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

View source: R/family.bivariate.R

Estimate the association parameter of Plackett's bivariate distribution (copula) by maximum likelihood estimation.

1 | ```
biplackettcop(link = "loglink", ioratio = NULL, imethod = 1, nsimEIM = 200)
``` |

`link` |
Link function applied to the (positive) odds ratio |

`ioratio` |
Numeric. Optional initial value for |

`imethod, nsimEIM` |
See |

The defining equation is

*
psi = H*(1-y1-y2+H) / ((y1-H)*(y2-H))*

where
*P(Y1 <= y1, Y2 <= y2)=
H(y1,y2)*
is the cumulative distribution function.
The density function is *h(y1,y2) =*

*
psi*[1 + (psi-1)*(y1 + y2 - 2*y1*y2) ] / (
[1 + (psi-1)*(y1 + y2)]^2 -
4*psi*(psi-1)*y1*y2)^(3/2)*

for *psi > 0*.
Some writers call *psi* 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 *psi=1* then
*h(y1,y2) = y1*y2*,
i.e., independence.
As the odds ratio tends to infinity one has *y1=y2*.
As the odds ratio tends to 0 one has *y2=1-y1*.

Fisher scoring is implemented using `rbiplackcop`

.
Convergence is often quite slow.

An object of class `"vglmff"`

(see `vglmff-class`

).
The object is used by modelling functions such as `vglm`

and `vgam`

.

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.

T. W. Yee

Plackett, R. L. (1965).
A class of bivariate distributions.
*Journal of the American Statistical Association*,
**60**, 516–522.

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