Influence Plots for Multivariate Linear Models

This function creates various types of “bubble” plots of influence measures with the areas of the circles representing the observations proportional to generalized Cook's distances.

Usage

# S3 method for mlm
influencePlot(
  model,
  scale = 12,
  type = c("stres", "LR", "cookd"),
  infl = mlm.influence(model, do.coef = FALSE),
  FUN = det,
  fill = TRUE,
  fill.col = "red",
  fill.alpha.max = 0.5,
  labels,
  id.method = "noteworthy",
  id.n = if (id.method[1] == "identify") Inf else 0,
  id.cex = 1,
  id.col = palette()[1],
  ref.col = "gray",
  ref.lty = 2,
  ref.lab = TRUE,
  ...
)

Arguments

model: An mlm object, as returned by lm with a multivariate response.
scale: a factor to adjust the radii of the circles, in relation to sqrt(CookD)
type: Type of plot: one of c("stres", "cookd", "LR"). See Details.
infl: influence measure structure as returned by mlm.influence
FUN: For m>1, the function to be applied to the \(H\) and \(Q\) matrices returning a scalar value. FUN=det and FUN=tr are possible choices, returning the \(|H|\) and \(tr(H)\) respectively.
fill, fill.col, fill.alpha.max: fill: logical, specifying whether the circles should be filled. When fill=TRUE, fill.col gives the base fill color to which transparency specified by fill.alpha.max is applied.
labels, id.method, id.n, id.cex, id.col: settings for labeling points; see showLabels for details. To omit point labeling, set id.n=0, the default. The default id.method="noteworthy" is used in this function to indicate setting labels for points with large Studentized residuals, hat-values or Cook's distances. See Details below. Set id.method="identify" for interactive point identification.
ref.col, ref.lty, ref.lab: arguments for reference lines. Incompletely implemented in this version
...: other arguments passed down

Value

If points are identified, returns a data frame with the hat values, Studentized residuals and Cook's distance of the identified points. If no points are identified, nothing is returned. This function is primarily used for its side-effect of drawing a plot.

Details

type="stres" plots squared (internally) Studentized residuals against hat values; type="cookd" plots Cook's distance against hat values; type="LR" plots residual components against leverage components, with the attractive property that contours of constant Cook's distance fall on diagonal lines with slope = -1. Adjacent reference lines represent multiples of influence.

The id.method="noteworthy" setting also requires setting id.n>0 to have any effect. Using id.method="noteworthy", and id.n>0, the number of points labeled is the union of the largest id.n values on each of L, R, and CookD.

References

Barrett, B. E. and Ling, R. F. (1992). General Classes of Influence Measures for Multivariate Regression. Journal of the American Statistical Association, 87(417), 184-191.

Barrett, B. E. (2003). Understanding Influence in Multivariate Regression Communications in Statistics - Theory and Methods, 32, 667-680.

McCulloch, C. E. & Meeter, D. (1983). Discussion of "Outliers..." by R. J. Beckman and R. D. Cook. Technometrics, 25, 152-155

Author

Michael Friendly

Examples


data(Rohwer, package="heplots")
Rohwer2 <- subset(Rohwer, subset=group==2)
Rohwer.mod <- lm(cbind(SAT, PPVT, Raven) ~ n+s+ns+na+ss, data=Rohwer2)

influencePlot(Rohwer.mod, id.n=4, type="stres")

#>        H      Q  CookD     L      R
#> 42 0.568 0.3439 0.8467 1.316 0.7964
#> 47 0.452 0.0324 0.0634 0.824 0.0591
#> 51 0.126 0.2997 0.1643 0.145 0.3431
#> 52 0.332 0.0105 0.0152 0.498 0.0158
#> 62 0.157 0.3820 0.2601 0.186 0.4532
#> 64 0.367 0.2128 0.3387 0.580 0.3363
#> 66 0.304 0.2295 0.3026 0.437 0.3299
influencePlot(Rohwer.mod, id.n=4, type="LR")

#>        H      Q  CookD     L      R
#> 42 0.568 0.3439 0.8467 1.316 0.7964
#> 47 0.452 0.0324 0.0634 0.824 0.0591
#> 51 0.126 0.2997 0.1643 0.145 0.3431
#> 52 0.332 0.0105 0.0152 0.498 0.0158
#> 62 0.157 0.3820 0.2601 0.186 0.4532
#> 64 0.367 0.2128 0.3387 0.580 0.3363
#> 66 0.304 0.2295 0.3026 0.437 0.3299
influencePlot(Rohwer.mod, id.n=4, type="cookd")

#>        H      Q  CookD     L      R
#> 42 0.568 0.3439 0.8467 1.316 0.7964
#> 47 0.452 0.0324 0.0634 0.824 0.0591
#> 51 0.126 0.2997 0.1643 0.145 0.3431
#> 52 0.332 0.0105 0.0152 0.498 0.0158
#> 62 0.157 0.3820 0.2601 0.186 0.4532
#> 64 0.367 0.2128 0.3387 0.580 0.3363
#> 66 0.304 0.2295 0.3026 0.437 0.3299

# Sake data
data(Sake, package="heplots")
  Sake.mod <- lm(cbind(taste,smell) ~ ., data=Sake)
  influencePlot(Sake.mod, id.n=3, type="stres")

#>        H      Q  CookD     L      R
#> 1  0.812 0.5757 1.0903 4.309 3.0564
#> 21 0.602 0.2129 0.2989 1.511 0.5346
#> 25 0.325 0.4486 0.3402 0.481 0.6646
#> 28 0.741 0.0167 0.0289 2.858 0.0645
  influencePlot(Sake.mod, id.n=3, type="LR")

#>        H      Q  CookD     L      R
#> 1  0.812 0.5757 1.0903 4.309 3.0564
#> 21 0.602 0.2129 0.2989 1.511 0.5346
#> 25 0.325 0.4486 0.3402 0.481 0.6646
#> 28 0.741 0.0167 0.0289 2.858 0.0645
  influencePlot(Sake.mod, id.n=3, type="cookd")

#>        H      Q  CookD     L      R
#> 1  0.812 0.5757 1.0903 4.309 3.0564
#> 21 0.602 0.2129 0.2989 1.511 0.5346
#> 25 0.325 0.4486 0.3402 0.481 0.6646
#> 28 0.741 0.0167 0.0289 2.858 0.0645

# Adopted data  
data(Adopted, package="heplots")
Adopted.mod <- lm(cbind(Age2IQ, Age4IQ, Age8IQ, Age13IQ) ~ AMED + BMIQ, data=Adopted)
influencePlot(Adopted.mod, id.n=3)

#>         H      Q CookD      L     R
#> 12 0.1315 0.1057 0.273 0.1514 0.122
#> 37 0.0599 0.1469 0.173 0.0638 0.156
#> 44 0.1414 0.0978 0.272 0.1648 0.114
#> 45 0.1986 0.1313 0.513 0.2479 0.164
#> 51 0.0857 0.1669 0.281 0.0938 0.182
influencePlot(Adopted.mod, id.n=3, type="LR", ylim=c(-4,-1.5))

#>         H      Q CookD      L     R
#> 12 0.1315 0.1057 0.273 0.1514 0.122
#> 37 0.0599 0.1469 0.173 0.0638 0.156
#> 44 0.1414 0.0978 0.272 0.1648 0.114
#> 45 0.1986 0.1313 0.513 0.2479 0.164
#> 51 0.0857 0.1669 0.281 0.0938 0.182