influence.measures
Regression Deletion Diagnostics

### Description

Utility functions used to compute regression deletion diagnostics for linear model or generalized linear model.

### Usage

    influence.measures(model)
    ## S3 method for class 'infl':
    print(x, digits = max(3, getOption("digits") - 4), ...)
    ## S3 method for class 'infl':
    summary(object, digits = max(2, getOption("digits") - 5), ...)
    hatvalues(model, ...)
    ## S3 method for class 'lm':
    hatvalues(model, infl = lm.influence(model, do.coef = FALSE), ...)
    rstandard(model, ...)
    ## S3 method for class 'lm':
    rstandard(model, infl = lm.influence(model, do.coef = FALSE),
        sd = sqrt(deviance(model)/df.residual(model)), ...)
    ## S3 method for class 'glm':
    rstandard(model, infl = influence(model, do.coef = FALSE),
        type = c("deviance", "pearson"), ...)
    rstudent(model, ...)
    ## S3 method for class 'lm':
    rstudent(model, infl = lm.influence(model, do.coef = FALSE),
        res = infl$wt.res, ...)
    ## S3 method for class 'glm':
    rstudent(model, infl = influence(model, do.coef = FALSE), ...)
    dfbeta(model, ...)
    ## S3 method for class 'lm':
    dfbeta(model, infl = lm.influence(model, do.coef = TRUE), ...)
    dfbetas(model, ...)
    ## S3 method for class 'lm':
    dfbetas(model, infl = lm.influence(model, do.coef = TRUE), ...)
    dffits(model, infl = lm.influence(model, do.coef = FALSE),
        res = weighted.residuals(model))
    covratio(model, infl = lm.influence(model, do.coef = FALSE),
        res = weighted.residuals(model))
    cooks.distance(model, ...)
    ## S3 method for class 'lm':
    cooks.distance(model, infl = lm.influence(model, do.coef = FALSE),
        res = weighted.residuals(model),
        sd = sqrt(deviance(model)/df.residual(model)), hat = infl$hat, ...)
    ## S3 method for class 'glm':
    cooks.distance(model, infl = influence(model, do.coef = FALSE),
        res = infl$pear.res,  dispersion = summary(model)$dispersion,
        hat = infl$hat, ...)

### Arguments

model | a linear model or generalized linear model representing fit. Normally, it is an object of class (or inherited from) "lm" or "glm", returned by function lm or glm.
x, object | an object of class "infl", returned by the function influence.measures normally.
digits | the number of significant digits to print.
infl | an influence structure returned by lm.influence or influence.
sd | standard deviation to use in the calculations.
res | residual to use in the calculations.
hat | the hat values to use in the calculations.
dispersion | the dispersion values to use in the calculations.
... | other arguments pass to the functions.

### Details

- print.infl is an S3 method of the generic function print for the class "infl". It prints the infmat component as a data frame, plus a column for the influential flag (marked with an asterisk for the rows of is.inf specified TRUE).
- summary.infl is an S3 method of the generic function summary for the class "infl". Unlike print.infl, summary.infl prints only the rows of infmat that contain influential elements. The numeric data is rounded and the influential element is suffixed with "_*" .

Value

influence.measures | returns an object of class "infl", which contains the following components:
infmat | an influence matrix. It contains the dfbetas for each model term, dffits, covariance ratios, cooks distances, and hat values.
is.inf | a logical matrix to indicate which element of infmat is influential.
call | a matched call of model frame.
hatvalues | returns the diagonal values of the hat matrix for model. Its method hatvalues.lm extracts the hat value from an infl structure, which is generated by the lm.influence function.
rstandard | generic. Methods rstandard.lm and rstandard.glm return the standardized residuals for linear and generalized linear models, respectively.
rstudent | generic. Methods rstudent.lm and rstudent.glm return the studentized residuals for linear and generalized linear models, respectively.
dfbeta | returns a matrix containing the differences in regression coefficients. (The i-th row shows the change in coefficients from omitting the i-th observation from the model.)
dfbetas | returns a standardized version of dfbeta.
dffits | returns the standardized change in fitted values from omitting the i-th observation from the model.
covratio | returns a measure of the change in the covariance of the coefficients from omitting the i-th observation from the model.
cooks.distance | returns the cooks distance for the model.

References
Belsley, D. A., Kuh, E., and Welsch, R. E. 1980. Regression Diagnostics. New York, NY: John Wiley & Sons.
Cook, R. D. and Weisberg, S. 1982. Residuals and Influence in Regression. London, UK: Chapman and Hall.
Fox, J. 1997. Applied Regression, Linear Models, and Related Methods. Thousand Oaks, CA: Sage Publications. http://www.socsci.mcmaster.ca/jfox/Books/Companion/.
Fox, J. 2002. An R and S-Plus Companion to Applied Regression. Thousand Oaks, CA: Sage Publications. http://www.socsci.mcmaster.ca/jfox/Books/Companion/.
Williams, D. A. 1987. Generalized linear model diagnostics using the deviance and single case deletions. Applied Statistics. Volume 36. 181-191.
See Also
lm, glm, lm.influence, influence
Examples

    numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16)
    ldose <- rep(0:5, 2)
    sex <- factor(rep(c("M", "F"), c(6, 6)))
    SF <- cbind(numdead, numalive = 20 - numdead)
    bwormGlm <- glm(SF ~ ldose + sex + ldose:sex, family = binomial)
    summary(bwormGlm)
    infl <- influence.measures(bwormGlm)
    print(infl)
    summary(infl)
    hatvalues(bwormGlm)
    rstandard(bwormGlm)
    rstudent(bwormGlm)
    dfbeta(bwormGlm)
    dfbetas(bwormGlm)
    dffits(bwormGlm)
    covratio(bwormGlm)
    cooks.distance(bwormGlm)

Package stats version 6.1.5-18
Package Index