bistudentt: Bivariate Student-t Family Function

In VGAM: Vector Generalized Linear and Additive Models

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 CommonVGAMffArguments. See Links for more link function choices.
parallel, zero	Details at CommonVGAMffArguments.

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

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)
## 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)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.