R: Bivariate Student-t Family Function

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 = "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`.

### Details

The density function is

f(y1, y2; nu, rho) = (1/(2*pi*sqrt(1-ρ^2))) * (1 + y1^2 + y_2^2 - 2*rho*y1*y2) / (nu*(1-rho^2))^((ν+2)/2)

for -1 < rho < 1, and real y1 and y2.

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. (2013) Derivatives and Fisher information of bivariate copulas. Statistical Papers.

### See Also

`dbistudentt`, `binormal`, `pt`.

### Examples

    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)
    ## Not run:  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)

[Package VGAM version 1.0-3 Index]