R/lm.R

In dustinfife/flexforest: Estimate Structural Equation Models with Bagging

#  File src/library/stats/R/lm.R
#  Part of the R package, https://www.R-project.org
#
#  Copyright (C) 1995-2015 The R Core Team
#
#  This program is free software; you can redistribute it and/or modify
#  it under the terms of the GNU General Public License as published by
#  the Free Software Foundation; either version 2 of the License, or
#  (at your option) any later version.
#
#  This program is distributed in the hope that it will be useful,
#  but WITHOUT ANY WARRANTY; without even the implied warranty of
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#  GNU General Public License for more details.
#
#  A copy of the GNU General Public License is available at
#  https://www.R-project.org/Licenses/


lm <- function (formula, data, subset, weights, na.action,
                method = "qr", model = TRUE, x = FALSE, y = FALSE,
                qr = TRUE, singular.ok = TRUE, contrasts = NULL,
                offset, ...)
{

  ret.x <- x
  ret.y <- y
  cl <- match.call()
  mf <- match.call(expand.dots = FALSE)
  m <- match(c("formula", "data", "subset", "weights", "na.action", "offset"),
             names(mf), 0L)
  mf <- mf[c(1L, m)]
  mf$drop.unused.levels <- TRUE
  ## need stats:: for non-standard evaluation
  mf[[1L]] <- quote(stats::model.frame)
  mf <- eval(mf, parent.frame())
  if (method == "model.frame")
    return(mf)
  else if (method != "qr")
    warning(gettextf("method = '%s' is not supported. Using 'qr'", method),
            domain = NA)
  mt <- attr(mf, "terms") # allow model.frame to update it
  y <- model.response(mf, "numeric")
  ## avoid any problems with 1D or nx1 arrays by as.vector.
  w <- as.vector(model.weights(mf))
  if(!is.null(w) && !is.numeric(w))
    stop("'weights' must be a numeric vector")
  offset <- as.vector(model.offset(mf))
  if(!is.null(offset)) {
    if(length(offset) != NROW(y))
      stop(gettextf("number of offsets is %d, should equal %d (number of observations)",
                    length(offset), NROW(y)), domain = NA)
  }

  if (is.empty.model(mt)) {
    x <- NULL
    z <- list(coefficients = if (is.matrix(y))
      matrix(,0,3) else numeric(), residuals = y,
      fitted.values = 0 * y, weights = w, rank = 0L,
      df.residual = if(!is.null(w)) sum(w != 0) else
        if (is.matrix(y)) nrow(y) else length(y))
    if(!is.null(offset)) {
      z$fitted.values <- offset
      z$residuals <- y - offset
    }
  }
  else {
    x <- model.matrix(mt, mf, contrasts)
    z <- if(is.null(w)) lm.fit(x, y, offset = offset,
                               singular.ok=singular.ok, ...)
    else lm.wfit(x, y, w, offset = offset, singular.ok=singular.ok, ...)
  }
  class(z) <- c(if(is.matrix(y)) "mlm", "lm")
  z$na.action <- attr(mf, "na.action")
  z$offset <- offset
  z$contrasts <- attr(x, "contrasts")
  z$xlevels <- .getXlevels(mt, mf)
  z$call <- cl
  z$terms <- mt
  if (model)
    z$model <- mf
  if (ret.x)
    z$x <- x
  if (ret.y)
    z$y <- y
  if (!qr) z$qr <- NULL
  z
}

## lm.fit() and lm.wfit() have *MUCH* in common  [say ``code re-use !'']
lm.fit <- function (x, y, offset = NULL, method = "qr", tol = 1e-07,
                    singular.ok = TRUE, ...)
{
  if (is.null(n <- nrow(x))) stop("'x' must be a matrix")
  if(n == 0L) stop("0 (non-NA) cases")
  p <- ncol(x)
  if (p == 0L) {
    ## oops, null model
    return(list(coefficients = numeric(), residuals = y,
                fitted.values = 0 * y, rank = 0,
                df.residual = length(y)))
  }
  ny <- NCOL(y)
  ## treat one-col matrix as vector
  if(is.matrix(y) && ny == 1)
    y <- drop(y)
  if(!is.null(offset))
    y <- y - offset
  if (NROW(y) != n)
    stop("incompatible dimensions")
  if(method != "qr")
    warning(gettextf("method = '%s' is not supported. Using 'qr'", method),
            domain = NA)
  chkDots(...)
  z <- .Call(C_Cdqrls, x, y, tol, FALSE)
  if(!singular.ok && z$rank < p) stop("singular fit encountered")
  coef <- z$coefficients
  pivot <- z$pivot
  ## careful here: the rank might be 0
  r1 <- seq_len(z$rank)
  dn <- colnames(x); if(is.null(dn)) dn <- paste0("x", 1L:p)
  nmeffects <- c(dn[pivot[r1]], rep.int("", n - z$rank))
  r2 <- if(z$rank < p) (z$rank+1L):p else integer()
  if (is.matrix(y)) {
    coef[r2, ] <- NA
    if(z$pivoted) coef[pivot, ] <- coef
    dimnames(coef) <- list(dn, colnames(y))
    dimnames(z$effects) <- list(nmeffects, colnames(y))
  } else {
    coef[r2] <- NA
    ## avoid copy
    if(z$pivoted) coef[pivot] <- coef
    names(coef) <- dn
    names(z$effects) <- nmeffects
  }
  z$coefficients <- coef
  r1 <- y - z$residuals ; if(!is.null(offset)) r1 <- r1 + offset
  ## avoid unnecessary copy
  if(z$pivoted) colnames(z$qr) <- colnames(x)[z$pivot]
  qr <- z[c("qr", "qraux", "pivot", "tol", "rank")]
  c(z[c("coefficients", "residuals", "effects", "rank")],
    list(fitted.values = r1, assign = attr(x, "assign"),
         qr = structure(qr, class="qr"),
         df.residual = n - z$rank))
}

.lm.fit <- function(x, y, tol = 1e-07) .Call(C_Cdqrls, x, y, tol, check=TRUE)

lm.wfit <- function (x, y, w, offset = NULL, method = "qr", tol = 1e-7,
                     singular.ok = TRUE, ...)
{
  if(is.null(n <- nrow(x))) stop("'x' must be a matrix")
  if(n == 0) stop("0 (non-NA) cases")
  ny <- NCOL(y)
  ## treat one-col matrix as vector
  if(is.matrix(y) && ny == 1L)
    y <- drop(y)
  if(!is.null(offset))
    y <- y - offset
  if (NROW(y) != n | length(w) != n)
    stop("incompatible dimensions")
  if (any(w < 0 | is.na(w)))
    stop("missing or negative weights not allowed")
  if(method != "qr")
    warning(gettextf("method = '%s' is not supported. Using 'qr'", method),
            domain = NA)
  chkDots(...)
  x.asgn <- attr(x, "assign")# save
  zero.weights <- any(w == 0)
  if (zero.weights) {
    save.r <- y
    save.f <- y
    save.w <- w
    ok <- w != 0
    nok <- !ok
    w <- w[ok]
    x0 <- x[!ok, , drop = FALSE]
    x <- x[ok,  , drop = FALSE]
    n <- nrow(x)
    y0 <- if (ny > 1L) y[!ok, , drop = FALSE] else y[!ok]
    y  <- if (ny > 1L) y[ ok, , drop = FALSE] else y[ok]
  }
  p <- ncol(x)
  if (p == 0) {
    ## oops, null model
    return(list(coefficients = numeric(), residuals = y,
                fitted.values = 0 * y, weights = w, rank = 0L,
                df.residual = length(y)))
  }
  if (n == 0) { # all cases have weight zero
    return(list(coefficients = rep(NA_real_, p), residuals = y,
                fitted.values = 0 * y, weights = w, rank = 0L,
                df.residual = 0L))
  }
  wts <- sqrt(w)
  z <- .Call(C_Cdqrls, x * wts, y * wts, tol, FALSE)
  if(!singular.ok && z$rank < p) stop("singular fit encountered")
  coef <- z$coefficients
  pivot <- z$pivot
  r1 <- seq_len(z$rank)
  dn <- colnames(x); if(is.null(dn)) dn <- paste0("x", 1L:p)
  nmeffects <- c(dn[pivot[r1]], rep.int("", n - z$rank))
  r2 <- if(z$rank < p) (z$rank+1L):p else integer()
  if (is.matrix(y)) {
    coef[r2, ] <- NA
    if(z$pivoted) coef[pivot, ] <- coef
    dimnames(coef) <- list(dn, colnames(y))
    dimnames(z$effects) <- list(nmeffects,colnames(y))
  } else {
    coef[r2] <- NA
    if(z$pivoted) coef[pivot] <- coef
    names(coef) <- dn
    names(z$effects) <- nmeffects
  }
  z$coefficients <- coef
  z$residuals <- z$residuals/wts
  z$fitted.values <- y - z$residuals
  z$weights <- w
  if (zero.weights) {
    coef[is.na(coef)] <- 0
    f0 <- x0 %*% coef
    if (ny > 1) {
      save.r[ok, ] <- z$residuals
      save.r[nok, ] <- y0 - f0
      save.f[ok, ] <- z$fitted.values
      save.f[nok, ] <- f0
    }
    else {
      save.r[ok] <- z$residuals
      save.r[nok] <- y0 - f0
      save.f[ok] <- z$fitted.values
      save.f[nok] <- f0
    }
    z$residuals <- save.r
    z$fitted.values <- save.f
    z$weights <- save.w
  }
  if(!is.null(offset))
    z$fitted.values <- z$fitted.values + offset
  if(z$pivoted) colnames(z$qr) <- colnames(x)[z$pivot]
  qr <- z[c("qr", "qraux", "pivot", "tol", "rank")]
  c(z[c("coefficients", "residuals", "fitted.values", "effects",
        "weights", "rank")],
    list(assign = x.asgn,
         qr = structure(qr, class="qr"),
         df.residual = n - z$rank))
}

print.lm <- function(x, digits = max(3L, getOption("digits") - 3L), ...)
{
  cat("\nCall:\n",
      paste(deparse(x$call), sep = "\n", collapse = "\n"), "\n\n", sep = "")
  if(length(coef(x))) {
    cat("Coefficients:\n")
    print.default(format(coef(x), digits = digits),
                  print.gap = 2L, quote = FALSE)
  } else cat("No coefficients\n")
  cat("\n")
  invisible(x)
}

summary.lm <- function (object, correlation = FALSE, symbolic.cor = FALSE, ...)
{
  z <- object
  p <- z$rank
  rdf <- z$df.residual
  if (p == 0) {
    r <- z$residuals
    n <- length(r)
    w <- z$weights
    if (is.null(w)) {
      rss <- sum(r^2)
    } else {
      rss <- sum(w * r^2)
      r <- sqrt(w) * r
    }
    resvar <- rss/rdf
    ans <- z[c("call", "terms", if(!is.null(z$weights)) "weights")]
    class(ans) <- "summary.lm"
    ans$aliased <- is.na(coef(object))  # used in print method
    ans$residuals <- r
    ans$df <- c(0L, n, length(ans$aliased))
    ans$coefficients <- matrix(NA, 0L, 4L)
    dimnames(ans$coefficients) <-
      list(NULL, c("Estimate", "Std. Error", "t value", "Pr(>|t|)"))
    ans$sigma <- sqrt(resvar)
    ans$r.squared <- ans$adj.r.squared <- 0
    return(ans)
  }
  if (is.null(z$terms))
    stop("invalid 'lm' object:  no 'terms' component")
  if(!inherits(object, "lm"))
    warning("calling summary.lm(<fake-lm-object>) ...")
  Qr <- qr.lm(object)
  n <- NROW(Qr$qr)
  if(is.na(z$df.residual) || n - p != z$df.residual)
    warning("residual degrees of freedom in object suggest this is not an \"lm\" fit")
  ## do not want missing values substituted here
  r <- z$residuals
  f <- z$fitted.values
  w <- z$weights
  if (is.null(w)) {
    mss <- if (attr(z$terms, "intercept"))
      sum((f - mean(f))^2) else sum(f^2)
    rss <- sum(r^2)
  } else {
    mss <- if (attr(z$terms, "intercept")) {
      m <- sum(w * f /sum(w))
      sum(w * (f - m)^2)
    } else sum(w * f^2)
    rss <- sum(w * r^2)
    r <- sqrt(w) * r
  }
  resvar <- rss/rdf
  ## see thread at https://stat.ethz.ch/pipermail/r-help/2014-March/367585.html
  if (is.finite(resvar) &&
      resvar < (mean(f)^2 + var(f)) * 1e-30)  # a few times .Machine$double.eps^2
    warning("essentially perfect fit: summary may be unreliable")
  p1 <- 1L:p
  R <- chol2inv(Qr$qr[p1, p1, drop = FALSE])
  se <- sqrt(diag(R) * resvar)
  est <- z$coefficients[Qr$pivot[p1]]
  tval <- est/se
  ans <- z[c("call", "terms", if(!is.null(z$weights)) "weights")]
  ans$residuals <- r
  ans$coefficients <-
    cbind(est, se, tval, 2*pt(abs(tval), rdf, lower.tail = FALSE))
  dimnames(ans$coefficients) <-
    list(names(z$coefficients)[Qr$pivot[p1]],
         c("Estimate", "Std. Error", "t value", "Pr(>|t|)"))
  ans$aliased <- is.na(coef(object))  # used in print method
  ans$sigma <- sqrt(resvar)
  ans$df <- c(p, rdf, NCOL(Qr$qr))
  if (p != attr(z$terms, "intercept")) {
    df.int <- if (attr(z$terms, "intercept")) 1L else 0L
    ans$r.squared <- mss/(mss + rss)
    ans$adj.r.squared <- 1 - (1 - ans$r.squared) * ((n - df.int)/rdf)
    ans$fstatistic <- c(value = (mss/(p - df.int))/resvar,
                        numdf = p - df.int, dendf = rdf)
  } else ans$r.squared <- ans$adj.r.squared <- 0
  ans$cov.unscaled <- R
  dimnames(ans$cov.unscaled) <- dimnames(ans$coefficients)[c(1,1)]
  if (correlation) {
    ans$correlation <- (R * resvar)/outer(se, se)
    dimnames(ans$correlation) <- dimnames(ans$cov.unscaled)
    ans$symbolic.cor <- symbolic.cor
  }
  if(!is.null(z$na.action)) ans$na.action <- z$na.action
  class(ans) <- "summary.lm"
  ans
}

print.summary.lm <-
  function (x, digits = max(3L, getOption("digits") - 3L),
            symbolic.cor = x$symbolic.cor,
            signif.stars = getOption("show.signif.stars"),	...)
  {
    cat("\nCall:\n", # S has ' ' instead of '\n'
        paste(deparse(x$call), sep="\n", collapse = "\n"), "\n\n", sep = "")
    resid <- x$residuals
    df <- x$df
    rdf <- df[2L]
    cat(if(!is.null(x$weights) && diff(range(x$weights))) "Weighted ",
        "Residuals:\n", sep = "")
    if (rdf > 5L) {
      nam <- c("Min", "1Q", "Median", "3Q", "Max")
      rq <- if (length(dim(resid)) == 2L)
        structure(apply(t(resid), 1L, quantile),
                  dimnames = list(nam, dimnames(resid)[[2L]]))
      else  {
        zz <- zapsmall(quantile(resid), digits + 1L)
        structure(zz, names = nam)
      }
      print(rq, digits = digits, ...)
    }
    else if (rdf > 0L) {
      print(resid, digits = digits, ...)
    } else { # rdf == 0 : perfect fit!
      cat("ALL", df[1L], "residuals are 0: no residual degrees of freedom!")
      cat("\n")
    }
    if (length(x$aliased) == 0L) {
      cat("\nNo Coefficients\n")
    } else {
      if (nsingular <- df[3L] - df[1L])
        cat("\nCoefficients: (", nsingular,
            " not defined because of singularities)\n", sep = "")
      else cat("\nCoefficients:\n")
      coefs <- x$coefficients
      if(!is.null(aliased <- x$aliased) && any(aliased)) {
        cn <- names(aliased)
        coefs <- matrix(NA, length(aliased), 4, dimnames=list(cn, colnames(coefs)))
        coefs[!aliased, ] <- x$coefficients
      }

      printCoefmat(coefs, digits = digits, signif.stars = signif.stars,
                   na.print = "NA", ...)
    }
    ##
    cat("\nResidual standard error:",
        format(signif(x$sigma, digits)), "on", rdf, "degrees of freedom")
    cat("\n")
    if(nzchar(mess <- naprint(x$na.action))) cat("  (",mess, ")\n", sep = "")
    if (!is.null(x$fstatistic)) {
      cat("Multiple R-squared: ", formatC(x$r.squared, digits = digits))
      cat(",\tAdjusted R-squared: ",formatC(x$adj.r.squared, digits = digits),
          "\nF-statistic:", formatC(x$fstatistic[1L], digits = digits),
          "on", x$fstatistic[2L], "and",
          x$fstatistic[3L], "DF,  p-value:",
          format.pval(pf(x$fstatistic[1L], x$fstatistic[2L],
                         x$fstatistic[3L], lower.tail = FALSE),
                      digits = digits))
      cat("\n")
    }
    correl <- x$correlation
    if (!is.null(correl)) {
      p <- NCOL(correl)
      if (p > 1L) {
        cat("\nCorrelation of Coefficients:\n")
        if(is.logical(symbolic.cor) && symbolic.cor) {# NULL < 1.7.0 objects
          print(symnum(correl, abbr.colnames = NULL))
        } else {
          correl <- format(round(correl, 2), nsmall = 2, digits = digits)
          correl[!lower.tri(correl)] <- ""
          print(correl[-1, -p, drop=FALSE], quote = FALSE)
        }
      }
    }
    cat("\n")#- not in S
    invisible(x)
  }

residuals.lm <-
  function(object,
           type = c("working","response", "deviance","pearson", "partial"),
           ...)
  {
    type <- match.arg(type)
    r <- object$residuals
    res <- switch(type,
                  working =, response = r,
                  deviance=, pearson =
                    if(is.null(object$weights)) r else r * sqrt(object$weights),
                  partial = r
    )
    res <- naresid(object$na.action, res)
    if (type=="partial") ## predict already does naresid
      res <- res + predict(object,type="terms")
    res
  }

## using qr(<lm>)  as interface to  <lm>$qr :
qr.lm <- function(x, ...) {
  if(is.null(r <- x$qr))
    stop("lm object does not have a proper 'qr' component.
 Rank zero or should not have used lm(.., qr=FALSE).")
  r
}

## The lm method includes objects of class "glm"
simulate.lm <- function(object, nsim = 1, seed = NULL, ...)
{
  if(!exists(".Random.seed", envir = .GlobalEnv, inherits = FALSE))
    runif(1)                     # initialize the RNG if necessary
  if(is.null(seed))
    RNGstate <- get(".Random.seed", envir = .GlobalEnv)
  else {
    R.seed <- get(".Random.seed", envir = .GlobalEnv)
    set.seed(seed)
    RNGstate <- structure(seed, kind = as.list(RNGkind()))
    on.exit(assign(".Random.seed", R.seed, envir = .GlobalEnv))
  }
  ftd <- fitted(object)             # == napredict(*, object$fitted)
  nm <- names(ftd)
  n <- length(ftd)
  ntot <- n * nsim
  fam <- if(inherits(object, "glm")) object$family$family else "gaussian"
  val <- switch(fam,
                "gaussian" = {
                  vars <- deviance(object)/ df.residual(object)
                  if (!is.null(object$weights)) vars <- vars/object$weights
                  ftd + rnorm(ntot, sd = sqrt(vars))
                },
                if(!is.null(object$family$simulate))
                  object$family$simulate(object, nsim)
                else stop(gettextf("family '%s' not implemented", fam),
                          domain = NA)
  )

  if(!is.list(val)) {
    dim(val) <- c(n, nsim)
    val <- as.data.frame(val)
  } else
    class(val) <- "data.frame"
  names(val) <- paste("sim", seq_len(nsim), sep="_")
  if (!is.null(nm)) row.names(val) <- nm
  attr(val, "seed") <- RNGstate
  val
}

deviance.lm <- function(object, ...)
  sum(weighted.residuals(object)^2, na.rm=TRUE)

formula.lm <- function(x, ...)
{
  form <- x$formula
  if( !is.null(form) ) {
    form <- formula(x$terms) # has . expanded
    environment(form) <- environment(x$formula)
    form
  } else formula(x$terms)
}

family.lm <- function(object, ...) { gaussian() }

model.frame.lm <- function(formula, ...)
{
  dots <- list(...)
  nargs <- dots[match(c("data", "na.action", "subset"), names(dots), 0)]
  if (length(nargs) || is.null(formula$model)) {
    ## mimic lm(method = "model.frame")
    fcall <- formula$call
    m <- match(c("formula", "data", "subset", "weights", "na.action",
                 "offset"), names(fcall), 0L)
    fcall <- fcall[c(1L, m)]
    fcall$drop.unused.levels <- TRUE
    ## need stats:: for non-standard evaluation
    fcall[[1L]] <- quote(stats::model.frame)
    fcall$xlev <- formula$xlevels
    ## We want to copy over attributes here, especially predvars.
    fcall$formula <- terms(formula)
    fcall[names(nargs)] <- nargs
    env <- environment(formula$terms)
    if (is.null(env)) env <- parent.frame()
    eval(fcall, env) # 2-arg form as env is an environment
  }
  else formula$model
}

variable.names.lm <- function(object, full = FALSE, ...)
{
  if(full) dimnames(qr.lm(object)$qr)[[2L]]
  else if(object$rank) dimnames(qr.lm(object)$qr)[[2L]][seq_len(object$rank)]
  else character()
}

case.names.lm <- function(object, full = FALSE, ...)
{
  w <- weights(object)
  dn <- names(residuals(object))
  if(full || is.null(w)) dn else dn[w!=0]
}

anova.lm <- function(object, ...)
{
  ## Do not copy this: anova.lmlist is not an exported object.
  ## See anova.glm for further comments.
  if(length(list(object, ...)) > 1L) return(anova.lmlist(object, ...))

  if(!inherits(object, "lm"))
    warning("calling anova.lm(<fake-lm-object>) ...")
  w <- object$weights
  ssr <- sum(if(is.null(w)) object$residuals^2 else w*object$residuals^2)
  mss <- sum(if(is.null(w)) object$fitted.values^2 else w*object$fitted.values^2)
  if(ssr < 1e-10*mss)
    warning("ANOVA F-tests on an essentially perfect fit are unreliable")
  dfr <- df.residual(object)
  p <- object$rank
  if(p > 0L) {
    p1 <- 1L:p
    comp <- object$effects[p1]
    asgn <- object$assign[qr.lm(object)$pivot][p1]
    nmeffects <- c("(Intercept)", attr(object$terms, "term.labels"))
    tlabels <- nmeffects[1 + unique(asgn)]
    ss <- c(unlist(lapply(split(comp^2,asgn), sum)), ssr)
    df <- c(lengths(split(asgn,  asgn)), dfr)
  } else {
    ss <- ssr
    df <- dfr
    tlabels <- character()
  }
  ms <- ss/df
  f <- ms/(ssr/dfr)
  P <- pf(f, df, dfr, lower.tail = FALSE)
  table <- data.frame(df, ss, ms, f, P)
  table[length(P), 4:5] <- NA
  dimnames(table) <- list(c(tlabels, "Residuals"),
                          c("Df","Sum Sq", "Mean Sq", "F value", "Pr(>F)"))
  if(attr(object$terms,"intercept")) table <- table[-1, ]
  structure(table, heading = c("Analysis of Variance Table\n",
                               paste("Response:", deparse(formula(object)[[2L]]))),
            class = c("anova", "data.frame"))# was "tabular"
}

anova.lmlist <- function (object, ..., scale = 0, test = "F")
{
  objects <- list(object, ...)
  responses <- as.character(lapply(objects,
                                   function(x) deparse(x$terms[[2L]])))
  sameresp <- responses == responses[1L]
  if (!all(sameresp)) {
    objects <- objects[sameresp]
    warning(gettextf("models with response %s removed because response differs from model 1",
                     sQuote(deparse(responses[!sameresp]))),
            domain = NA)
  }

  ns <- sapply(objects, function(x) length(x$residuals))
  if(any(ns != ns[1L]))
    stop("models were not all fitted to the same size of dataset")

  ## calculate the number of models
  nmodels <- length(objects)
  if (nmodels == 1)
    return(anova.lm(object))

  ## extract statistics

  resdf  <- as.numeric(lapply(objects, df.residual))
  resdev <- as.numeric(lapply(objects, deviance))

  ## construct table and title

  table <- data.frame(resdf, resdev, c(NA, -diff(resdf)),
                      c(NA, -diff(resdev)) )
  variables <- lapply(objects, function(x)
    paste(deparse(formula(x)), collapse="\n") )
  dimnames(table) <- list(1L:nmodels,
                          c("Res.Df", "RSS", "Df", "Sum of Sq"))

  title <- "Analysis of Variance Table\n"
  topnote <- paste("Model ", format(1L:nmodels),": ",
                   variables, sep = "", collapse = "\n")

  ## calculate test statistic if needed

  if(!is.null(test)) {
    bigmodel <- order(resdf)[1L]
    scale <- if(scale > 0) scale else resdev[bigmodel]/resdf[bigmodel]
    table <- stat.anova(table = table, test = test,
                        scale = scale,
                        df.scale = resdf[bigmodel],
                        n = length(objects[[bigmodel]]$residuals))
  }
  structure(table, heading = c(title, topnote),
            class = c("anova", "data.frame"))
}

## code originally from John Maindonald 26Jul2000
predict.lm <-
  function(object, newdata, se.fit = FALSE, scale = NULL, df = Inf,
           interval = c("none", "confidence", "prediction"),
           level = .95,  type = c("response", "terms"),
           terms = NULL, na.action = na.pass, pred.var = res.var/weights,
           weights = 1, ...)
  {
    tt <- terms(object)
    if(!inherits(object, "lm"))
      warning("calling predict.lm(<fake-lm-object>) ...")
    if(missing(newdata) || is.null(newdata)) {
      mm <- X <- model.matrix(object)
      mmDone <- TRUE
      offset <- object$offset
    }
    else {
      Terms <- delete.response(tt)
      m <- model.frame(Terms, newdata, na.action = na.action,
                       xlev = object$xlevels)
      if(!is.null(cl <- attr(Terms, "dataClasses"))) .checkMFClasses(cl, m)
      X <- model.matrix(Terms, m, contrasts.arg = object$contrasts)
      offset <- rep(0, nrow(X))
      if (!is.null(off.num <- attr(tt, "offset")))
        for(i in off.num)
          offset <- offset + eval(attr(tt, "variables")[[i+1]], newdata)
      if (!is.null(object$call$offset))
        offset <- offset + eval(object$call$offset, newdata)
      mmDone <- FALSE
    }
    n <- length(object$residuals) # NROW(qr(object)$qr)
    p <- object$rank
    p1 <- seq_len(p)
    piv <- if(p) qr.lm(object)$pivot[p1]
    if(p < ncol(X) && !(missing(newdata) || is.null(newdata)))
      warning("prediction from a rank-deficient fit may be misleading")
    ### NB: Q[p1,] %*% X[,piv] = R[p1,p1]
    beta <- object$coefficients
    predictor <- drop(X[, piv, drop = FALSE] %*% beta[piv])
    if (!is.null(offset))
      predictor <- predictor + offset

    interval <- match.arg(interval)
    if (interval == "prediction") {
      if (missing(newdata))
        warning("predictions on current data refer to _future_ responses\n")
      if (missing(newdata) && missing(weights)) {
        w <-  weights.default(object)
        if (!is.null(w)) {
          weights <- w
          warning("assuming prediction variance inversely proportional to weights used for fitting\n")
        }
      }
      if (!missing(newdata) && missing(weights) && !is.null(object$weights) && missing(pred.var))
        warning("Assuming constant prediction variance even though model fit is weighted\n")
      if (inherits(weights, "formula")){
        if (length(weights) != 2L)
          stop("'weights' as formula should be one-sided")
        d <- if(missing(newdata) || is.null(newdata))
          model.frame(object)
        else
          newdata
        weights <- eval(weights[[2L]], d, environment(weights))
      }
    }

    type <- match.arg(type)
    if(se.fit || interval != "none") {
      ## w is needed for interval = "confidence"
      w <- object$weights
      res.var <-
        if (is.null(scale)) {
          r <- object$residuals
          rss <- sum(if(is.null(w)) r^2 else r^2 * w)
          df <- object$df.residual
          rss/df
        } else scale^2
      if(type != "terms") {
        if(p > 0) {
          XRinv <-
            if(missing(newdata) && is.null(w))
              qr.Q(qr.lm(object))[, p1, drop = FALSE]
          else
            X[, piv] %*% qr.solve(qr.R(qr.lm(object))[p1, p1])
          #	NB:
          #	 qr.Q(qr.lm(object))[, p1, drop = FALSE] / sqrt(w)
          #	looks faster than the above, but it's slower, and doesn't handle zero
          #	weights properly
          #
          ip <- drop(XRinv^2 %*% rep(res.var, p))
        } else ip <- rep(0, n)
      }
    }

    if (type == "terms") { ## type == "terms" ------------
      if(!mmDone) {
        mm <- model.matrix(object)
        mmDone <- TRUE
      }
      aa <- attr(mm, "assign")
      ll <- attr(tt, "term.labels")
      hasintercept <- attr(tt, "intercept") > 0L
      if (hasintercept) ll <- c("(Intercept)", ll)
      aaa <- factor(aa, labels = ll)
      asgn <- split(order(aa), aaa)
      if (hasintercept) {
        asgn$"(Intercept)" <- NULL
        avx <- colMeans(mm)
        termsconst <- sum(avx[piv] * beta[piv])
      }
      nterms <- length(asgn)
      if(nterms > 0) {
        predictor <- matrix(ncol = nterms, nrow = NROW(X))
        dimnames(predictor) <- list(rownames(X), names(asgn))

        if (se.fit || interval != "none") {
          ip <- matrix(ncol = nterms, nrow = NROW(X))
          dimnames(ip) <- list(rownames(X), names(asgn))
          Rinv <- qr.solve(qr.R(qr.lm(object))[p1, p1])
        }
        if(hasintercept)
          X <- sweep(X, 2L, avx, check.margin=FALSE)
        unpiv <- rep.int(0L, NCOL(X))
        unpiv[piv] <- p1
        ## Predicted values will be set to 0 for any term that
        ## corresponds to columns of the X-matrix that are
        ## completely aliased with earlier columns.
        for (i in seq.int(1L, nterms, length.out = nterms)) {
          iipiv <- asgn[[i]]      # Columns of X, ith term
          ii <- unpiv[iipiv]      # Corresponding rows of Rinv
          iipiv[ii == 0L] <- 0L
          predictor[, i] <-
            if(any(iipiv > 0L)) X[, iipiv, drop = FALSE] %*% beta[iipiv]
          else 0
          if (se.fit || interval != "none")
            ip[, i] <-
            if(any(iipiv > 0L))
              as.matrix(X[, iipiv, drop = FALSE] %*%
                          Rinv[ii, , drop = FALSE])^2 %*% rep.int(res.var, p)
          else 0
        }
        if (!is.null(terms)) {
          predictor <- predictor[, terms, drop = FALSE]
          if (se.fit)
            ip <- ip[, terms, drop = FALSE]
        }
      } else {                        # no terms
        predictor <- ip <- matrix(0, n, 0L)
      }
      attr(predictor, 'constant') <- if (hasintercept) termsconst else 0
    }

    ### Now construct elements of the list that will be returned

    if(interval != "none") {
      tfrac <- qt((1 - level)/2, df)
      hwid <- tfrac * switch(interval,
                             confidence = sqrt(ip),
                             prediction = sqrt(ip+pred.var)
      )
      if(type != "terms") {
        predictor <- cbind(predictor, predictor + hwid %o% c(1, -1))
        colnames(predictor) <- c("fit", "lwr", "upr")
      } else {
        if (!is.null(terms)) hwid <- hwid[, terms, drop = FALSE]
        lwr <- predictor + hwid
        upr <- predictor - hwid
      }
    }
    if(se.fit || interval != "none") {
      se <- sqrt(ip)
      if(type == "terms" && !is.null(terms) && !se.fit)
        se <- se[, terms, drop = FALSE]
    }
    if(missing(newdata) && !is.null(na.act <- object$na.action)) {
      predictor <- napredict(na.act, predictor)
      if(se.fit) se <- napredict(na.act, se)
    }
    if(type == "terms" && interval != "none") {
      if(missing(newdata) && !is.null(na.act)) {
        lwr <- napredict(na.act, lwr)
        upr <- napredict(na.act, upr)
      }
      list(fit = predictor, se.fit = se, lwr = lwr, upr = upr,
           df = df, residual.scale = sqrt(res.var))
    } else if (se.fit)
      list(fit = predictor, se.fit = se,
           df = df, residual.scale = sqrt(res.var))
    else predictor
  }

effects.lm <- function(object, set.sign = FALSE, ...)
{
  eff <- object$effects
  if(is.null(eff)) stop("'object' has no 'effects' component")
  if(set.sign) {
    dd <- coef(object)
    if(is.matrix(eff)) {
      r <- 1L:dim(dd)[1L]
      eff[r,  ] <- sign(dd) * abs(eff[r,	])
    } else {
      r <- seq_along(dd)
      eff[r] <- sign(dd) * abs(eff[r])
    }
  }
  structure(eff, assign = object$assign, class = "coef")
}

## plot.lm --> now in ./plot.lm.R

model.matrix.lm <- function(object, ...)
{
  if(n_match <- match("x", names(object), 0L)) object[[n_match]]
  else {
    data <- model.frame(object, xlev = object$xlevels, ...)
    NextMethod("model.matrix", data = data,
               contrasts.arg = object$contrasts)
  }
}

##---> SEE ./mlm.R  for more methods, etc. !!
predict.mlm <-
  function(object, newdata, se.fit = FALSE, na.action = na.pass, ...)
  {
    if(missing(newdata)) return(object$fitted.values)
    if(se.fit)
      stop("the 'se.fit' argument is not yet implemented for \"mlm\" objects")
    if(missing(newdata)) {
      X <- model.matrix(object)
      offset <- object$offset
    }
    else {
      tt <- terms(object)
      Terms <- delete.response(tt)
      m <- model.frame(Terms, newdata, na.action = na.action,
                       xlev = object$xlevels)
      if(!is.null(cl <- attr(Terms, "dataClasses"))) .checkMFClasses(cl, m)
      X <- model.matrix(Terms, m, contrasts.arg = object$contrasts)
      offset <- if (!is.null(off.num <- attr(tt, "offset")))
        eval(attr(tt, "variables")[[off.num+1]], newdata)
      else if (!is.null(object$offset))
        eval(object$call$offset, newdata)
    }
    piv <- qr.lm(object)$pivot[seq(object$rank)]
    pred <- X[, piv, drop = FALSE] %*% object$coefficients[piv,]
    if ( !is.null(offset) ) pred <- pred + offset
    if(inherits(object, "mlm")) pred else pred[, 1L]
  }

## from base/R/labels.R
labels.lm <- function(object, ...)
{
  tl <- attr(object$terms, "term.labels")
  asgn <- object$assign[qr.lm(object)$pivot[1L:object$rank]]
  tl[unique(asgn)]
}