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

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influence(model, ...)
## S3 method for class 'lm'
influence(model, do.coef = TRUE, ...)
## S3 method for class '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.

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.

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.

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

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## 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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