VGAM (version 1.1-13)

betabinomial.rho: Beta-binomial Distribution Family Function (with known rho)

Description

Fits a beta-binomial distribution by maximum likelihood estimation, where the correlation coefficient rho is inputted. The parameter estimated is the mean.

Usage

betabinomial.rho(lmu = "logitlink", imethod = 1, ishrinkage = 0.95)

Value

Same as betabinomial.

Arguments

lmu, imethod, ishrinkage

Same as betabinomial.

Author

T. W. Yee

Details

This family function conducts a logistic-like regression where the correlation parameter \(\rho\) of a betabinomial distribution is inputted by the user. The family function is somewhat like a simplified betabinomial. The argument form2 (see vglm) is used to input the \(\rho\) values, which must lie in \([0, 1]\).

The default model has \(\eta_1 = logit(\mu)\).

See Also

betabinomial, extbetabinomial, betabinomialff, Betabinom, vglm, binomialff, betaff.

Examples

if (FALSE) {
# Example 1
nn <- 10000; NN <- 100
bdata <- data.frame(N = NN, x2 = rnorm(nn),
                    x3 = rnorm(nn))
bdata <-
    transform(bdata,
              mu1  = logitlink(-0.5, inverse = TRUE),
              rho1 = logitlink( 0.5, inverse = TRUE),
              mu2  = logitlink(-0.5 + x2, inverse = TRUE),
              rho2 = logitlink(-0.5 + x3, inverse = TRUE))
bdata <- transform(bdata,
         y1 = rbetabinom(nn, size = N, prob = mu1, rho = rho1),
         y2 = rbetabinom(nn, size = N, prob = mu2, rho = rho2))
fit1 <- vglm(cbind(y1, N - y1) ~ 1, betabinomial.rho,
         form2 = ~ rho1, crit = "c", bdata, trace = TRUE)
coef(fit1, matrix = TRUE)
head(fit1@extra$rho)
max(abs(fitted(fit1) - with(bdata, mu1)))  # Should be 0

# Example 2
fit2 <- vglm(cbind(y2, N - y2) ~ x2, form2 = ~ rho2,
         betabinomial.rho, crit = "c",
         bdata, trace = TRUE)
coef(fit2, matrix = TRUE)
max(abs(fit2@extra$rho - with(bdata, rho2)))  # Should be 0
max(abs(fitted(fit2) - with(bdata, mu2)))  # Should be 0
}