Description Usage Arguments Details Value Author(s) References

Finds the maximum likelihood estimate of an additive negative binomial (NB1) model using an ECME algorithm, where each of the mean coefficients is restricted to be non-negative.

1 2 3 |

`y` |
non-negative integer response vector. |

`x` |
non-negative covariate matrix. |

`standard` |
standardising vector, where each element is a positive constant that (multiplicatively) standardises the fitted value of the corresponding element of the response vector. The default is a vector of ones. |

`offset` |
non-negative additive offset vector. The default is a vector of zeros. |

`start` |
vector of starting values for the parameter estimates. The last element is
the starting value of the |

`control` |
an |

`accelerate` |
a character string that determines the acceleration
algorithm to be used, (partially) matching one of |

`control.method` |
a list of control parameters for the acceleration algorithm. See |

This is a workhorse function for `addreg`

, and runs the ECME algorithm to find the
constrained non-negative MLE associated with an additive NB1 model.

A list containing the following components

`coefficients` |
the constrained non-negative maximum likelihood estimate of the mean parameters. |

`scale` |
the maximum likelihood estimate of the scale parameter. |

`residuals` |
the residuals at the MLE, that is |

`fitted.values` |
the fitted mean values. |

`rank` |
the number of parameters in the model (named “ |

`family` |
included for compatibility — will always be |

`linear.predictors` |
included for compatibility — same as |

`deviance` |
up to a constant, minus twice the maximised log-likelihood (with respect to
a saturated NB1 model with the same |

`aic` |
a version of Akaike's |

`aic.c` |
a small-sample corrected
version of Akaike's |

`null.deviance` |
the deviance for the null model, comparable with |

`iter` |
the number of iterations of the EM algorithm used. |

`weights` |
included for compatibility — a vector of ones. |

`prior.weights` |
included for compatibility — a vector of ones. |

`standard` |
the |

`df.residual` |
the residual degrees of freedom. |

`df.null` |
the residual degrees of freedom for the null model. |

`y` |
the |

`converged` |
logical. Did the ECME algorithm converge
(according to |

`boundary` |
logical. Is the MLE on the boundary of the parameter
space — i.e. are any of the |

`loglik` |
the maximised log-likelihood. |

`nn.design` |
the non-negative |

Mark W. Donoghoe [email protected].

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.

Hurvich, C. M., J. S. Simonoff and C.-L. Tsai (1998). Smoothing parameter
selection in non-parametric regression using an improved Akaike
information criterion.
*Journal of the Royal Statistical Society: Series B (Statistical Methodology)* 60(2): 271–293.

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