Regression Deletion Diagnostics for Multivariate Linear Models

The functions cooks.distance.mlm and hatvalues.mlm are designed as extractor functions for regression deletion diagnostics for multivariate linear models following Barrett & Ling (1992). These 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

# S3 method for class 'mlm'
cooks.distance(model, infl = mlm.influence(model, do.coef = FALSE), ...)

# S3 method for class 'mlm'
hatvalues(model, m = 1, infl, ...)

Arguments

model: A mlm object, as returned by lm with a multivariate response
do.coef: logical. Should the coefficients be returned in the inflmlm object?
m: Size of the subsets for deletion diagnostics
infl: An influence structure, of class inflmlm as returned by mlm.influence
...: Other arguments, passed on

Value

When m=1, these functions return a vector, corresponding to the observations in the data set.

When m>1, they return a list of \(m \times m\) matrices, corresponding to deletion of subsets of size m.

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.

Author

Michael Friendly

Examples

data(Rohwer, package="heplots")
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)

hatvalues(Rohwer.mod)
#>          1          2          3          4          5          6          7 
#> 0.16700926 0.21845327 0.14173469 0.07314341 0.56821462 0.15432157 0.04530969 
#>          8          9         10         11         12         13         14 
#> 0.17661104 0.05131298 0.45161152 0.14542776 0.17050399 0.10374592 0.12649927 
#>         15         16         17         18         19         20         21 
#> 0.33246744 0.33183461 0.17320579 0.26353864 0.29835817 0.07880597 0.14023750 
#>         22         23         24         25         26         27         28 
#> 0.19380286 0.04455330 0.20641708 0.15712604 0.15333879 0.36726467 0.11189754 
#>         29         30         31         32 
#> 0.30426999 0.08655434 0.08921878 0.07320950 
cooks.distance(Rohwer.mod)
#>           1           2           3           4           5           6 
#> 0.110668789 0.035758983 0.074110633 0.006454502 0.846717339 0.014584590 
#>           7           8           9          10          11          12 
#> 0.025295531 0.147676200 0.040403408 0.063391985 0.045680183 0.116293594 
#>          13          14          15          16          17          18 
#> 0.042671229 0.164273594 0.015190817 0.118323491 0.144482540 0.056707069 
#>          19          20          21          22          23          24 
#> 0.173206386 0.037332773 0.151642786 0.040245143 0.030356681 0.072943655 
#>          25          26          27          28          29          30 
#> 0.260083518 0.042608984 0.338661595 0.034223968 0.302596343 0.045051960 
#>          31          32 
#> 0.097583942 0.055032090