Bivariate Student-t Family Function
Estimate the degrees of freedom and correlation parameters of the (bivariate) Student-t distribution by maximum likelihood estimation.
bistudentt(ldf = "logloglink", lrho = "rhobitlink",
idf = NULL, irho = NULL, imethod = 1,
parallel = FALSE, zero = "rho")ldf, lrho, idf, irho, imethod |
Details at |
parallel, zero |
Details at |
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.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm
and vgam.
The working weight matrices have not been fully checked.
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.
T. W. Yee, with help from Thibault Vatter.
Schepsmeier, U. and Stober, J. (2014). Derivatives and Fisher information of bivariate copulas. Statistical Papers 55, 525–542.
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.