plot.lm
Plot Diagnostics for an lm Object
Six plots (selectable by which
) are currently available: a plot
of residuals against fitted values, a Scale-Location plot of
$sqrt(| residuals |)$
against fitted values, a Normal Q-Q plot, a
plot of Cook's distances versus row labels, a plot of residuals
against leverages, and a plot of Cook's distances against
leverage/(1-leverage). By default, the first three and 5
are
provided.
- Keywords
- hplot, regression
Usage
"plot"(x, which = c(1:3, 5), caption = list("Residuals vs Fitted", "Normal Q-Q", "Scale-Location", "Cook's distance", "Residuals vs Leverage", expression("Cook's dist vs Leverage " * h[ii] / (1 - h[ii]))), panel = if(add.smooth) panel.smooth else points, sub.caption = NULL, main = "", ask = prod(par("mfcol")) < length(which) && dev.interactive(), ..., id.n = 3, labels.id = names(residuals(x)), cex.id = 0.75, qqline = TRUE, cook.levels = c(0.5, 1.0), add.smooth = getOption("add.smooth"), label.pos = c(4,2), cex.caption = 1, cex.oma.main = 1.25)
Arguments
- x
lm
object, typically result oflm
orglm
.- which
- if a subset of the plots is required, specify a subset of
the numbers
1:6
. - caption
- captions to appear above the plots;
character
vector orlist
of valid graphics annotations, seeas.graphicsAnnot
, of length 6, the j-th entry corresponding towhich[j]
. Can be set to""
orNA
to suppress all captions. - panel
- panel function. The useful alternative to
points
,panel.smooth
can be chosen byadd.smooth = TRUE
. - sub.caption
- common title---above the figures if there are more
than one; used as
sub
(s.title
) otherwise. IfNULL
, as by default, a possible abbreviated version ofdeparse(x$call)
is used. - main
- title to each plot---in addition to
caption
. - ask
- logical; if
TRUE
, the user is asked before each plot, seepar(ask=.)
. - ...
- other parameters to be passed through to plotting functions.
- id.n
- number of points to be labelled in each plot, starting with the most extreme.
- labels.id
- vector of labels, from which the labels for extreme
points will be chosen.
NULL
uses observation numbers. - cex.id
- magnification of point labels.
- qqline
- logical indicating if a
qqline()
should be added to the normal Q-Q plot. - cook.levels
- levels of Cook's distance at which to draw contours.
- add.smooth
- logical indicating if a smoother should be added to
most plots; see also
panel
above. - label.pos
- positioning of labels, for the left half and right half of the graph respectively, for plots 1-3.
- cex.caption
- controls the size of
caption
. - cex.oma.main
- controls the size of the
sub.caption
only if that is above the figures when there is more than one.
Details
sub.caption
---by default the function call---is shown as
a subtitle (under the x-axis title) on each plot when plots are on
separate pages, or as a subtitle in the outer margin (if any) when
there are multiple plots per page.
The Scale-Location plot, also called Spread-Location or S-L plot, takes the square root of the absolute residuals in order to diminish skewness ($sqrt(|E|)$) is much less skewed than $| E |$ for Gaussian zero-mean $E$).
The S-L, the Q-Q, and the Residual-Leverage plot, use
standardized residuals which have identical variance (under the
hypothesis). They are given as
$R[i] / (s * sqrt(1 - h.ii))$
where $h.ii$ are the diagonal entries of the hat matrix,
influence()$hat
(see also hat
), and
where the Residual-Leverage plot uses standardized Pearson residuals
(residuals.glm(type = "pearson")
) for $R[i]$.
The Residual-Leverage plot shows contours of equal Cook's distance,
for values of cook.levels
(by default 0.5 and 1) and omits
cases with leverage one with a warning. If the leverages are constant
(as is typically the case in a balanced aov
situation)
the plot uses factor level combinations instead of the leverages for
the x-axis. (The factor levels are ordered by mean fitted value.)
In the Cook's distance vs leverage/(1-leverage) plot, contours of standardized residuals that are equal in magnitude are lines through the origin. The contour lines are labelled with the magnitudes.
References
Belsley, D. A., Kuh, E. and Welsch, R. E. (1980) Regression Diagnostics. New York: Wiley.
Cook, R. D. and Weisberg, S. (1982) Residuals and Influence in Regression. London: Chapman and Hall.
Firth, D. (1991) Generalized Linear Models. In Hinkley, D. V. and Reid, N. and Snell, E. J., eds: Pp.\ifelse{latex}{\out{~}}{ } 55-82 in Statistical Theory and Modelling. In Honour of Sir David Cox, FRS. London: Chapman and Hall.
Hinkley, D. V. (1975) On power transformations to symmetry. Biometrika 62, 101--111.
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.
See Also
Examples
library(stats)
require(graphics)
## Analysis of the life-cycle savings data
## given in Belsley, Kuh and Welsch.
lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings)
plot(lm.SR)
## 4 plots on 1 page;
## allow room for printing model formula in outer margin:
par(mfrow = c(2, 2), oma = c(0, 0, 2, 0))
plot(lm.SR)
plot(lm.SR, id.n = NULL) # no id's
plot(lm.SR, id.n = 5, labels.id = NULL) # 5 id numbers
## Was default in R <= 2.1.x:
## Cook's distances instead of Residual-Leverage plot
plot(lm.SR, which = 1:4)
## Fit a smooth curve, where applicable:
plot(lm.SR, panel = panel.smooth)
## Gives a smoother curve
plot(lm.SR, panel = function(x, y) panel.smooth(x, y, span = 1))
par(mfrow = c(2,1)) # same oma as above
plot(lm.SR, which = 1:2, sub.caption = "Saving Rates, n=50, p=5")