nnnegbin {addreg}

ECME Algorithm for Additive Negative Binomial 1 Model

Description

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.

Usage

nnnegbin(y, x, standard, offset, start, control = addreg.control(),
         accelerate = c("em", "squarem", "pem", "qn"),
         control.method = list())

Arguments

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 scale, and must be > 1. The remaining elements are for the additive mean parameters, and must be greater than control$bound.tol.

control

an addreg.control object, which controls the fitting process.

accelerate

a character string that determines the acceleration algorithm to be used, (partially) matching one of "em" (no acceleration – the default), "squarem", "pem" or "qn". See turboem for further details. Note that "decme" is not permitted.

control.method

a list of control parameters for the acceleration algorithm. See turboem for details of the parameters that apply to each algorithm. If not specified, the defaults are used.

Details

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.

Value

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 y - fitted.values

fitted.values

the fitted mean values.

rank

the number of parameters in the model (named “rank" for compatibility — we assume that models have full rank)

family

included for compatibility — will always be negbin1(identity).

linear.predictors

included for compatibility — same as fitted.values (as this is an identity-link model).

deviance

up to a constant, minus twice the maximised log-likelihood (with respect to a saturated NB1 model with the same scale).

aic

a version of Akaike's An Information Criterion, minus twice the maximised log-likelihood plus twice the number of parameters.

aic.c

a small-sample corrected version of Akaike's An Information Criterion (Hurvich, Simonoff and Tsai, 1998).

null.deviance

the deviance for the null model, comparable with deviance. The null model will include the offset and an intercept.

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 standard vector passed to this function.

df.residual

the residual degrees of freedom.

df.null

the residual degrees of freedom for the null model.

y

the y vector used.

converged

logical. Did the ECME algorithm converge (according to conv.test)?

boundary

logical. Is the MLE on the boundary of the parameter space — i.e. are any of the coefficients < control$bound.tol?

loglik

the maximised log-likelihood.

nn.design

the non-negative x matrix used.

Author(s)

Mark W. Donoghoe [e-mail].

References

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.