LL.Regression.Binary {BinaryEPPM}

Function called by optim to calculate the log likelihood from the probabilities and hence perform the fitting of regression models to the binary data.

Description

Fits specified regression models to the data.

Usage

LL.Regression.Binary(parameter,model.type,model.name,link,ntrials,nsuccess,
                     covariates.matrix.p,covariates.matrix.scalef,
                     offset.p,offset.scalef,weights,grad.method)

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 linear predictor functions to the probability of a success 'p' as in Faddy and Smith (2012). The 'p and scale-factor' value fits linear predictor functions to both the 'p' and the scale-factor. The default is 'p and scale-factor'.

model.name

If model.type is 'p only' the model being fitted is one of the four 'binomial', 'EPPM extended binomial', 'beta binomial' or 'correlated binomial'. If model.type is 'p and scale-factor' the model being fitted is one of the three 'EPPM extended binomial', 'beta binomial' or 'correlated binomial'. Information about these models is given in Faddy and Smith (2012). The default is 'EPPM extended 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

A vector length 'n+1' representing the number of trials 'n' i.e., a vector with all elements equal to 'n'.

nsuccess

A vector representing the frequency distribution of the binomial distribution for fixed number of trials 'n'.

covariates.matrix.p

A matrix of covariates for the mean where rows are the number of values in list.binary 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 variance where rows are the number of values in list.binary 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 the probability of success p. The default is a vector of ones.

offset.scalef

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

weights

A vector or list of weights for the modeling of probability of success. The default is a vector of ones.

grad.method

Numerical method used to calculate gradients either simple or Richardson. The default is simple.

Value

The log likelihood is returned.

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)
nsuccess <- list(c(rep(0,5),352,479,530,291,101,17))
ntrials  <- list(c(rep(10,11)))
parameter <- c(0.06363398,-0.47085362)
LL.Regression.Binary(parameter, model.type = "p and scale-factor",
            model.name = "EPPM extended binomial", link, ntrials, nsuccess, 
            covariates.matrix.p = matrix(c(1), nrow=1),
            covariates.matrix.scalef = matrix(c(1), nrow=1),
            offset.p = c(0), offset.scalef = c(0),
            weights = list(c(rep(1,11))))