| bistudentt {VGAM} | R Documentation |
Bivariate Student-t Family Function
Description
Estimate the degrees of freedom and correlation parameters of the (bivariate) Student-t distribution by maximum likelihood estimation.
Usage
bistudentt(ldf = "logloglink", lrho = "rhobitlink",
idf = NULL, irho = NULL, imethod = 1,
parallel = FALSE, zero = "rho")
Arguments
ldf, lrho, idf, irho, imethod |
Details at |
parallel, zero |
Details at |
Details
The density function is
f(y_1, y_2; \nu, \rho) =
\frac{1}{2\pi\sqrt{1-\rho^2}}
(1 + (y_1^2 + y_2^2 -
2\rho y_1 y_2) / (\nu (1-\rho^2)))^{-(\nu+2)/2}
for -1 < \rho < 1,
and real y_1 and y_2.
This VGAM family function can handle multiple responses, for example, a six-column matrix where the first 2 columns is the first out of three responses, the next 2 columns being the next response, etc.
Value
An object of class "vglmff"
(see vglmff-class).
The object is used by modelling functions
such as vglm
and vgam.
Warning
The working weight matrices have not been fully checked.
Note
The response matrix must have a multiple of two-columns. Currently, the fitted value is a matrix with the same number of columns and values equal to 0.0.
Author(s)
T. W. Yee, with help from Thibault Vatter.
References
Schepsmeier, U. and Stober, J. (2014). Derivatives and Fisher information of bivariate copulas. Statistical Papers 55, 525–542.
See Also
Examples
nn <- 1000
mydof <- logloglink(1, inverse = TRUE)
ymat <- cbind(rt(nn, df = mydof), rt(nn, df = mydof))
bdata <- data.frame(y1 = ymat[, 1], y2 = ymat[, 2],
y3 = ymat[, 1], y4 = ymat[, 2],
x2 = runif(nn))
summary(bdata)
## Not run: plot(ymat, col = "blue")
fit1 <- # 2 responses, e.g., (y1,y2) is the 1st
vglm(cbind(y1, y2, y3, y4) ~ 1,
bistudentt, # crit = "coef", # Sometimes a good idea
data = bdata, trace = TRUE)
coef(fit1, matrix = TRUE)
Coef(fit1)
head(fitted(fit1))
summary(fit1)