EB") lower.bound = bounds.default[5,1]
  }
  if (is.null(upper.bound)) {
    if (model %in% OU) 
      upper.bound = bounds.default[1,2]
    if (model=="lambda") upper.bound = bounds.default[2,2]
    if (model=="kappa") upper.bound = bounds.default[3,2]
    if (model=="delta") upper.bound = bounds.default[4,2]
    if (model=="EB") upper.bound = bounds.default[5,2]
  }
  if (is.null(starting.value)) {
    if (model %in% OU) 
      starting.value = starting.values.default[1]
    if (model=="lambda") starting.value = starting.values.default[2]
    if (model=="kappa") starting.value = starting.values.default[3]
    if (model=="delta") starting.value = starting.values.default[4]
    if (model=="EB") starting.value = starting.values.default[5]
  } else {
    if (model %in% OU) starting.value = starting.value$alpha
    if (model=="lambda") starting.value = starting.value$lambda
    if (model=="kappa") starting.value = starting.value$kappa
    if (model=="delta") starting.value = starting.value$delta
    if (model=="EB") starting.value = starting.value$rate
  }

  if (measurement_error) {
    lower.bound = c(lower.bound, bounds.default[6,1])
    upper.bound = c(upper.bound, bounds.default[6,2])
    starting.value = c(starting.value, starting.values.default[6])
  }


  ## preparing for general use of "parameter" for branch length transformation
  prm = list(myname = starting.value[1])
  names(prm) = model # good for lambda, kappa, delta
  if (model %in% OU) names(prm) = "alpha"
  if (model == "EB") names(prm) = "rate"
  if (measurement_error) {
    if (model %in% c("BM","trend")) names(prm) = "sigma2_error"
    else prm[["sigma2_error"]] = starting.value[2]
  }

  ## log-likelihood, computation using the three-point structure
  ole= 4 + 2*d + d*d # output length
  loglik <- function(parameters,y,X) {
    tree = transf.branch.lengths(phy,model,parameters=parameters,
      check.pruningwise=F,check.ultrametric=F,D=D,check.names=F)$tree
    if (flag) { # need diagonal terms in D
      y = exp(-parameters$alpha*D) * y # variables local to this function
      X = exp(-parameters$alpha*D) * X
    }
    tmp=.C("threepoint", as.integer(N),as.integer(n),as.integer(phy$Nnode),
      as.integer(1),as.integer(d),as.integer(ROOT),as.double(tree$root.edge),as.double(tree$edge.length),
      as.integer(des), as.integer(anc), as.double(as.vector(y)), as.double(as.vector(X)),
      result=double(ole))$result # tmp has, in this order:
    ## logdetV, 1'V^{-1}1, y'V^{-1}1, y'V^{-1}y, X'V^{-1}1, X'V^{-1}X, X'V^{-1}y
    comp = list(vec11=tmp[2], y1=tmp[3], yy=tmp[4], X1=tmp[5:(4+d)],
                XX=matrix(tmp[(5+d):(ole-d)], d,d),Xy=tmp[(ole-d+1):ole],logd=tmp[1])
    invXX = solve(comp$XX)
    betahat = invXX%*%comp$Xy
    sigma2hat = as.numeric((comp$yy - 2*t(betahat)%*%comp$Xy + t(betahat)%*%comp$XX%*%betahat)/n)
    if (sigma2hat<0) {
      resdl = X%*%betahat - y
      tmpyy=.C("threepoint", as.integer(N),as.integer(n),as.integer(phy$Nnode),
        as.integer(1),as.integer(d),as.integer(ROOT),as.double(tree$root.edge),as.double(tree$edge.length),
        as.integer(des), as.integer(anc), as.double(as.vector(resdl)), as.double(as.vector(X)),
        result=double(ole))$result[4]
      sigma2hat = tmpyy/n
    }
    n2llh = as.numeric( n*log(2*pi) + n + n*log(sigma2hat) + comp$logd) # -2 log-likelihood
    if (flag)
      n2llh = n2llh + parameters$alpha * 2*sum(D)
    ## because diag matrix used for generalized 3-point structure is exp(alpha diag(D))
    vcov = sigma2hat*invXX*n/(n-d)
    return(list(n2llh=n2llh, betahat = as.vector(betahat), sigma2hat=sigma2hat,vcov=vcov))
  }

  ## Fitting
  lower = lower.bound
  upper = upper.bound
  start = starting.value

  if ((model %in% c("BM","trend"))&&(!measurement_error)) {
    BMest = loglik(prm, y, X) # root edge taken to be 0
    results <- list(coefficients=BMest$betahat, sigma2=BMest$sigma2hat, optpar=NULL, sigma2_error = 0,
                    logLik=-BMest$n2llh/2, p=1+d, aic=2*(1+d)+BMest$n2llh, vcov = BMest$vcov)
  } else {
    ##------- Optimization of phylogenetic correlation parameter is needed ---------#
    # first: checks of bounds
    if (sum(lower>start)+sum(upper<start)>0 )
      stop("The starting value is not within the bounds of the parameter.")

    # def of function to be optimized
    # minus2llh_sinvar: return the -loglik given a single variable: measure-err
    #    logvalue=log of measure-err variance
    #    if not BM: prm[[1]] needs up-to-date before calling this fcn:
    #               prm[[1]] = alpha or lamda or kappa or rate
    minus2llh_sinvar=function(logvalue) {
      if(model %in% c("BM","trend")){
        prm[[1]] = exp(logvalue)
      } else
        prm[[2]] = exp(logvalue)
      loglik(prm, y, X)$n2llh
    }
    # minus2llh: returns -loglik given 'alpha' and possibly measurement error
    minus2llh <- function(logvalue, y) {
      if (model == "EB") prm[[1]]=logvalue[1] # which is 'rate', not log(rate)
      else prm[[1]]=exp(logvalue[1]) # first element is the parameter of the model
      if ((measurement_error)&&(!(model %in% c("BM","trend")))){
        prm[[2]]=exp(logvalue[2])
      }
      loglik(prm, y, X)$n2llh
    }

    # get objects to start the search, and to bound the search
    if (lower[1]==upper[1] && !(measurement_error)) { # no optimization in fact
      prm[[1]] = lower[1]
      BMest = loglik(prm, y, X)
    }  else {
      if(model !="EB"){   # logstart = (log(alpha/lambda...), log(m.e. variance)) or just log(alpha,...)
        logstart = log(start)
        loglower = log(lower)
        logupper = log(upper)
      } else{
        # logstart = (rate, log(m.e. variance)) or just rate
        logstart = start  # do *not* log transform 'rate' because it is <= 0
        loglower = lower
        logupper = upper
        if(measurement_error){
          logstart[2] = log(start[2])
          loglower[2] = log(lower[2])
          logupper[2] = log(upper[2])
        }
      }
      if (!(model %in% c("BM","trend")) && lower[1] != upper[1]){
        opt <- optim(logstart, fn = minus2llh, method = "L-BFGS-B",lower=loglower, upper = logupper, y = y, ...)
        # next: get (co)variance parameters alpha/lambda... and m.e. variance into "prm"
        #       to be used later in loglik to get the estimated beta and sigma2.
        if (model == "EB") MLEvalue = as.numeric(opt$par[1]) else MLEvalue = as.numeric(exp(opt$par[1]))
        prm[[1]] = MLEvalue
        if ((isTRUE(all.equal(MLEvalue,lower[1], tol=tol)))||(isTRUE(all.equal(MLEvalue,upper[1],tol=tol)))) {
          matchbound = 1
          if ((model %in% c("lambda","kappa"))&&(MLEvalue == 1)) matchbound=0
          if ((model == "EB")&&(MLEvalue == 0)) matchbound=0
          if (matchbound)
            warning(paste("the estimation of", names(prm)[1],
                          'matches the upper/lower bound for this parameter.
                          You may change the bounds using options "upper.bound" and "lower.bound".\n'))
        }
        if (measurement_error){
            MLEsigma2_error = as.numeric(exp(opt$par[2]))
            prm[[2]] = MLEsigma2_error
        }
      } else { # then there must be measurement error
          # if BM or trend, logstart = log(m.e. variance), already set above.
          if (!(model %in% c("BM","trend"))) { # then we must have (lower[1]==upper[1])
            prm[[1]]=lower[1]
            logstart=logstart[2]
            loglower=loglower[2]
            logupper=logupper[2]
          }
          opt <- optim(logstart, fn = minus2llh_sinvar,method = "L-BFGS-B",lower=loglower, upper = logupper, ...)
          MLEsigma2_error = as.numeric(exp(opt$par[1]))
          if (model %in% c("BM","trend")){
            prm[[1]] = MLEsigma2_error
          } else {
            prm[[2]] = MLEsigma2_error
          }
      }
      # estimate beta and sigma2:
      BMest = loglik(prm, y, X)
    }
    # rescaling measurement error by sigma2
    sigma2_errorhat = 0
    if (measurement_error)
     sigma2_errorhat = MLEsigma2_error * BMest$sigma2hat
    # rescale sigma2 if OU, because it was "gamma" originally: sigma2 = 2 alpha gamma:
    if (model %in% OU)
      BMest$sigma2hat = 2*prm[[1]] * BMest$sigma2hat
      results <- list(coefficients=BMest$betahat, sigma2=BMest$sigma2hat, optpar=prm[[1]], sigma2_error = sigma2_errorhat,
                    logLik=-BMest$n2llh/2, p=2+d, aic=2*(2+d)+BMest$n2llh, vcov = BMest$vcov)
    if (model %in% c("BM","trend")) { # adjust for BM and trend models
      results$optpar = NULL
      results$p = results$p - 1
      results$aic = results$aic - 2
    }
    if (measurement_error) {
      results$p = results$p + 1 # adjust the number of parameters
      results$aic = results$aic + 2 # adjust AIC value
    }
  } # end of cases that are not BM only

  names(results$coefficients) = colnames(X)
  colnames(results$vcov) = colnames(X)
  rownames(results$vcov) = colnames(X)
  results$fitted.values = drop(X %*% results$coefficients)
  # drop: simplifies to vector, instead of matrix with 1 column
  results$residuals = y - results$fitted.values
  results$mean.tip.height = Tmax
  results$y = y
  results$X = X
  results$n = n
  results$d = d
  results$formula = formula
  results$call = match.call()
  results$model = model
  results$boot = boot

  ## starting the bootstrap
  if (boot>0) {
    # Turn off warnings
    options(warn=-1)
    # simulate all bootstrap data sets
    simmodel=model
    OU = c("OUrandomRoot","OUfixedRoot")
    if (model %in% OU){
      simmodel="OU"
    }
    # prm has "alpha" and "sigma2_error". Here we want "alpha" and "sigma2"
    prmsimul = list(sigma2 = results$sigma2)
    if (!(simmodel %in% c("BM","trend"))){
      Noname=prm[[1]]
      names(Noname)=NULL
      prmsimul[[2]] = Noname
      names(prmsimul)[2] = names(prm)[1]
    }

    # booty = bootstrap y response. parameter list depends on the model
    booty <- results$fitted.values +
     rTrait(n = boot, phy = phy,model = simmodel, parameters=prmsimul)
     # by default: ancestral.state=0 and optimal.value=0 --used for OU model only
    if (measurement_error){
      booty <- booty + rnorm(boot*n, mean=0, sd=sqrt(results$sigma2_error))
    }

    # analyze these bootstrapped data
    ncoeff = length(results$coefficients)
    colnumberalpha=ncoeff+2
    # nparam_var: number of parameters that affect the variances and covariances
    nparam_var = 1 # for sigma2
    if (measurement_error){
        nparam_var = nparam_var+1
        colnumberalpha=colnumberalpha+1
    }
    if (!(model %in% c("BM","trend"))) { nparam_var=nparam_var+1}
    # initialize bootvector: vector with bootstrap estimated parameters
    bootvector <- vector(length = ncoeff + nparam_var)
    names(bootvector) <- paste0("v",1:(ncoeff + nparam_var)) # temporary names, to initialize
    names(bootvector)[1:ncoeff] <- names(results$coefficients)
    names(bootvector)[ncoeff+1] <- "sigma2"
    if (measurement_error){
      names(bootvector)[ncoeff+2] <- "sigma2_error"
    }
    if (!(model %in% c("BM","trend"))) {
      names(bootvector)[colnumberalpha] <- names(prm)[1]
    }
    
    # define a function that will calculate the boot statistics. It is only dependent on `y`
    boot_model <- function(y) {
      # all other cases: first get 'prm' up-to-date.
      if (!(model %in% c("BM","trend")) && lower[1]==upper[1])
        bootvector[colnumberalpha] = lower[1] # will be used later to update 'prm'
      
      # otherwise: something needs to be optimized: m.e., alpha, or both.
      # below: storing 'standardized' estimated of m.e. variance in MLEsigma2_error. Rescaled later.
      if (!(model %in% c("BM","trend")) && lower[1] != upper[1]){
        try(opt <- optim(logstart, fn = minus2llh, method = "L-BFGS-B",lower=loglower, upper = logupper, y = y, ...),silent=TRUE)
        if (!inherits(opt, 'try-error')){
          if (model == "EB") {
            bootvector[colnumberalpha] = as.numeric(opt$par[1]); # will be used later to update 'prm'
          } else {
            bootvector[colnumberalpha] = as.numeric(exp(opt$par[1]));
          }
          if(measurement_error)  MLEsigma2_error = as.numeric(exp(opt$par[2]))
        } else {
          if(measurement_error){
            try(opt <- optim(logstart, fn = minus2llh_sinvar,method = "L-BFGS-B",lower=loglower, upper = logupper, ...),silent = TRUE)
            if (!inherits(opt, 'try-error')){
              MLEsigma2_error = as.numeric(exp(opt$par[1]))
            }
          }
        }
      }
      if (!(model %in% c("BM","trend")))
        prm[[1]] = bootvector[colnumberalpha] # update of 'prm'
      if (measurement_error){
        if (!(model %in% c("BM","trend"))) {
          prm[[2]] = MLEsigma2_error
        } else {
          prm[[1]] = MLEsigma2_error
        }
      }
      
      BMest = loglik(prm, y, X)
      if (model %in% OU)
        BMest$sigma2hat = 2*prm[[1]] * BMest$sigma2hat # was "gamma" originally: sigma2 = 2 alpha gamma
      if (measurement_error)
        bootvector[ncoeff+2] <- MLEsigma2_error * BMest$sigma2hat
      bootvector[1:ncoeff] <- BMest$betahat
      bootvector[ncoeff+1] <- BMest$sigma2hat
      return(bootvector)
    }
    
    bootmatrix <- future.apply::future_lapply(as.data.frame(booty), boot_model)
    bootmatrix <- do.call(rbind, bootmatrix)
    
    # summarize bootstrap estimates
    ind.na <- which(is.na(bootmatrix[,1]))
    # indices of replicates that failed: phylolm had an error
    if (length(ind.na)>0) {
      bootmatrix <- bootmatrix[-ind.na,]
      numOnes <- range(apply(booty[,ind.na],2,sum))
    }
    bootmean <- apply(bootmatrix, 2, mean)
    bootsd <- apply(bootmatrix, 2, sd)
    bootconfint95 <- apply(bootmatrix, 2, quantile, probs = c(.025, .975))
    bootmeansdLog = matrix(NA,2,nparam_var) # will give NaN for rate, but won't be printed.
    colnames(bootmeansdLog) = colnames(bootmatrix)[(ncoeff+1):(ncoeff+nparam_var)]
    for (i in 1:nparam_var){
      bootmeansdLog[1,i] <- mean(log(bootmatrix[, ncoeff + i]))
      bootmeansdLog[2,i] <- sd(log(bootmatrix[, ncoeff + i]))
    }

    results$bootmean = bootmean
    results$bootsd = bootsd
    results$bootconfint95 = bootconfint95
    results$bootmeansdLog = bootmeansdLog
    results$bootnumFailed = length(ind.na)
    if (full.matrix) results$bootstrap = bootmatrix

    ### Turn on warnings
    options(warn=0)
  }
  
  ## R squared
  if (model %in% OU) {
    RMS <- results$sigma2 / 2/results$optpar * n/(n-d)
    RSSQ <- results$sigma2 / 2/results$optpar * n
    
  } else {
    RMS <- results$sigma2 * n/(n-d)
    RSSQ <- results$sigma2 * n
  }
  
  xdummy <- matrix(rep(1, length(y)))
  # local variables used in loglik function
  d <- ncol(xdummy)
  ole <- 4 + 2*d + d*d # output length
  nullMod <- loglik(prm, y, xdummy)
  
  NMS <- nullMod$sigma2hat * n/(n-1)
  NSSQ <- nullMod$sigma2hat * n

  results$r.squared <- (NSSQ - RSSQ) / NSSQ
  results$adj.r.squared <- (NMS - RMS) / NMS

  class(results) = "phylolm"
  return(results)
}

################################################
################################################

print.phylolm <- function(x, digits = max(3, getOption("digits") - 3), ...){
  cat("Call:\n")
  print(x$call)
  cat("\n")
  aiclogLik = c(x$aic,x$logLik)
  names(aiclogLik) = c("AIC","logLik")
  print(aiclogLik, digits = digits)
  cat("\nParameter estimate(s) using ML:\n")
  if (!is.null(x$optpar)) {
    if (x$model %in% c("OUrandomRoot","OUfixedRoot")) cat("alpha:",x$optpar)
    if (x$model %in% c("lambda","kappa","delta")) cat(x$model,":",x$optpar)
    if (x$model=="EB") cat("rate:",x$optpar)
    cat("\n")
  }
  cat("sigma2:",x$sigma2,"\n")
  if (x$sigma2_error > 0) cat("sigma2_error:",x$sigma2_error,"\n")
  cat("\nCoefficients:\n")
  print(x$coefficients)
}
################################################
summary.phylolm <- function(object, ...) {
  se <- sqrt(diag(object$vcov))
  tval <- coef(object) / se

  if (object$boot == 0)
    TAB <- cbind(Estimate = coef(object), StdErr = se, t.value = tval,
                 p.value = 2*pt(-abs(tval), df=object$n - object$d))
  else
    TAB <- cbind(Estimate = coef(object), StdErr = se, t.value = tval,
                 lowerbootCI = object$bootconfint95[1,1:object$d],
                 upperbootCI = object$bootconfint95[2,1:object$d],
                 p.value = 2*pt(-abs(tval), df=object$n - object$d)) # need p-value last for printCoefmat

  res <- list(call=object$call, coefficients=TAB,
              residuals = object$residuals, sigma2 = object$sigma2,
              optpar=object$optpar, sigma2_error = object$sigma2_error, logLik=object$logLik,
              df=object$p, aic=object$aic, model=object$model,
              mean.tip.height=object$mean.tip.height,
              bootNrep = ifelse(object$boot>0, object$boot - object$bootnumFailed, 0),
              r.squared=object$r.squared, adj.r.squared=object$adj.r.squared)
  if (res$bootNrep>0) {
    res$bootmean = object$bootmean
    res$bootsd = object$bootsd
    res$bootconfint95 = object$bootconfint95
    res$bootmeansdLog <- object$bootmeansdLog
  }
  class(res) = "summary.phylolm"
  res
}
################################################
print.summary.phylolm <- function(x, digits = max(3, getOption("digits") - 3), ...){
  cat("\nCall:\n")
  print(x$call)
  cat("\n")
  aiclogLik = c(x$aic,x$logLik)
  names(aiclogLik) = c("AIC","logLik")
  print(aiclogLik, digits = digits)
  r <- zapsmall(quantile(x$residuals), digits + 1)
  names(r) <- c("Min", "1Q", "Median", "3Q", "Max")
  cat("\nRaw residuals:\n")
  print(r, digits = digits)

  cat("\nMean tip height:",x$mean.tip.height)
  cat("\nParameter estimate(s) using ML:\n")
  if (!is.null(x$optpar)) {
    if (x$model %in% c("OUrandomRoot","OUfixedRoot")) cat("alpha:",x$optpar)
    if (x$model %in% c("lambda","kappa","delta")) cat(x$model,":",x$optpar)
    if (x$model=="EB") cat("rate:",x$optpar)
    cat("\n")
  }

  cat("sigma2:",x$sigma2,"\n")
  if (x$sigma2_error > 0) cat("sigma2_error:",x$sigma2_error,"\n")

  cat("\nCoefficients:\n")
  printCoefmat(x$coefficients, P.values=TRUE, has.Pvalue=TRUE)
  
  cat("\nR-squared:", formatC(x$r.squared, digits = digits))
  cat("\tAdjusted R-squared:", formatC(x$adj.r.squared, digits = digits), "\n")
  
  if (!is.null(x$optpar)) {
    cat("\nNote: p-values and R-squared are conditional on ")
    if (x$model %in% c("OUrandomRoot","OUfixedRoot")) cat("alpha=",x$optpar,".",sep="")
    if (x$model %in% c("lambda","kappa","delta")) cat(x$model,"=",x$optpar,".",sep="")
    if (x$model=="EB") cat("rate=",x$optpar,".",sep="")
    cat("\n")
  }

  if (x$bootNrep > 0) {
    cat("\n")
    ncoef = nrow(x$coefficients)
    nparam_var=length(x$bootmean)-ncoef # number of variance/covariance parameters

    for (i in 1:nparam_var){
      tmp = colnames(x$bootmeansdLog)[i]# sigma2, sigma2_error or lambda/alpha/...
      tmp = ifelse(tmp %in% c("sigma2", "sigma2_error"), tmp, "optpar")
      cat(colnames(x$bootmeansdLog)[i],": ",x[[tmp]],"\n", sep="")
      cat("      bootstrap mean: ",    x$bootmean[ncoef+i]   ," (on raw scale)","\n",sep="")
      if (!(x$model %in% c("EB","lambda")) || tmp != "optpar")
        cat("                      ",exp(x$bootmeansdLog[1,i])," (on log scale, then back transformed)","\n",sep="")
      cat("      bootstrap 95% CI: (",x$bootconfint95[1,ncoef+i],",",x$bootconfint95[2,ncoef+i],")\n\n", sep="")
    }
    cat("Parametric bootstrap results based on",x$bootNrep,"fitted replicates\n")
  }
}
################################################
residuals.phylolm <-function(object,type=c("response"), ...){
  type <- match.arg(type)
  object$residuals	 
}
################################################
vcov.phylolm <- function(object, ...){
  object$vcov
}
################################################
logLik.phylolm <- function(object, ...){
  res = list(logLik = object$logLik, df = object$p)
  class(res) = "logLik.phylolm"
  res
}
print.logLik.phylolm <- function (x, ...) {
  cat("'log Lik.' ",x$logLik," (df=",x$df,")\n", sep = "")
}
AIC.logLik.phylolm <- function(object, k=2, ...) {
  return(k*object$df - 2*object$logLik)
}
AIC.phylolm <- function(object, k=2, ...) {
  return(AIC(logLik(object),k))
}
extractAIC.phylolm <- function(fit, scale, k=2, ...) {
    c(fit$p, - 2*fit$logLik + k * fit$p)
}
nobs.phylolm <- function(object, ...){
  return(object$n)
}
################################################
predict.phylolm <- function(object, newdata=NULL, ...){
  if (object$model=="trend")
    stop("Predicting for trend model has not been implemented.")
  if(is.null(newdata)) y <- fitted(object)
  else{			
    X = model.matrix(delete.response(terms(formula(object))),data = newdata)
    y <- X %*% coef(object)
  }
  y
}
################################################
plot.phylolm <-function(x, ...){
  plot(x$y, fitted(x), xlab = "Observed value", ylab = "Fitted value", ...)
}
################################################