biplackettcop {VGAM} | R Documentation |
Plackett's Bivariate Copula Family Function
Description
Estimate the association parameter of Plackett's bivariate distribution (copula) by maximum likelihood estimation.
Usage
biplackettcop(link = "loglink", ioratio = NULL, imethod = 1,
nsimEIM = 200)
Arguments
link |
Link function applied to the (positive) odds ratio |
ioratio |
Numeric. Optional initial value for |
imethod , nsimEIM |
Details
The defining equation is
where
is the cumulative distribution function.
The density function is
for .
Some writers call
the cross product ratio
but it is called the odds ratio here.
The support of the function is the unit square.
The marginal distributions here are the standard uniform although
it is commonly generalized to other distributions.
If then
,
i.e., independence.
As the odds ratio tends to infinity one has
.
As the odds ratio tends to 0 one has
.
Fisher scoring is implemented using rbiplackcop
.
Convergence is often quite slow.
Value
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions
such as vglm
and vgam
.
Note
The response must be a two-column matrix. Currently, the fitted value is a 2-column matrix with 0.5 values because the marginal distributions correspond to a standard uniform distribution.
Author(s)
T. W. Yee
References
Plackett, R. L. (1965). A class of bivariate distributions. Journal of the American Statistical Association, 60, 516–522.
See Also
Examples
## Not run:
ymat <- rbiplackcop(n = 2000, oratio = exp(2))
plot(ymat, col = "blue")
fit <- vglm(ymat ~ 1, fam = biplackettcop, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit)
vcov(fit)
head(fitted(fit))
summary(fit)
## End(Not run)