lm.influence
Regression Diagnostics
This function provides the basic quantities which are used in forming a wide variety of diagnostics for checking the quality of regression fits.
 Keywords
 regression
Usage
influence(model, ...)
"influence"(model, do.coef = TRUE, ...)
"influence"(model, do.coef = TRUE, ...)
lm.influence(model, do.coef = TRUE)
Arguments
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 onestep 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 dropone diagnostics.)
naresid
is applied to the results and so will fill in
with NA
s it the fit had na.action = na.exclude
.
Value

A list containing the following components of the same length or
number of rows $n$, which is the number of nonzero weights.
Cases omitted in the fit are omitted unless a
 hat
 a vector containing the diagonal of the ‘hat’ matrix.
 coefficients
 (unless
do.coef
is false) a matrix whose ith row contains the change in the estimated coefficients which results when the ith case is dropped from the regression. Note that aliased coefficients are not included in the matrix.  sigma
 a vector whose ith element contains the estimate
of the residual standard deviation obtained when the ith
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.
na.action
method was used (such as na.exclude
) which restores them.Note
The coefficients
returned by the R version
of 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.
Since these need $O(n^2 p)$ computing time, they can be omitted by
do.coef = FALSE
.
Note that cases with weights == 0
are dropped (contrary
to the situation in S).
If a model has been fitted with na.action = na.exclude
(see
na.exclude
), cases excluded in the fit are
considered here.
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.
See Also
summary.lm
for summary
and related methods;
influence.measures
,
hat
for the hat matrix diagonals,
dfbetas
,
dffits
,
covratio
,
cooks.distance
,
lm
.
Examples
library(stats)
## Analysis of the lifecycle 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)