# influence.mlm: Regression Deletion Diagnostics for Multivariate Linear... In mvinfluence: Influence Measures and Diagnostic Plots for Multivariate Linear Models

## Description

This collection of functions is designed to compute regression deletion diagnostics for multivariate linear models following Barrett & Ling (1992) that are close analogs of methods for univariate and generalized linear models handled by the influence.measures in the stats package.

In addition, the functions provide diagnostics for deletion of subsets of observations of size m>1.

## Usage

 1 2 3 4 5 6 7 8 ## S3 method for class 'mlm' influence(model, do.coef = TRUE, m = 1, ...) ## S3 method for class 'inflmlm' as.data.frame(x, ..., FUN = det, funnames = TRUE) ## S3 method for class 'inflmlm' print(x, digits = max(3, getOption("digits") - 4), FUN = det, ...) 

## Arguments

 model An mlm object, as returned by lm do.coef logical. Should the coefficients be returned in the inflmlm object? m Size of the subsets for deletion diagnostics x An inflmlm object, 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. funnames logical. Should the FUN name be prepended to the statistics when creating a data frame? ... Other arguments passed to methods digits Number of digits for the print method

## Details

influence.mlm is a simple wrapper for the computational function, mlm.influence designed to provide an S3 method for class "mlm" objects.

There are still infelicities in the methods for the m>1 case in the current implementation. In particular, for m>1, you must call influence.mlm directly, rather than using the S3 generic influence().

## Value

influence.mlm returns an S3 object of class inflmlm, a list with the following components

 m Deletion subset size H Hat values, H_I. If m=1, a vector of diagonal entries of the ‘hat’ matrix. Otherwise, a list of m \times m matrices corresponding to the subsets. Q Residuals, Q_I. CookD Cook's distance values L Leverage components R Residual components subsets Indices of the observations in the subsets of size m labels Observation labels call Model call for the mlm object Beta Deletion regression coefficients– included if do.coef=TRUE

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.

influencePlot.mlm, mlm.influence
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 # Rohwer data Rohwer2 <- subset(Rohwer, subset=group==2) rownames(Rohwer2)<- 1:nrow(Rohwer2) Rohwer.mod <- lm(cbind(SAT, PPVT, Raven) ~ n+s+ns+na+ss, data=Rohwer2) # m=1 diagnostics influence(Rohwer.mod) # try an m=2 case res2 <- influence.mlm(Rohwer.mod, m=2, do.coef=FALSE) res2.df <- as.data.frame(res2) head(res2.df) scatterplotMatrix(log(res2.df)) influencePlot(Rohwer.mod, id.n=4, type="cookd") # Sake data Sake.mod <- lm(cbind(taste,smell) ~ ., data=Sake) influence(Sake.mod) influencePlot(Sake.mod, id.n=3, type="cookd")