VGAM (version 0.8-1)

nbolf: Negative Binomial-Ordinal Link Function

Description

Computes the negative binomial-ordinal transformation, including its inverse and the first two derivatives.

Usage

nbolf(theta, earg = stop("'earg' must be given"), inverse = FALSE,
      deriv = 0, short = TRUE, tag = FALSE)

Arguments

theta

Numeric or character. See below for further details.

earg

Extra argument for passing in additional information. This must be list with components cutpoint and k. Here, k is the $k$ parameter associated with the negative binomial distribution; see

inverse

Logical. If TRUE the inverse function is computed.

deriv

Order of the derivative. Integer with value 0, 1 or 2.

short

Used for labelling the blurb slot of a vglmff-class object.

tag

Used for labelling the linear/additive predictor in the initialize slot of a vglmff-class object. Contains a little more information if TRUE.

Value

• See Yee (2007) for details.

Warning

Prediction may not work on vglm or vgam etc. objects if this link function is used.

Details

The negative binomial-ordinal link function (NBOLF) can be applied to a parameter lying in the unit interval. Its purpose is to link cumulative probabilities associated with an ordinal response coming from an underlying negative binomial distribution.

The arguments short and tag are used only if theta is character.

See Links for general information about VGAM link functions.

References

Yee, T. W. (2007) Ordinal ordination with normalizing link functions for count data, (in preparation).

See Also

Links, negbinomial, polf, golf, nbolf2, cumulative.

Examples

earg = list(cutpoint=2, k=1)
nbolf("p", earg=earg, short=FALSE)
nbolf("p", earg=earg, tag=TRUE)

p = seq(0.02, 0.98, by=0.01)
y = nbolf(p, earg=earg)
y. = nbolf(p, earg=earg, deriv=1)
max(abs(nbolf(y, earg=earg, inv=TRUE) - p)) # Should be 0

par(mfrow=c(2,1), las=1)
plot(p, y, type="l", col="blue", main="nbolf()")
abline(h=0, v=0.5, col="red", lty="dashed")

plot(p, y., type="l", col="blue",
     main="(Reciprocal of) first NBOLF derivative")

# Another example
nn = 1000
x2 = sort(runif(nn))
x3 = runif(nn)
mymu = exp( 3 + 1 * x2 - 2 * x3)
k = 4
y1 = rnbinom(nn, mu=mymu, size=k)
cutpoints = c(-Inf, 10, 20, Inf)
cuty = Cut(y1, breaks=cutpoints)
plot(x2, x3, col=cuty, pch=as.character(cuty))
table(cuty) / sum(table(cuty))
fit = vglm(cuty ~ x2 + x3, fam = cumulative(link="nbolf",
           reverse=TRUE, parallel=TRUE, intercept.apply=TRUE,
           mv=TRUE, earg=list(cutpoint=cutpoints[2:3], k=k)),
           trace=TRUE)
head(fit@y)
head(fitted(fit))
head(predict(fit))
coef(fit)
coef(fit, matrix=TRUE)
constraints(fit)
fit@misc$earg