Residual Plots and Curvature Tests for Linear Model Fits
Plots the residuals versus each term in a mean function and versus fitted values. Also computes a curvature test for each of the plots by adding a quadratic term and testing the quadratic to be zero. This is Tukey's test for nonadditivity when plotting against fitted values.
### This is a generic function with only one required argument: residualPlots (model, ...) ## S3 method for class 'default': residualPlots(model, terms = ~., layout = NULL, ask, main = "", fitted = TRUE, AsIs=TRUE, plot = TRUE, tests = TRUE, groups, ...) ## S3 method for class 'lm': residualPlots(model, ...) ## S3 method for class 'glm': residualPlots(model, ...) ### residualPlots calls residualPlot, so these arguments can be ### used with either function residualPlot(model, ...) ## S3 method for class 'default': residualPlot(model, variable = "fitted", type = "pearson", groups, plot = TRUE, linear = TRUE, quadratic = if(missing(groups)) TRUE else FALSE, smoother=NULL, smoother.args=list(), col.smooth=palette(), labels, id.method = "r", id.n = if(id.method=="identify") Inf else 0, id.cex=1, id.col=palette(), col = palette(), col.quad = palette(), pch=1, xlab, ylab, lwd = 1, lty = 1, grid=TRUE, key=!missing(groups), ...) ## S3 method for class 'lm': residualPlot(model, ...) ## S3 method for class 'glm': residualPlot(model, variable = "fitted", type = "pearson", plot = TRUE, quadratic = FALSE, smoother = loessLine, smoother.args=list(k=3), ...)
- A regression object.
- A one-sided formula that specifies a subset of the predictors. One
residual plot is drawn for each specified. The default
~ .is to plot against all predictors. For example, the specification
terms = ~ . - X3would plot agai
- If set to a value like
c(4, 3), the layout of the graph will have this many rows and columns. If not set, the program will select an appropriate layout. If the number of graphs exceed nine, you must select the la
TRUE, ask the user before drawing the next plot; if
FALSE, don't ask.
- Main title for the graphs. The default is
main=""for no title.
TRUE, the default, include the plot against fitted values.
FALSE, terms that use the
Iare skipped; if
TRUE, the default, they are included.
TRUE, draw the plot(s).
TRUE, display the curvature tests. With glm's, the argument
startis ignored in computing the curvature tests.
- Additional arguments passed to
residualPlotand then to
- Quoted variable name for the horizontal axis, or
"fitted"to plot versus fitted values.
- Type of residuals to be used. Pearson residuals are
lmobjects since these are equivalent to ordinary residuals with ols and correctly weighted residuals with wls. Any quoted string that is an appropriate value of the
- A list of group indicators. Points in different
groups will be plotted with different colors and symbols. If missing, no grouping.
residualPlots, the grouping variable can also be set in the
termsargument, as described ab
TRUE, adds a horizontal line at zero if no groups. With groups, display the within level of groups ols regression of the residuals as response and the horizontal axis as the regressor.
TRUE, fits the quadratic regression of the vertical axis on the horizontal axis and displays a lack of fit test. Default is
- the name of the smoother to use, selected from the choices
lmobjects the default is
- arguments passed to the smoother.
ScatterplotSmoothers. For generalized linear models the number of elements in the spline basis is set to
k=3; this is done to allow fi
- color for the smoother if groups missing, and ignored if groups is set.
- Arguments for the labelling of
points. The default is
id.n=0for labeling no points. See
showLabelsfor details of these arguments.
- default color for points. If groups is set, col can abe a list at least as long as the number of levels for groups giving the colors for each groups.
- default color for quadratic fit if groups is missing. Ignored if groups are used.
- plotting character. The default is pch=1. If groups are used, pch can be set to a vector at least as long as the number of groups.
- X-axis label. If not specified, a useful label is constructed by the function.
- Y-axis label. If not specified, a useful label is constructed by the function.
- line width for lines.
- line type for quadratic.
- If TRUE, the default, a light-gray background grid is put on the graph
- Should a key be added to the plot? Default is
residualPlots draws one or more residuals plots depending on the
value of the
fitted arguments. If
terms = ~ .,
the default, then a plot is produced of residuals versus each first-order
term in the formula used to create the model. Interaction terms, spline terms,
and polynomial terms of more than one predictor are
skipped. In addition terms that use the
will also be skipped unless you set the argument
AsIs=TRUE. A plot of
residuals versus fitted values is also included unless
In addition to plots, a table of curvature tests is displayed. For plots
against a term in the model formula, say
X1, the test displayed is
the t-test for for
I(X^2) in the fit of
update, model, ~. + I(X^2)).
Econometricians call this a specification test. For factors, the displayed
plot is a boxplot, no curvature test is computed, and grouping is ignored.
For fitted values, the test is Tukey's one-degree-of-freedom test for
nonadditivity. You can suppress the tests with the argument
If grouping is used curvature tests are not displayed.
residualPlot, which is called by
should be viewed as an internal function, and is included here to display its
arguments, which can be used with
residualPlots as well. The
residualPlot function returns the curvature test as an invisible result.
residCurvTest computes the curvature test only. For any factors a
boxplot will be drawn. For any polynomials, plots are against the linear term.
Other non-standard predictors like B-splines are skipped.
lmobjects, returns a data.frame with one row for each plot drawn, one column for the curvature test statistic, and a second column for the corresponding p-value. This function is used primarily for its side effect of drawing residual plots.
Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition. Sage. Weisberg, S. (2014) Applied Linear Regression, Fourth Edition, Wiley, Chapter 8
m1 <- lm(prestige ~ income, data=Prestige) residualPlots(m1) residualPlots(m1, terms= ~ 1 | type) # plot vs. yhat grouping by type