# influencePlot.mlm: Influence Plots for Multivariate Linear Models In mvinfluence: Influence Measures and Diagnostic Plots for Multivariate Linear Models

## Description

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

`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 property that contours of constant Cook's distance fall on diagonal lines with slope = -1.

## Usage

 ```1 2 3 4 5 6 7 8``` ```## S3 method for class '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")` `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. `labels, id.method, id.n, id.cex, id.col` settings for labelling points; see `link{showLabels}` for details. To omit point labelling, 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. `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. `ref.col, ref.lty, ref.lab` arguments for reference lines. Incompletely implemented in this version `...` other arguments passed down

## Details

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.

## 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.

Michael Friendly

## 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

`mlm.influence`, `lrPlot`
`influencePlot` in the car package
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```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") influencePlot(Rohwer.mod, id.n=4, type="LR") influencePlot(Rohwer.mod, id.n=4, type="cookd") # Sake data data(Sake, package="heplots") Sake.mod <- lm(cbind(taste,smell) ~ ., data=Sake) influencePlot(Sake.mod, id.n=3, type="stres") influencePlot(Sake.mod, id.n=3, type="LR") influencePlot(Sake.mod, id.n=3, type="cookd") # Adopted data data(Adopted, package="heplots") Adopted.mod <- lm(cbind(Age2IQ, Age4IQ, Age8IQ, Age13IQ) ~ AMED + BMIQ, data=Adopted) influencePlot(Adopted.mod, id.n=3) influencePlot(Adopted.mod, id.n=3, type="LR", ylim=c(-4,-1.5)) ```