| % File src/library/stats/man/lm.influence.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2015 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{lm.influence} |
| \title{Regression Diagnostics} |
| \usage{ |
| influence(model, \dots) |
| \method{influence}{lm}(model, do.coef = TRUE, \dots) |
| \method{influence}{glm}(model, do.coef = TRUE, \dots) |
| |
| lm.influence(model, do.coef = TRUE) |
| } |
| \alias{lm.influence} |
| \alias{influence} |
| \alias{influence.lm} |
| \alias{influence.glm} |
| \arguments{ |
| \item{model}{an object as returned by \code{\link{lm}} or \code{\link{glm}}.} |
| \item{do.coef}{logical indicating if the changed \code{coefficients} |
| (see below) are desired. These need \eqn{O(n^2 p)} computing time.} |
| \item{\dots}{further arguments passed to or from other methods.} |
| } |
| \description{ |
| This function provides the basic quantities which are |
| used in forming a wide variety of diagnostics for |
| checking the quality of regression fits. |
| } |
| \details{ |
| The \code{\link{influence.measures}()} and other functions listed in |
| \bold{See Also} provide a more user oriented way of computing a |
| variety of regression diagnostics. These all build on |
| \code{lm.influence}. Note that for GLMs (other than the Gaussian |
| family with identity link) these are based on one-step approximations |
| which may be inadequate if a case has high influence. |
| |
| An attempt is made to ensure that computed hat values that are |
| probably one are treated as one, and the corresponding rows in |
| \code{sigma} and \code{coefficients} are \code{NaN}. (Dropping such a |
| case would normally result in a variable being dropped, so it is not |
| possible to give simple drop-one diagnostics.) |
| |
| \code{\link{naresid}} is applied to the results and so will fill in |
| with \code{NA}s it the fit had \code{na.action = na.exclude}. |
| } |
| \value{ |
| A list containing the following components of the same length or |
| number of rows \eqn{n}, which is the number of non-zero weights. |
| Cases omitted in the fit are omitted unless a \code{\link{na.action}} |
| method was used (such as \code{\link{na.exclude}}) which restores them. |
| |
| \item{hat}{a vector containing the diagonal of the \sQuote{hat} matrix.} |
| \item{coefficients}{(unless \code{do.coef} is false) a matrix whose |
| i-th row contains the change in the estimated coefficients which |
| results when the i-th case is dropped from the regression. Note |
| that aliased coefficients are not included in the matrix.} |
| \item{sigma}{a vector whose i-th element contains the estimate |
| of the residual standard deviation obtained when the i-th |
| case is dropped from the regression. (The approximations needed for |
| GLMs can result in this being \code{NaN}.)} |
| \item{wt.res}{a vector of \emph{weighted} (or for class \code{glm} |
| rather \emph{deviance}) residuals.} |
| } |
| \note{ |
| The \code{coefficients} returned by the \R version |
| of \code{lm.influence} differ from those computed by S. |
| Rather than returning the coefficients which result |
| from dropping each case, we return the changes in the coefficients. |
| This is more directly useful in many diagnostic measures.\cr |
| Since these need \eqn{O(n p^2)} computing time, they can be omitted by |
| \code{do.coef = FALSE}. (Prior to R 4.0.0, this was much worse, using |
| an \eqn{O(n^2 p)} algorithm.) |
| |
| Note that cases with \code{weights == 0} are \emph{dropped} (contrary |
| to the situation in S). |
| |
| If a model has been fitted with \code{na.action = na.exclude} (see |
| \code{\link{na.exclude}}), cases excluded in the fit \emph{are} |
| considered here. |
| } |
| \references{ |
| See the list in the documentation for \code{\link{influence.measures}}. |
| |
| 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. |
| } |
| \seealso{ |
| \code{\link{summary.lm}} for \code{\link{summary}} and related methods;\cr |
| \code{\link{influence.measures}},\cr |
| \code{\link{hat}} for the hat matrix diagonals,\cr |
| \code{\link{dfbetas}}, |
| \code{\link{dffits}}, |
| \code{\link{covratio}}, |
| \code{\link{cooks.distance}}, |
| \code{\link{lm}}. |
| } |
| \examples{ |
| ## Analysis of the life-cycle savings data |
| ## given in Belsley, Kuh and Welsch. |
| summary(lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, |
| data = LifeCycleSavings), |
| correlation = TRUE) |
| utils::str(lmI <- lm.influence(lm.SR)) |
| |
| ## For more "user level" examples, use example(influence.measures) |
| } |
| \keyword{regression} |