R: Hat Values and Regression Deletion Diagnostics

hatvalues {VGAM} | R Documentation

## Hat Values and Regression Deletion Diagnostics

### Description

When complete, a suite of functions that can be used to compute some of the regression (leave-one-out deletion) diagnostics, for the VGLM class.

### Usage

    hatvalues(model, ...)
    hatvaluesvlm(model, type = c("diagonal", "matrix", "centralBlocks"), ...)
    hatplot(model, ...)
    hatplot.vlm(model, multiplier = c(2, 3), lty = "dashed",
                xlab = "Observation", ylab = "Hat values", ylim = NULL, ...)
    dfbetavlm(model, maxit.new = 1,
              trace.new = FALSE,
              smallno = 1.0e-8, ...)

### Arguments

`model` | an R object, typically returned by `vglm`.
`type` | Character. The default is the first choice, which is a nM x nM matrix. If `type = "matrix"` then the entire hat matrix is returned. If `type = "centralBlocks"` then n central M x M block matrices, in matrix-band format.

`multiplier` | Numeric, the multiplier. The usual rule-of-thumb is that values greater than two or three times the average leverage (at least for the linear model) should be checked.
`lty, xlab, ylab, ylim` | Graphical parameters, see `par` etc. The default of `ylim` is `c(0, max(hatvalues(model)))` which means that if the horizontal dashed lines cannot be seen then there are no particularly influential observations.
`maxit.new, trace.new, smallno` | Having `maxit.new = 1` will give a one IRLS step approximation from the ordinary solution (and no warnings!). Else having `maxit.new = 10`, say, should usually mean convergence will occur for all observations when they are removed one-at-a-time. Else having `maxit.new = 2`, say, should usually mean some lack of convergence will occur when observations are removed one-at-a-time. Setting `trace.new = TRUE` will produce some running output at each IRLS iteration and for each individual row of the model matrix. The argument `smallno` multiplies each value of the original prior weight (often unity); setting it identically to zero will result in an error, but setting a very small value effectively removes that observation.

`...` | further arguments, for example, graphical parameters for `hatplot.vlm()`.

### Details

The invocation `hatvalues(vglmObject)` should return a n x M matrix of the diagonal elements of the hat (projection) matrix of a `vglm` object. To do this, the QR decomposition of the object is retrieved or reconstructed, and then straightforward calculations are performed.

The invocation `hatplot(vglmObject)` should plot the diagonal of the hat matrix for each of the M linear/additive predictors. By default, two horizontal dashed lines are added; hat values higher than these ought to be checked.

### Note

It is hoped, soon, that the full suite of functions described at `influence.measures` will be written for VGLMs. This will enable general regression deletion diagnostics to be available for the entire VGLM class.

### Author(s)

T. W. Yee.

### See Also

`vglm`, `cumulative`, `influence.measures`.

### Examples

    # Proportional odds model, p.179, in McCullagh and Nelder (1989)
    pneumo <- transform(pneumo, let = log(exposure.time))
    fit <- vglm(cbind(normal, mild, severe) ~ let, cumulative, data = pneumo)
    hatvalues(fit)  # n x M matrix, with positive values
    all.equal(sum(hatvalues(fit)), fit@rank)  # Should be TRUE
    ## Not run:  par(mfrow = c(1, 2))
    hatplot(fit, ylim = c(0, 1), las = 1, col = "blue")
    ## End(Not run)

[Package VGAM version 1.0-3 Index]