Finds the maximum likelihood estimate of an identity-link Poisson GLM using an EM algorithm, where each of the coefficients is restricted to be non-negative.
nnpois(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.
starting values for the parameter estimates. Each element must be
greater than control$bound.tol.
an addreg.control object, which controls the fitting process.
a character string that determines the acceleration
algorithm to be used, (partially) matching one of "em" (no acceleration -- the default),
"squarem", "pem" or "qn". See turboem
for further details. Note that "decme" is not permitted.
a list of control parameters for the acceleration algorithm. See turboem
for details of the parameters that apply to each algorithm. If not specified, the defaults are used.
A list containing the following components
the constrained non-negative maximum likelihood estimate of the parameters.
the residuals at the MLE, that is y - fitted.values
the fitted mean values.
the number of parameters in the model (named ``rank" for compatibility ---
we assume that models have full rank)
included for compatibility --- will always be poisson(identity).
included for compatibility --- same as fitted.values (as this is
an identity-link model).
up to a constant, minus twice the maximised log-likelihood.
a version of Akaike's An Information Criterion, minus twice the maximised log-likelihood plus twice the number of parameters.
a small-sample corrected version of Akaike's An Information Criterion (Hurvich, Simonoff and Tsai, 1998).
the deviance for the null model, comparable with deviance.
The null model will include the offset and an intercept.
the number of iterations of the EM algorithm used.
included for compatibility --- a vector of ones.
included for compatibility --- a vector of ones.
the standard vector passed to this function.
the residual degrees of freedom.
the residual degrees of freedom for the null model.
the y vector used.
logical. Did the EM algorithm converge
(according to conv.test)?
logical. Is the MLE on the boundary of the parameter
space --- i.e. are any of the coefficients < control$bound.tol?
the maximised log-likelihood.
the non-negative x matrix used.
This is a workhorse function for addreg, and runs the EM algorithm to find the
constrained non-negative MLE associated with an identity-link Poisson GLM. See Marschner (2010)
for full details.
Hurvich, C. M., J. S. Simonoff and C.-L. Tsai (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 60(2): 271--293.
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., A. C. Gillett and R. L. O'Connell (2012). Stratified additive Poisson models: Computational methods and applications in clinical epidemiology. Computational Statistics and Data Analysis 56(5): 1115--1130.