Model.Binary {BinaryEPPM}

Function for obtaining output from distributional models.

Description

Produces output of model, parameters and probabilities from the various models.

Usage

Model.Binary(parameter, model.type, model.name, link, ntrials, covariates.matrix.p, 
covariates.matrix.scalef, offset.p, offset.scalef)

Arguments

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

model.type

Takes one of two values i.e. 'p only' or 'p and scale-factor'. The 'p only' value fits a linear predictor function to the parameter p which is the 'm(1)' in equation (6) of Faddy and Smith (2012) divided by 'N'. The 'p and scale-factor' value fits linear predictor functions to both p and the scale-factor.

model.name

If model.type is 'p only' the model being fitted is one of the six 'binomial', 'over-dispersed-one', 'over-dispersed-two', 'EPPM binomial', 'beta binomial' or 'correlated binomial'. If model.type is 'p and scale-factor' the model being fitted is one of the three 'EPPM binomial', 'beta binomial' or 'correlated binomial'.

link

Takes one of nine values i.e., 'logit', 'probit', 'cloglog', 'cauchit', 'log', 'loglog', 'double exponential', 'double reciprocal', 'power logit'. The default is 'cloglog'. The 'power logit' has an attribute of 'power' for which the default is 1 i.e., a logit link.

ntrials

This is a scalar representing the denominator i.e., the length of the probability mass function returned is this scalar + 1.

covariates.matrix.p

A matrix of covariates for p where rows are the number of values in listbinary and columns the covariates. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

covariates.matrix.scalef

A matrix of covariates for the scale-factor where rows are the number of values in listbinary and columns the covariates. The default is a vector of ones. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

offset.p

An offset vector for p. The default is a vector of ones.

offset.scalef

An offset vector for the scale-factor. The default is a vector of ones.

Value

The output from either Model.BCBinProb, Model.GB, Model.Binary, Model.JMVGB, or Model.ODB.

Author(s)

David M. Smith <[e-mail]>

References

Faddy M, Smith D. (2012). Extended Poisson Process Modeling and Analysis of Grouped Binary Data. Biometrical Journal, 54, 426-435. doi:10.1002/bimj.201100214.

Examples

link <- 'cloglog'
attr(link, which="p") <- make.link(link)
parameter <- c(-0.68294630,0.03451481)
names(parameter) <- c('p','rho')
model.type <- 'p and scale-factor'
model.name <- 'correlated binomial'
ntrials    <- list(c(rep(10,11)))
Model.Binary(parameter, model.type, model.name, link, ntrials,
             covariates.matrix.p = matrix(c(1),nrow=1), 
             covariates.matrix.scalef = matrix(c(1),nrow=1),
             offset.p = c(0), offset.scalef = c(0))