smooth.influence.measures {npreg}

Nonparametric Regression Deletion Diagnostics

Description

These functions compute several regression (leave-one-out deletion) diagnostics for a fit smoothing spline (fit by ss), smooth model (fit by sm), or generalized smooth model (fit by gsm).

Usage

smooth.influence.measures(model, infl = smooth.influence(model))

## S3 method for class 'ss'
rstandard(model, infl = NULL, sd = model$sigma, 
          type = c("sd.1", "predictive"), ...)
## S3 method for class 'sm'
rstandard(model, infl = NULL, sd = model$sigma, 
          type = c("sd.1", "predictive"), ...)
## S3 method for class 'gsm'
rstandard(model, infl = NULL, 
          type = c("deviance", "pearson"), ...)

## S3 method for class 'ss'
rstudent(model, infl = influence(model, do.coef = FALSE), 
         res = infl$wt.res, ...)
## S3 method for class 'sm'
rstudent(model, infl = influence(model, do.coef = FALSE), 
         res = infl$wt.res, ...)
## S3 method for class 'gsm'
rstudent(model, infl = influence(model, do.coef = FALSE), ...)

## S3 method for class 'ss'
dfbeta(model, infl = NULL, ...)
## S3 method for class 'sm'
dfbeta(model, infl = NULL, ...)
## S3 method for class 'gsm'
dfbeta(model, infl = NULL, ...)

## S3 method for class 'ss'
dfbetas(model, infl = smooth.influence(model, do.coef = TRUE), ...)
## S3 method for class 'sm'
dfbetas(model, infl = smooth.influence(model, do.coef = TRUE), ...)
## S3 method for class 'gsm'
dfbetas(model, infl = smooth.influence(model, do.coef = TRUE), ...)

cov.ratio(model, infl = smooth.influence(model, do.coef = FALSE),
          res = weighted.residuals(model))

## S3 method for class 'ss'
cooks.distance(model, infl = NULL, res = weighted.residuals(model), 
               sd = model$sigma, hat = hatvalues(model), ...)
## S3 method for class 'sm'
cooks.distance(model, infl = NULL, res = weighted.residuals(model), 
               sd = model$sigma, hat = hatvalues(model), ...)
## S3 method for class 'gsm'
cooks.distance(model, infl = NULL, res = residuals(model, type = "pearson"), 
               dispersion = model$dispersion, hat = hatvalues(model), ...)

## S3 method for class 'ss'
hatvalues(model, ...)
## S3 method for class 'sm'
hatvalues(model, ...)
## S3 method for class 'gsm'
hatvalues(model, ...)

Arguments

model

an object of class "gsm" output by the gsm function, "sm" output by the sm function, or "ss" output by the ss function

infl

influence structure as returned by smooth.influence

res

(possibly weighted) residuals with proper defaults

sd

standard deviation to use, see defaults

dispersion

dispersion (for gsm objects) to use, see defaults

hat

hat values S_{ii}, see defaults

type

type of residuals for rstandard

...

additional arguments (currently ignored)

Details

Inspired by influence.measures and related functions in R's stats package.

The function smooth.influence.measures produces a class "infl" object, which displays the DFBETAS for each coefficient, DFFITS, covariance ratios, Cook's distance, and the diagonals of the smoothing matrix. Cases which are influential with respect to any of these measures are marked with an asterisk.

The S3 methods dfbetas, dffits, covratio, and cooks.distance provide direct access to the corresponding diagnostic quantities. The S3 methods rstandard and rstudent give the standardized and Studentized residuals, respectively. (These re-normalize the residuals to have unit variance, using an overall and leave-one-out measure of the error variance, respectively.)

Values for generalized smoothing models are approximations, as described in Williams (1987) (except that Cook's distances are scaled as F rather than chi-square values). THe approximations can be poor when some cases have large influence.

The optional infl, res, and sd arguments are there to encourage the use of these direct access functions in situations where the underlying basic influence measures, e.g., from smooth.influence, are already available.

For ss and sm objects, the code rstandard(*, type = "predictive") returns the leave-one-out (ordinary) cross-validation residuals, and the PRESS (PREdictive Sum of Squares) statistic is defined as

PRESS <- sum(rstandard(model, type = "predictive")^2)

Note that OCV = PRESS / n, where OCV = ordinary cross-validation criterion

Note

Note: the dffits function in R's stats package can be used with the following syntax

dffits(model, infl = smooth.influence(model, do.coef = FALSE), res = weighted.residuals(model))

Author(s)

Nathaniel E. Helwig <[e-mail]>

References

See references listed in influence.measures

Williams, D. A. (1987). Generalized linear model diagnostics using the deviance and single case deletions. Applied Statistics, 36, 181-191. doi:10.2307/2347550

See Also

ss, sm, gsm for modeling functions

smooth.influence for some basic influence information

diagnostic.plots for regression diagnostic plots

Examples

# generate data
set.seed(1)
n <- 100
x <- seq(0, 1, length.out = n)
fx <- 2 + 3 * x + sin(2 * pi * x)
y <- fx + rnorm(n, sd = 0.5)

# fit models
mod.ss <- ss(x, y, nknots = 10)
mod.sm <- sm(y ~ x, knots = 10)
mod.gsm <- gsm(y ~ x, knots = 10)

# calculate influence
infl.ss <- smooth.influence.measures(mod.ss)
infl.sm <- smooth.influence.measures(mod.sm)
infl.gsm <- smooth.influence.measures(mod.gsm)

# standardized residuals
rstan.ss <- rstandard(mod.ss)
rstan.sm <- rstandard(mod.sm)
rstan.gsm <- rstandard(mod.gsm)

# studentized residuals
rstud.ss <- rstudent(mod.ss)
rstud.sm <- rstudent(mod.sm)
rstud.gsm <- rstudent(mod.gsm)