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.
nnnegbin(y, x, standard, offset, start, control = addreg.control(),
accelerate = c("em", "squarem", "pem", "qn"),
control.method = list())non-negative integer response vector.
non-negative covariate matrix.
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.
non-negative additive offset vector. The default is a vector of zeros.
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$bound.tol.
an addreg.control object, which controls the fitting process.
a character string that determines the acceleration
algorithm to be used, (partially) matching one of "em" (no acceleration -- the default),
"squarem", "pem" or "qn". See turboem
for further details. Note that "decme" is not permitted.
a list of control parameters for the acceleration algorithm. See turboem
for details of the parameters that apply to each algorithm. If not specified, the defaults are used.
A list containing the following components
the constrained non-negative maximum likelihood estimate of the mean parameters.
the maximum likelihood estimate of the scale parameter.
the residuals at the MLE, that is y - fitted.values
the fitted mean values.
the number of parameters in the model (named ``rank" for compatibility ---
we assume that models have full rank)
included for compatibility --- will always be negbin1(identity).
included for compatibility --- same as fitted.values (as this is
an identity-link model).
up to a constant, minus twice the maximised log-likelihood (with respect to
a saturated NB1 model with the same scale).
a version of Akaike's An Information Criterion, minus twice the maximised log-likelihood plus twice the number of parameters.
a small-sample corrected version of Akaike's An Information Criterion (Hurvich, Simonoff and Tsai, 1998).
the deviance for the null model, comparable with deviance.
The null model will include the offset and an intercept.
the number of iterations of the EM algorithm used.
included for compatibility --- a vector of ones.
included for compatibility --- a vector of ones.
the standard vector passed to this function.
the residual degrees of freedom.
the residual degrees of freedom for the null model.
the y vector used.
logical. Did the ECME algorithm converge
(according to conv.test)?
logical. Is the MLE on the boundary of the parameter
space --- i.e. are any of the coefficients < control$bound.tol?
the maximised log-likelihood.
the non-negative x matrix used.
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.
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.