\Header{effects}{Effects from Fitted Model}
\methalias{effects.glm}{effects}
\methalias{effects.lm}{effects}
\keyword{models}{effects}
\keyword{regression}{effects}
\begin{Description}\relax
Returns (orthogonal) effects from a fitted model, usually a linear
model. This is a generic function, but currently only has a method for
objects inheriting from class \code{"lm"}.\end{Description}
\begin{Usage}
\begin{verbatim}
effects(object, ...)
effects.lm(object, set.sign=FALSE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{object}] an \R{} object; typically, the result of a model fitting function
such as \code{\Link{lm}}.
\item[\code{set.sign}] logical. If \code{TRUE}, the sign of the effects
corresponding to coefficients in the model will be set to agree with the
signs of the corresponding coefficients, otherwise the sign is
arbitrary.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
For a linear model fitted by \code{\Link{lm}} or \code{\Link{aov}},
the effects are the uncorrelated single-degree-of-freedom values
obtained by projecting the data onto the successive orthogonal
subspaces generated by the QR decomposition during the fitting
process. The first \eqn{r}{} (the rank of the model) are associated with
coefficients and the remainder span the space of residuals (but are
not associated with particular residuals).\end{Details}
\begin{Value}
A (named) numeric vector of the same length as
\code{\Link{residuals}}, or a matrix if there were multiple responses
in the fitted model, in either case of class \code{"coef"}.

The first \eqn{r}{} rows are labelled by the corresponding coefficients,
and the remaining rows are unlabelled.  Note that in rank-deficient
models the ``corresponding''
coefficients will be in a different order if pivoting occurred.\end{Value}
\begin{SeeAlso}\relax
\code{\Link{coef}}\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
y <- c(1:3,7,5)
x <- c(1:3,6:7)
( ee <- effects(lm(y ~ x)) )
c(round(ee - effects(lm(y+10 ~ I(x-3.8))),3))# just the first is different
\end{ExampleCode}
\end{Examples}

