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.

hplot, regression
### 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",
                 plot = TRUE,
                 linear = TRUE,
                 quadratic = if(missing(groups)) TRUE else FALSE,
                 smoother=NULL, smoother.args=list(),
                 id.method = "r",
                 id.n = if(id.method[1]=="identify") Inf else 0,
                 id.cex=1, id.col=palette()[1],
                 col = palette()[1], col.quad = palette()[2],
                 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 = ~ . - X3 would plot agai
If set to a value like c(1, 1) or 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
If 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.
If TRUE, the default, include the plot against fitted values.
If FALSE, terms that use the as-is function I are skipped; if TRUE, the default, they are included.
If TRUE, draw the plot(s).
If TRUE, display the curvature tests. With glm's, the argument start is ignored in computing the curvature tests.
Additional arguments passed to residualPlot and then to plot.
Quoted variable name for the horizontal axis, or "fitted" to plot versus fitted values.
Type of residuals to be used. Pearson residuals are appropriate for lm objects 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. In residualPlots, the grouping variable can also be set in the terms argument, as described ab
If 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.
if TRUE, fits the quadratic regression of the vertical axis on the horizontal axis and displays a lack of fit test. Default is TRUE for lm and FALSE for glm or if groups no
the name of the smoother to use, selected from the choices described at ScatterplotSmoothers For lm objects the default is NULL. For glm object the
arguments passed to the smoother. See 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=0 for labeling no points. See showLabels for 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 !is.null(groups).

residualPlots draws one or more residuals plots depending on the value of the terms and 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 as-is function, e.g., I(X^2), will also be skipped unless you set the argument AsIs=TRUE. A plot of residuals versus fitted values is also included unless fitted=FALSE. 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 tests=FALSE. If grouping is used curvature tests are not displayed. residualPlot, which is called by residualPlots, 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.


  • For lm objects, 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

See Also

See Also lm, identify, showLabels

  • residualPlots
  • residualPlots.default
  • residualPlots.lm
  • residualPlots.glm
  • residualPlot
  • residualPlot.default
  • residualPlot.lm
  • residualPlot.glm
  • residCurvTest
  • residCurvTest.lm
  • residCurvTest.glm
  • tukeyNonaddTest
m1 <- lm(prestige ~ income, data=Prestige)
residualPlots(m1, terms= ~ 1 | type) # plot vs. yhat grouping by type
Documentation reproduced from package car, version 2.0-20, License: GPL (>= 2)

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