betabinomial.rho {VGAM} | R Documentation |
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)
Arguments
lmu , imethod , ishrinkage |
Same as |
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)
.
Value
Same as betabinomial
.
Author(s)
T. W. Yee
See Also
betabinomial
,
extbetabinomial
,
betabinomialff
,
Betabinom
,
vglm
,
binomialff
,
betaff
.
Examples
## Not run:
# 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
## End(Not run)
[Package VGAM version 1.1-13 Index]