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 = "loglog", lrho = "rhobit",
           idf = NULL, irho = NULL, imethod = 1,
           parallel = FALSE, zero = "rho")

Arguments

ldf, lrho, idf, irho, imethod

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

parallel, zero

Details at CommonVGAMffArguments.

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.

Details

The density function is

f (y_{1}, y_{2}; ν, ρ) = \frac{1}{2 π \sqrt{1 - ρ^{2}}} (1 + y_{1}^{2} + y_{2}^{2} - 2 ρ y_{1} y_{2}) / (ν (1 - ρ^{2}))^{(ν + 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. (2013) Derivatives and Fisher information of bivariate copulas. Statistical Papers.

Examples

Run this code

nn <- 1000
mydof <- loglog(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)
plot(ymat, col = "blue")
fit1 <- vglm(cbind(y1, y2, y3, y4) ~ 1,  # 2 responses, e.g., (y1,y2) is the 1st
             fam = bistudentt,  # crit = "coef",  # Sometimes a good idea
             data = bdata, trace = TRUE)

coef(fit1, matrix = TRUE)
Coef(fit1)
head(fitted(fit1))
summary(fit1)

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