R: Plot Diagnostics for an lm Object

plot.lm {stats} | R Documentation

## Plot Diagnostics for an lm Object

### Description

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.

### Usage

    ## S3 method for class 'lm'
    plot(x, which = c(1,2,3,5),
         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) 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, labels.id = names(residuals(x)), cex.id = 0.75,
         qqline = TRUE, cook.levels = c(0.5, 1.0),
         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)

### Arguments

`x` | `lm` object, typically result of `lm` or `glm`.
`which` | if a subset of the plots is required, specify a subset of the numbers `1:6`, see `caption` below (and the ‘Details’) for the different kinds.
`caption` | 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]`. Can be set to `""` or `NA` to suppress all captions.
`panel` | panel function. The useful alternative to `points`, `panel.smooth` can be chosen by `add.smooth = TRUE`.
`sub.caption` | 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.
`main` | title to each plot—in addition to `caption`.
`ask` | logical; if `TRUE`, the user is asked before each plot, see `par(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.
`iter.smooth` | 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.
`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 (`rstandard(.)`) that are equal in magnitude are lines through the origin. The contour lines are labelled with the magnitudes.

Notice that some plots may not make much sense for the `glm` case; e.g., the normal Q-Q plot only makes sense if the distribution is approximately normal.

### Author(s)

John Maindonald and Martin Maechler.

### 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. 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.

### See Also

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

### Examples

    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")

[Package stats version 4.0.5 Index]