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% File src/library/stats/man/add1.Rd
% Part of the R package, https://www.R-project.org
% Copyright 1995-2013 R Core Team
% Distributed under GPL 2 or later

\name{add1}
\alias{add1}
\alias{add1.default}
\alias{add1.lm}
\alias{add1.glm}
\alias{drop1}
\alias{drop1.default}
\alias{drop1.lm}
\alias{drop1.glm}
\title{Add or Drop All Possible Single Terms to a Model}
\usage{
add1(object, scope, \dots)

\method{add1}{default}(object, scope, scale = 0, test = c("none", "Chisq"),
     k = 2, trace = FALSE, \dots)

\method{add1}{lm}(object, scope, scale = 0, test = c("none", "Chisq", "F"),
     x = NULL, k = 2, \dots)

\method{add1}{glm}(object, scope, scale = 0,
     test = c("none", "Rao", "LRT", "Chisq", "F"),
     x = NULL, k = 2, \dots)

drop1(object, scope, \dots)

\method{drop1}{default}(object, scope, scale = 0, test = c("none", "Chisq"),
      k = 2, trace = FALSE, \dots)

\method{drop1}{lm}(object, scope, scale = 0, all.cols = TRUE,
      test = c("none", "Chisq", "F"), k = 2, \dots)

\method{drop1}{glm}(object, scope, scale = 0,
      test = c("none", "Rao", "LRT", "Chisq", "F"),
      k = 2, \dots)
}
\arguments{
  \item{object}{a fitted model object.}
  \item{scope}{a formula giving the terms to be considered for adding or
    dropping.}
  \item{scale}{an estimate of the residual mean square to be
    used in computing \eqn{C_p}{Cp}. Ignored if \code{0} or \code{NULL}.}
  \item{test}{should the results include a test statistic relative to the
    original model?  The F test is only appropriate for \code{\link{lm}} and
    \code{\link{aov}} models or perhaps for \code{\link{glm}} fits with
    estimated dispersion.
    The \eqn{\chi^2}{Chisq} test can be an exact test
    (\code{lm} models with known scale) or a likelihood-ratio test or a
    test of the reduction in scaled deviance depending on the method.
    For \code{\link{glm}} fits, you can also choose \code{"LRT"} and
    \code{"Rao"} for likelihood ratio tests and Rao's efficient score test.
    The former is synonymous with \code{"Chisq"} (although both have
    an asymptotic chi-square distribution).
    Values can be abbreviated.
    }
  \item{k}{the penalty constant in AIC / \eqn{C_p}{Cp}.}
  \item{trace}{if \code{TRUE}, print out progress reports.}
  \item{x}{a model matrix containing columns for the fitted model and all
    terms in the upper scope.  Useful if \code{add1} is to be called
    repeatedly.  \bold{Warning:} no checks are done on its validity.}
  \item{all.cols}{(Provided for compatibility with S.)  Logical to specify
    whether all columns of the design matrix should be used.  If
    \code{FALSE} then non-estimable columns are dropped, but the result
    is not usually statistically meaningful.}
  \item{\dots}{further arguments passed to or from other methods.}
}
\description{
  Compute all the single terms in the \code{scope} argument that can be
  added to or dropped from the model, fit those models and compute a
  table of the changes in fit.
}
\details{
  For \code{drop1} methods, a missing \code{scope} is taken to be all
  terms in the model. The hierarchy is respected when considering terms
  to be added or dropped: all main effects contained in a second-order
  interaction must remain, and so on.

  In a \code{scope} formula \code{.} means \sQuote{what is already there}.

  The methods for \code{\link{lm}} and \code{\link{glm}} are more
  efficient in that they do not recompute the model matrix and call the
  \code{fit} methods directly.

  The default output table gives AIC, defined as minus twice log
  likelihood plus \eqn{2p} where \eqn{p} is the rank of the model (the
  number of effective parameters).  This is only defined up to an
  additive constant (like log-likelihoods).  For linear Gaussian models
  with fixed scale, the constant is chosen to give Mallows' \eqn{C_p}{Cp},
  \eqn{RSS/scale + 2p - n}.  Where \eqn{C_p}{Cp} is used,
  the column is labelled as \code{Cp} rather than \code{AIC}.

  The F tests for the \code{"glm"} methods are based on analysis of
  deviance tests, so if the dispersion is estimated it is based on the
  residual deviance, unlike the F tests of \code{\link{anova.glm}}.
}
\value{
  An object of class \code{"anova"} summarizing the differences in fit
  between the models.
}
\author{
  The design was inspired by the S functions of the same names described
  in Chambers (1992).
}
\references{
  Chambers, J. M. (1992)
  \emph{Linear models.}
  Chapter 4 of \emph{Statistical Models in S}
  eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.
}
\note{
  These are not fully equivalent to the functions in S.  There is no
  \code{keep} argument, and the methods used are not quite so
  computationally efficient.

  Their authors' definitions of Mallows' \eqn{C_p}{Cp} and Akaike's AIC
  are used, not those of the authors of the models chapter of S.
}
\section{Warning}{
  The model fitting must apply the models to the same dataset. Most
  methods will attempt to use a subset of the data with no missing
  values for any of the variables if \code{na.action = na.omit}, but
  this may give biased results.  Only use these functions with data
  containing missing values with great care.

  The default methods make calls to the function \code{\link{nobs}} to
  check that the number of observations involved in the fitting process
  remained unchanged.
}
\seealso{
  \code{\link{step}}, \code{\link{aov}}, \code{\link{lm}},
  \code{\link{extractAIC}}, \code{\link{anova}}
}
\examples{
\dontshow{od <- options(digits = 5)}
require(graphics); require(utils)
## following example(swiss)
lm1 <- lm(Fertility ~ ., data = swiss)
add1(lm1, ~ I(Education^2) + .^2)
drop1(lm1, test = "F")  # So called 'type II' anova

## following example(glm)
\dontshow{example(glm, echo = FALSE)}
drop1(glm.D93, test = "Chisq")
drop1(glm.D93, test = "F")
add1(glm.D93, scope = ~outcome*treatment, test = "Rao") ## Pearson Chi-square
\dontshow{options(od)}
}
\keyword{models}