bistudentt: Bivariate Student-t Family Function

Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

View source: R/family.bivariate.R

Description

Estimate the degrees of freedom and correlation parameters of the (bivariate) Student-t distribution by maximum likelihood estimation.

Usage

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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(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. (2014). Derivatives and Fisher information of bivariate copulas. Statistical Papers 55, 525–542.

See Also

dbistudentt, binormal, pt.

Examples

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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 <- 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)

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.