nbordlink: Negative Binomial-Ordinal Link Function

Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

View source: R/links.q

Description

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

Usage

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nbordlink(theta, cutpoint = NULL, k = NULL,
          inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)

Arguments

theta

Numeric or character. See below for further details.

cutpoint, k

Here, k is the k parameter associated with the negative binomial distribution; see negbinomial. The cutpoints should be non-negative integers. If nbordlink() is used as the link function in cumulative then one should choose reverse = TRUE, parallel = TRUE.

inverse, deriv, short, tag

Details at Links.

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.

See Links for general information about VGAM link functions.

Value

See Yee (2018) for details.

Warning

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

Note

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.

Author(s)

Thomas W. Yee

References

Yee, T. W. (2020). Ordinal ordination with normalizing link functions for count data, (in preparation).

See Also

Links, negbinomial, pordlink, gordlink, nbord2link, cumulative, CommonVGAMffArguments.

Examples

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## 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

## End(Not run)

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.