plot.lm {stats}R Documentation

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 Q-Q plot of residuals, 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.


## S3 method for class 'lm'
plot(x, which = c(1,2,3,5), 
     caption = list("Residuals vs Fitted", "Q-Q Residuals",
       "Scale-Location", "Cook's distance",
       "Residuals vs Leverage",
       expression("Cook's dist vs Leverage* " * h[ii] / (1 - h[ii]))),
     panel = if(add.smooth) function(x, y, ...)
              panel.smooth(x, y, iter=iter.smooth, ...) else points,
     sub.caption = NULL, main = "",
     ask = prod(par("mfcol")) < length(which) && dev.interactive(),
     id.n = 3, = names(residuals(x)), = 0.75,
     qqline = TRUE, cook.levels = c(0.5, 1.0),
     cook.col = 8, cook.lty = 2, cook.legendChanges = list(),
     add.smooth = getOption("add.smooth"),
     iter.smooth = if(isGlm) 0 else 3,
     label.pos = c(4,2),
     cex.caption = 1, cex.oma.main = 1.25
   , extend.ylim.f = 0.08



lm object, typically result of lm or glm.


a subset of the numbers 1:6, by default 1:3, 5, referring to

  1. "Residuals vs Fitted", aka ‘Tukey-Anscombe’ plot

  2. "Residual Q-Q" plot

  3. "Scale-Location"

  4. "Cook's distance"

  5. "Residuals vs Leverage"

  6. "Cook's dist vs Lev./(1-Lev.)"

See also ‘Details’ below.


captions to appear above the plots; character vector or list of valid graphics annotations, see as.graphicsAnnot, of length 6, the j-th entry corresponding to which[j], see also the default vector in ‘Usage’. Can be set to "" or NA to suppress all captions.


panel function. The useful alternative to points, panel.smooth can be chosen by add.smooth = TRUE.


common title—above the figures if there are more than one; used as sub (s.title) otherwise. If NULL, as by default, a possible abbreviated version of deparse(x$call) is used.


title to each plot—in addition to caption.


logical; if TRUE, the user is asked before each plot, see par(ask=.).


other parameters to be passed through to plotting functions.


number of points to be labelled in each plot, starting with the most extreme.

vector of labels, from which the labels for extreme points will be chosen. NULL uses observation numbers.

magnification of point labels.


logical indicating if a qqline() should be added to the normal Q-Q plot.


levels of Cook's distance at which to draw contours.

cook.col, cook.lty

color and line type to use for these contour lines.


a list (or NULL to suppress the call) of arguments to legend which should be modified from (or added to) the plot.lm() default list(x = "bottomleft", legend = "Cook's distance", lty = cook.lty, col = cook.col, text.col = cook.col, bty = "n", x.intersp = 1/4, y.intersp = 1/8) .


logical indicating if a smoother should be added to most plots; see also panel above.


the number of robustness iterations, the argument iter in panel.smooth(); the default uses no such iterations for glm fits which is particularly desirable for the (predominant) case of binary observations, but also for other models where the response distribution can be highly skewed.


positioning of labels, for the left half and right half of the graph respectively, for plots 1-3, 5, 6.


controls the size of caption.


controls the size of the sub.caption only if that is above the figures when there is more than one.


a numeric vector of length 1 or 2, to be used in ylim <- extendrange(r=ylim, f = *) for plots 1 and 5 when id.n is non-empty.


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 (which=3), 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 (which=5) plot use standardized residuals which have identical variance (under the hypothesis). They are given as R_i / (s \times \sqrt{1 - h_{ii}}) where the ‘leverages’ h_{ii} are the diagonal entries of the hat matrix, influence()$hat (see also hat), and where the Residual-Leverage plot uses the standardized Pearson residuals (residuals.glm(type = "pearson")) for R[i].

The Residual-Leverage plot (which=5) 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) (= “leverage*”) plot (which=6), contours of standardized residuals (rstandard(.)) that are equal in magnitude are lines through the origin. These lines are labelled with the magnitudes. The x-axis is labeled with the (non equidistant) leverages h_{ii}.

For the glm case, the Q-Q plot is based on the absolute value of the standardized deviance residuals. When the saddlepoint approximation applies, these have an approximate half-normal distribution. The saddlepoint approximation is exact for the normal and inverse Gaussian family, and holds approximately for the Gamma family with small dispersion (large shape) and for the Poisson and binomial families with large counts (Dunn and Smyth 2018).


John Maindonald and Martin Maechler.


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. 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. doi:10.2307/2334491.

McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models. London: Chapman and Hall.

Dunn, P.K. and Smyth G.K. (2018) Generalized Linear Models with Examples in R. New York: Springer-Verlag.

See Also

termplot, lm.influence, cooks.distance, hatvalues.



## Analysis of the life-cycle savings data
## given in Belsley, Kuh and Welsch.
lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings)

## 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)) -> opar
plot(lm.SR, id.n = NULL)                 # no id's
plot(lm.SR, id.n = 5, = 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)

## All the above fit a smooth curve where applicable
## by default unless "add.smooth" is changed.
## Give a smoother curve by increasing the lowess span :
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")

## Cook's distance tweaking
par(mfrow = c(2,3)) # same oma ...
plot(lm.SR, which = 1:6, cook.col = "royalblue")

## A case where over plotting of the "legend" is to be avoided:
if(dev.interactive(TRUE)) getOption("device")(height = 6, width = 4)
par(mfrow = c(3,1), mar = c(5,5,4,2)/2 +.1, mgp = c(1.4, .5, 0))
plot(lm.SR, which = 5, extend.ylim.f = c(0.2, 0.08))
plot(lm.SR, which = 5, cook.lty = "dotdash",
     cook.legendChanges = list(x = "bottomright", legend = "Cook"))
plot(lm.SR, which = 5, cook.legendChanges = NULL)  # no "legend"

par(opar) # reset par()s

[Package stats version 4.5.0 Index]