VGAM (version 1.1-9)

bistudentt: 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")

Value

An object of class "vglmff"

(see vglmff-class). The object is used by modelling functions such as vglm

and vgam.

Arguments

ldf, lrho, idf, irho, imethod

Details at CommonVGAMffArguments. See Links for more link function choices.

parallel, zero

Details at CommonVGAMffArguments.

Author

T. W. Yee, with help from Thibault Vatter.

Warning

The working weight matrices have not been fully checked.

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.

References

Schepsmeier, U. and Stober, J. (2014). Derivatives and Fisher information of bivariate copulas. Statistical Papers 55, 525--542.

See Also

dbistudentt, binormal, pt.

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)
if (FALSE)  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)