seq2binomial {VGAM}R Documentation

The Two-stage Sequential Binomial Distribution Family Function

Description

Estimation of the probabilities of a two-stage binomial distribution.

Usage

seq2binomial(lprob1 = "logit", lprob2 = "logit", eprob1 = list(),
             eprob2 = list(), iprob1 = NULL, iprob2 = NULL, zero = NULL)

Arguments

lprob1, lprob2 Parameter link functions applied to the two probabilities, called p and q below. See Links for more choices.
eprob1, eprob2 Lists. Extra arguments for the links. See earg in Links for general information.
iprob1, iprob2 Optional initial value for the first and second probabilities respectively. A NULL means a value is obtained in the initialize slot.
zero An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. If used, the value must be from the set {1,2} which correspond to the first and second probabilities respectively. A NULL value means none.

Details

This VGAM family function fits the model described by Crowder and Sweeting (1989) which is described as follows. Each of m spores has a probability p of germinating. Of the y1 spores that germinate, each has a probability q of bending in a particular direction. Let y2 be the number that bend in the specified direction. The probability model for this data is P(y1,y2) =

{choose(m,y1)} p^{y1} (1-p)^{m-y1} {choose(y1,y2)} q^{y2} (1-q)^{y1-y2}

for 0 < p < 1, 0 < q < 1, y1=1,...,m and y2=1,...,y1. Here, p is prob1, q is prob2.

Although the Authors refer to this as the bivariate binomial model, I have named it the (two-stage) sequential binomial model. Fisher scoring is used.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

Note

The response must be a two-column matrix of sample proportions corresponding to y1 and y2. The m values should be inputted with the weights argument of vglm and vgam. The fitted value is a two-column matrix of estimated probabilities p and q.

Author(s)

Thomas W. Yee

References

Crowder, M. and Sweeting, T. (1989). Bayesian inference for a bivariate binomial distribution. Biometrika, 76, 599–603.

See Also

binomialff.

Examples

mvector = round(rnorm(n <- 100, m=10, sd=2))
x = runif(n)
prob1 = logit(+2-x, inverse=TRUE)
prob2 = logit(-2+x, inverse=TRUE)
successes1 = rbinom(n=n, size=mvector, prob=prob1)
successes2 = rbinom(n=n, size=successes1, prob=prob2)
y1 = successes1 / mvector
y2 = successes2 / successes1
fit = vglm(cbind(y1,y2) ~ x, seq2binomial, trace=TRUE, weight=mvector)
coef(fit)
coef(fit, mat=TRUE)
fitted(fit)[1:5,]

[Package VGAM version 0.7-7 Index]