Regression Deletion Diagnostics for Multivariate Linear Models

Description

This collection of functions is designed to compute regression deletion diagnostics for multivariate linear models following Barrett & Ling (1992) that are close analogs of methods for univariate and generalized linear models handled by the influence.measures in the stats package.

In addition, the functions provide diagnostics for deletion of subsets of observations of size m>1.

Usage

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## S3 method for class 'mlm'
influence(model, do.coef = TRUE, m = 1, ...)

## S3 method for class 'inflmlm'
as.data.frame(x, ..., FUN = det, funnames = TRUE)

## S3 method for class 'inflmlm'
print(x, digits = max(3, getOption("digits") - 4), FUN = det, ...)

Arguments

model

An mlm object, as returned by lm

do.coef

logical. Should the coefficients be returned in the inflmlm object?

m

Size of the subsets for deletion diagnostics

x

An inflmlm object, as returned by mlm.influence

FUN

For m>1, the function to be applied to the H and Q matrices returning a scalar value. FUN=det and FUN=tr are possible choices, returning the |H| and tr(H) respectively.

funnames

logical. Should the FUN name be prepended to the statistics when creating a data frame?

...

Other arguments passed to methods

digits

Number of digits for the print method

Details

influence.mlm is a simple wrapper for the computational function, mlm.influence designed to provide an S3 method for class "mlm" objects.

There are still infelicities in the methods for the m>1 case in the current implementation. In particular, for m>1, you must call influence.mlm directly, rather than using the S3 generic influence().

Value

influence.mlm returns an S3 object of class inflmlm, a list with the following components

m

Deletion subset size

H

Hat values, H_I. If m=1, a vector of diagonal entries of the ‘hat’ matrix. Otherwise, a list of m \times m matrices corresponding to the subsets.

Q

Residuals, Q_I.

CookD

Cook's distance values

L

Leverage components

R

Residual components

subsets

Indices of the observations in the subsets of size m

labels

Observation labels

call

Model call for the mlm object

Beta

Deletion regression coefficients– included if do.coef=TRUE

Author(s)

Michael Friendly

References

Barrett, B. E. and Ling, R. F. (1992). General Classes of Influence Measures for Multivariate Regression. Journal of the American Statistical Association, 87(417), 184-191.

See Also

influencePlot.mlm, mlm.influence

Examples

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# Rohwer data
Rohwer2 <- subset(Rohwer, subset=group==2)
rownames(Rohwer2)<- 1:nrow(Rohwer2)
Rohwer.mod <- lm(cbind(SAT, PPVT, Raven) ~ n+s+ns+na+ss, data=Rohwer2)

# m=1 diagnostics
influence(Rohwer.mod)

# try an m=2 case
res2 <- influence.mlm(Rohwer.mod, m=2, do.coef=FALSE)
res2.df <- as.data.frame(res2)
head(res2.df)
scatterplotMatrix(log(res2.df))


influencePlot(Rohwer.mod, id.n=4, type="cookd")


# Sake data
Sake.mod <- lm(cbind(taste,smell) ~ ., data=Sake)
influence(Sake.mod)
influencePlot(Sake.mod, id.n=3, type="cookd")