Influence Function (S4 generic) of a Fitted Model

Returns a matrix containing the influence function of a fitted model, e.g., a "vglm" object.

Influence(object, ...)
Influence.vglm(object, weighted = TRUE, ...)

Arguments

object

an object, especially that of class "vglm"—see vglm-class. Currently other classes such as "vgam" are not yet implemented.

weighted

Logical. Include the prior weights? Currently only TRUE is accepted. This might change in the future and/or the default value might change.

...

any additional arguments such as to allow or disallow the prior weights.

Value

An n by p.vlm matrix.

Details

Influence functions are useful in fields such as sample survey theory, e.g., survey, svyVGAM. For each \(i=1,\ldots,n\), the formula is approximately \(-I U\) where \(I\) is the weighted Fisher information matrix and U is the \(i\)th score vector.

Warning

This function is currently experimental and defaults may change. Use with caution! The functions here should not be confused with lm.influence.

See also

vglm, vglm-class, survey.

Examples

pneumo <- transform(pneumo, let = log(exposure.time))
fit <- vglm(cbind(normal, mild, severe) ~ let, acat, data = pneumo)
coef(fit)  # 8-vector
#> (Intercept):1 (Intercept):2         let:1         let:2 
#>    -8.9360297    -3.0390622     2.1653729     0.9020936 
Influence(fit)  # 8 x 4
#>   (Intercept):1 (Intercept):2       let:1        let:2
#> 1   -0.73827808    0.35415869  0.20987191 -0.100483419
#> 2   -0.20653006   -0.08847618  0.05691954  0.024135324
#> 3    0.68701036   -0.53528307 -0.17723146  0.138551572
#> 4   -0.14332598    0.72736516  0.03367589 -0.182188428
#> 5   -0.01184705   -0.07833113  0.01542707  0.006407492
#> 6    0.19287499    0.13332817 -0.06828049 -0.045333144
#> 7    0.05572438   -0.15655193 -0.01821525  0.049445161
#> 8    0.16437144   -0.35620972 -0.05216720  0.109465443
all(abs(colSums(Influence(fit))) < 1e-6)  # TRUE
#> [1] TRUE