Model.GB {BinaryEPPM} R Documentation

## Probabilities for binomial and generalized binomial distributions given p's and b.

### Description

Calculates the probabilities for binomial and generalized binomial given values for p's and b.

### Usage

```Model.GB(parameter, model.name, link, ntrials, covariates.matrix.p,
offset.p = c(rep(0, length(ntrials))))
```

### Arguments

 `parameter` A vector of the parameters of the model which is set to initial estimates on function call. `model.name` The model being fitted is one of the two 'binomial' or 'generalized 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. `offset.p` An offset vector for p. The default is a vector of ones.

### Value

List of arguments input together with a list of probabilities vectors and a data frame of values of a and b of Equation (5) of Faddy and Smith (2012).

 `model` The model is either 'binomial' or 'generalized binomial'. `link` The link is either 'logit' or 'cloglog'. `parameter` A vector of the parameters of the model which is set to initial estimates on function call. `probabilities` A list of the vectors of probabilities of the model. `Dparameters` A data frame of values of a and b of Equation (5) of Faddy and Smith (2012).

### Author(s)

David M. Smith <smithdm1@us.ibm.com>

### 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'