Influence Measures and Diagnostic Plots for Multivariate Linear Models
Functions in this package compute regression deletion diagnostics for multivariate linear models following methods proposed by Barrett & Ling (1992) and provide some associated diagnostic plots. The diagnostic measures include hat-values (leverages), generalized Cook's distance, and generalized squared 'studentized' residuals. Several types of plots to detect influential observations are provided.
In addition, the functions provide diagnostics for deletion of subsets of observations of size m>1. This case is theoretically interesting because sometimes pairs (m=2) of influential observations can mask each other, sometimes they can have joint influence far exceeding their individual effects, as well as other interesting phenomena described by Lawrence (1995). Associated methods for the case m>1 are still under development in this package.
Get the released version from CRAN:
install.packages("mvinfluence")
The design goal for this package is that, as an extension of standard methods for univariate linear models, you should be able to fit a linear model with a multivariate response,
mymlm <- lm( cbind(y1, y2, y3) ~ x1 + x2 + x3, data=mydata)
and then get useful diagnostics and plots with:
influence(mymlm)
hatvalues(mymlm)
influencePlot(mymlm, ...)
Fit a MLM to a subset of the Rohwer data (the Low SES group).
The default influence plot (type="stres") shows the squared standardized residual against the Hat value. The areas of the circles representing the observations are proportional to generalized Cook's distances.
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)
#> H Q CookD L R
#> 42 0.5682146 0.34387765 0.84671734 1.3159654 0.79640874
#> 47 0.4516115 0.03239271 0.06339198 0.8235248 0.05906890
#> 51 0.1264993 0.29967992 0.16427359 0.1448187 0.34307919
#> 52 0.3324674 0.01054411 0.01519082 0.4980543 0.01579565
#> 62 0.1571260 0.38198170 0.26008352 0.1864170 0.45318959
#> 64 0.3672647 0.21279661 0.33866160 0.5804397 0.33631219
#> 66 0.3042700 0.22949988 0.30259634 0.4373392 0.32986917
An alternative (type="stres") plots residual components against leverage components, with the property that contours of constant Cook's distance fall on diagonal lines with slope = -1.
influencePlot(Rohwer.mod, id.n=4, type="LR")
#> H Q CookD L R
#> 42 0.5682146 0.34387765 0.84671734 1.3159654 0.79640874
#> 47 0.4516115 0.03239271 0.06339198 0.8235248 0.05906890
#> 51 0.1264993 0.29967992 0.16427359 0.1448187 0.34307919
#> 52 0.3324674 0.01054411 0.01519082 0.4980543 0.01579565
#> 62 0.1571260 0.38198170 0.26008352 0.1864170 0.45318959
#> 64 0.3672647 0.21279661 0.33866160 0.5804397 0.33631219
#> 66 0.3042700 0.22949988 0.30259634 0.4373392 0.32986917
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, 3, 667-680.
A. J. Lawrence (1995). Deletion Influence and Masking in Regression Journal of the Royal Statistical Society. Series B (Methodological) , 57, No. 1, pp. 181-189.