coefplot: Coefficient plots for Multivariate Linear Models

In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

Coefficient plots for Multivariate Linear Models

Description

Displays bivariate confidence ellipses for all parameters in an multivariate linear model, for a given pair of variables. In contrast to univariate coefficient plots for an ordinary linear model (e.g., parameters::model_parameters(), plotted via its plot() method), which show confidence intervals for parameters one at a time, these plots show how each predictor moves a pair of responses jointly, in a way that can readily be compared.

Usage

coefplot(object, ...)

## S3 method for class 'mlm'
coefplot(
  object,
  variables = 1:2,
  parm = NULL,
  df = NULL,
  level = 0.95,
  intercept = FALSE,
  std = FALSE,
  Scheffe = FALSE,
  bars = TRUE,
  fill = FALSE,
  fill.alpha = 0.2,
  labels = !add,
  label.pos = NULL,
  xlab,
  ylab,
  xlim = NULL,
  ylim = NULL,
  axes = TRUE,
  main = "",
  add = FALSE,
  lwd = 1,
  lty = 1,
  pch = 19,
  col = palette(),
  cex = 2,
  cex.label = 1.5,
  cex.lab = par("cex.lab"),
  lty.zero = 3,
  col.zero = 1,
  pch.zero = "+",
  verbose = FALSE,
  ...
)

Arguments

object	A multivariate linear model, such as fit by lm(cbind(y1, y2, ...) ~ terms, ...)
...	Other parameters passed to graphics::plot()
variables	Response variables to plot, given as their indices or names
parm	Parameters to plot, given as their indices or names
df	Degrees of freedom for hypothesis tests
level	Confidence level for the confidence ellipses
intercept	logical. Include the intercept?
std	logical. If TRUE, plot standardized coefficients instead – see stdmodel() for the standardization convention (response(s) and numeric predictors are standardized; factor predictors are left on their raw 0/1 scale). Not generally useful together with intercept = TRUE, since the intercept becomes ~0 once standardized.
Scheffe	If TRUE, confidence intervals for all parameters have Scheffe coverage, otherwise, individual coverage.
bars	Draw univariate confidence intervals for each of the variables?
fill	a logical value or vector. TRUE means the confidence ellipses will be filled.
fill.alpha	Opacity of the confidence ellipses
labels	Labels for the confidence ellipses
label.pos	Positions of the labels for each ellipse. See label.ellipse()
xlab, ylab	x, y axis labels
xlim, ylim	Axis limits
axes	Draw axes?
main	Plot title
add	logical. Add to an existing plot?
lwd	Line widths
lty	Line types
pch	Point symbols for the parameter estimates
col	Colors for the confidence ellipses, points, lines
cex	Character size for points showing parameter estimates
cex.label	Character size for ellipse labels
cex.lab	Character size for axis labels. Defaults to par("cex.lab").
lty.zero, col.zero, pch.zero	Line type, color and point symbol for horizontal and vertical lines at 0, 0. These default to lty.zero = 3, col.zero = 1 (black) and pch.zero = '+'.
verbose	logical. Print parameter estimates and variance-covariance for each parameter?

Details

This function is also a generalization of car::confidenceEllipse() to a multivariate setting. Note that confidenceEllipse() also has an mlm method (via car::confidenceEllipse()), but it answers a different question: it fixes a pair of coefficients (for one or more responses) as the plot axes, and shows their joint confidence region. coefplot() instead fixes a pair of responses as the axes and overlays one ellipse per predictor – use it when the question is "how does each predictor move these two responses together?", and confidenceEllipse() when the question is about the relationship between two specific coefficients.

Value

Returns invisibly a list of the coordinates of the ellipses drawn

Author(s)

Michael Friendly

See Also

car::confidenceEllipse(), parameters::model_parameters()

Other multivariate linear models: glance.mlm(), stdcoef(), stdmodel()

Examples

rohwer.mlm <- lm(cbind(SAT,PPVT,Raven)~n+s+ns, data=Rohwer)

coefplot(rohwer.mlm, lwd=2, 
         main="Bivariate coefficient plot for SAT and PPVT", fill=TRUE)
coefplot(rohwer.mlm, add=TRUE, Scheffe=TRUE, fill=TRUE)

coefplot(rohwer.mlm, var=c(1,3))

mod1 <- lm(cbind(SAT,PPVT,Raven)~n+s+ns+na+ss, data=Rohwer)
coefplot(mod1, lwd=2, fill=TRUE, parm=(1:5),
	main="Bivariate 68% coefficient plot for SAT and PPVT", level=0.68)

# standardized coefficients, with a factor predictor (SES) in the model
# but excluded from the plotted parm range
mod2 <- lm(cbind(SAT,PPVT,Raven) ~ SES+n+s+ns+na+ss, data=Rohwer)
coefplot(mod2, parm=2:6, std=TRUE, fill=TRUE, level=0.68)

heplots documentation built on Sept. 13, 2026, 5:06 p.m.