Negative Binomial-Ordinal Link Function
Computes the negative binomial-ordinal transformation, including its inverse and the first two derivatives.
nbordlink(theta, cutpoint = NULL, k = NULL,
inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)theta |
Numeric or character. See below for further details. |
cutpoint, k |
Here, |
inverse, deriv, short, tag |
Details at |
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.
See Links for general information about VGAM
link functions.
See Yee (2018) for details.
Numerical values of theta too close to 0 or 1 or out of range
result in large positive or negative values, or maybe 0 depending on
the arguments.
Although measures have been taken to handle cases where
theta is too close to 1 or 0,
numerical instabilities may still arise.
In terms of the threshold approach with cumulative probabilities for
an ordinal response this link function corresponds to the negative
binomial distribution (see negbinomial) that has been
recorded as an ordinal response using known cutpoints.
Thomas W. Yee
Yee, T. W. (2020). Ordinal ordination with normalizing link functions for count data, (in preparation).
Links,
negbinomial,
pordlink,
gordlink,
nbord2link,
cumulative,
CommonVGAMffArguments.
## Not run:
nbordlink("p", cutpoint = 2, k = 1, short = FALSE)
nbordlink("p", cutpoint = 2, k = 1, tag = TRUE)
p <- seq(0.02, 0.98, by = 0.01)
y <- nbordlink(p,cutpoint = 2, k = 1)
y. <- nbordlink(p,cutpoint = 2, k = 1, deriv = 1)
max(abs(nbordlink(y,cutpoint = 2, k = 1, inv = TRUE) - p)) # Should be 0
#\ dontrun{ par(mfrow = c(2, 1), las = 1)
#plot(p, y, type = "l", col = "blue", main = "nbordlink()")
#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)
#\ dontrun{ plot(x2, x3, col = cuty, pch = as.character(cuty)) }
table(cuty) / sum(table(cuty))
fit <- vglm(cuty ~ x2 + x3, trace = TRUE,
cumulative(reverse = TRUE, multiple.responses = TRUE,
parallel = TRUE,
link = nbordlink(cutpoint = cutpoints[2:3], k = k)))
head(depvar(fit))
head(fitted(fit))
head(predict(fit))
coef(fit)
coef(fit, matrix = TRUE)
constraints(fit)
fit@misc
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