addreg-package {addreg} | R Documentation |

## Additive Regression for Discrete Data

### Description

Methods for fitting identity-link GLMs and GAMs to discrete data, using EM-type algorithms with more stable convergence properties than standard methods.

### Details

Package: | addreg |

Type: | Package |

Version: | 3.0 |

Date: | 2017-12-20 |

License: | GPL (>= 2) |

This package provides methods to fit generalised linear models (GLMs) and generalised additive models (GAMs) with identity link functions to discrete data using binomial, Poisson and negative binomial models. It is planned that future versions will incorporate other types of discrete data models, such as multinomial regression.

The package has two primary functions: `addreg`

and `addreg.smooth`

,
together with various supporting functions. It is useful in two main situations. The first is
when a standard GLM routine, such as `glm`

, fails to converge with such a model.
The second is when a flexible semi-parametric component is desired in these models. One of the
main purposes of this package is to provide parametric and semi-parametric adjustment of risk
differences and rate differences.

Two approaches based on the EM algorithm can be used. These methods accommodate the required parameter constraints and are more stable than iteratively reweighted least squares. In a combinatorial EM algorithm (Marschner, 2014), a collection of restricted parameter spaces is defined which covers the full parameter space, and the EM algorithm is applied within each restricted parameter space in order to find a collection of restricted maxima of the log-likelihood function, from which can be obtained the global maximum over the full parameter space.

In the expanded EM approach, additional parameters are added to the model, and an EM algorithm finds the MLE of this overparameterised model by imposing constraints on each individual parameter. This requires a single application of the EM algorithm.

In either case, the EM algorithm may be accelerated by using the capabilities of the turboEM package.

### Author(s)

Mark W. Donoghoe markdonoghoe@gmail.com

Maintainer: Mark W. Donoghoe markdonoghoe@gmail.com

### References

Donoghoe, M. W. and I. C. Marschner (2014). Stable computational methods
for additive binomial models with application to adjusted risk differences.
*Computational Statistics and Data Analysis* 80: 184–196.

Donoghoe, M. W. and I. C. Marschner (2015). Flexible regression models for rate
differences, risk differences and relative risks. *International Journal of
Biostatistics* 11(1): 91–108.

Donoghoe, M. W. and I. C. Marschner (2016). Estimation of adjusted rate
differences using additive negative binomial regression. *Statistics
in Medicine* 35(18): 3166–3178.

Marschner, I. C. (2010). Stable computation of maximum likelihood estimates
in identity link Poisson regression. *Journal of Computational and
Graphical Statistics* 19(3): 666–683.

Marschner, I. C. (2014). Combinatorial EM algorithms.
*Statistics and Computing* 24(6): 921–940.

### See Also

### Examples

```
## For examples, see example(addreg) and example(addreg.smooth)
```

*addreg*version 3.0 Index]