lm.influence: Regression Diagnostics

Description

This function provides the basic quantities which are used in forming a wide variety of diagnostics for checking the quality of regression fits.

Usage

influence(model, …)
# S3 method for lm
influence(model, do.coef = TRUE, …)
# S3 method for glm
influence(model, do.coef = TRUE, …)
lm.influence(model, do.coef = TRUE)

Arguments

model

an object as returned by lm or glm.

do.coef

logical indicating if the changed coefficients (see below) are desired. These need $O (n^{2} p)$ computing time.

…

further arguments passed to or from other methods.

Value

A list containing the following components of the same length or number of rows $n$ , which is the number of non-zero weights. Cases omitted in the fit are omitted unless a na.action method was used (such as na.exclude) which restores them.

hat

a vector containing the diagonal of the ‘hat’ matrix.

coefficients

(unless 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.

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 NaN.)

wt.res

a vector of weighted (or for class glm rather deviance) residuals.

Details

The influence.measures() and other functions listed in See Also provide a more user oriented way of computing a variety of regression diagnostics. These all build on 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 sigma and coefficients are NaN. (Dropping such a case would normally result in a variable being dropped, so it is not possible to give simple drop-one diagnostics.)

naresid is applied to the results and so will fill in with NAs it the fit had na.action = na.exclude.

References

See the list in the documentation for influence.measures.

Chambers, J. M. (1992) Linear models. Chapter 4 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

Examples

Run this code

## Analysis of the life-cycle savings data
## given in Belsley, Kuh and Welsch.
summary(lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi,
                    data = LifeCycleSavings),
        corr = TRUE)
utils::str(lmI <- lm.influence(lm.SR))

## For more "user level" examples, use example(influence.measures)

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