VLMC (version 1.3-13)

residuals.vlmc: Compute Residuals of a Fitted VLMC Object

Description

Compute residuals of a fitted vlmc object.

This is yet a matter of research and may change in the future.

Usage

## S3 method for class 'vlmc':
residuals(object,
        type = c("classwise",
                 "deviance", "pearson", "working", "response", "partial"),
        y = object$y, ...)

Arguments

object

typically the result of vlmc(..).

type

The type of residuals to compute, defaults to "classwise" which returns an $n \times m$ matrix, see below. The other types only make sense when the discrete values of y are ordered which always includes the binary case

y

discrete time series with respect to which the residuals are to be computed.

...

possibly further arguments (none at the moment).

Value

• If type = "classwise" (the default), a numeric matrix of dimension $n \times m$ of values $I_{i,j} - p_{i,j}$ where the indicator $I_{i,j}$ is 1 iff y[i] == a[j] and a is the alphabet (or levels) of y, and $p_{i,j}$ are the elements of the estimated (1-step ahead) predicted probabilities, p <- predict(object). Hence, for each $i$, the only positive residual stands for the observed class.

  For all other types, the result is a numeric vector of the length of the original time-series (with first element NA). For type = "deviance", $r_i = \pm\sqrt{-2\log(P_i)}$ where $P_i$ is the predicted probability for the i-th observation which is the same as $p_{i,y_i}$ above (now assuming $y_i \in {1,2,\dots,m$). The sum of the squared deviance residuals is the deviance of the fitted model.

See Also

vlmc,deviance.vlmc, and RCplot for a novel residual plot.

Examples

example(vlmc)
rp <- residuals(vlmc.pres)
stopifnot(all(abs(apply(rp[-1,],1,sum)) < 1e-15))
matplot(seq(presidents), rp, ylab = "residuals", type="l")
## ``Tukey-Anscombe'' (the following is first stab at plot method):
matplot(fitted(vlmc.pres), rp, ylab = "residuals", xaxt = "n",
        type="b", pch=vlmc.pres$alpha)
axis(1, at = 0:(vlmc.pres$alpha.len-1),
     labels = strsplit(vlmc.pres$alpha,"")[[1]])


summary(rd <- residuals(vlmc.pres, type = "dev"))
rd[1:7]
## sum of squared dev.residuals === deviance :
all.equal(sum(rd[-1] ^ 2),
          deviance(vlmc.pres))
stopifnot(all.equal(sum(rd[-1] ^ 2),
                    deviance(vlmc.pres),tol=1e-12))