Jtr {mvinfluence}R Documentation

General Classes of Influence Measures

Description

These functions implement the general classes of influence measures for multivariate regression models defined in Barrett and Ling (1992), Eqn 2.3, 2.4, as shown in their Table 1.

Usage

Jtr(H, Q, a, b, f)

Jdet(H, Q, a, b, f)

COOKD(H, Q, n, p, r, m)

DFFITS(H, Q, n, p, r, m)

COVRATIO(H, Q, n, p, r, m)

Arguments

H

a scalar or m×mm \times m matrix giving the hat values for subset II

Q

a scalar or m×mm \times m matrix giving the residual values for subset II

a

the aa parameter for the JdetJ^{det} and JtrJ^{tr} classes

b

the bb parameter for the JdetJ^{det} and JtrJ^{tr} classes

f

scaling factor for the JdetJ^{det} and JtrJ^{tr} classes

n

sample size

p

number of predictor variables

r

number of response variables

m

deletion subset size

Details

There are two classes of functions, denoted JIdetJ_I^{det} and JItrJ_I^{tr}, with parameters n,p,qn, p, q of the data, mm of the subset size and aa and bb which define powers of terms in the formulas, typically in the set -2, -1, 0.

They are defined in terms of the submatrices for a deleted index subset II,

HI=XI(XTX)1XIH_I = X_I (X^T X)^{-1} X_I

QI=EI(ETE)1EIQ_I = E_I (E^T E)^{-1} E_I

corresponding to the hat and residual matrices in univariate models.

For subset size m=1m = 1 these evaluate to scalar equivalents of hat values and studentized residuals.

For subset size m>1m > 1 these are m×mm \times m matrices and functions in the JdetJ^{det} class use HI|H_I| and QI|Q_I|, while those in the JtrJ^{tr} class use tr(HI)tr(H_I) and tr(QI)tr(Q_I).

The functions COOKD, COVRATIO, and DFFITS implement some of the standard influence measures in these terms for the general cases of multivariate linear models and deletion of subsets of size m>1, but they have not yet been incorporated into our main functions mlm.influence and influence.mlm.

Value

The scalar result of the computation.

Author(s)

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.


[Package mvinfluence version 0.9.0 Index]