nplbin: Non-Positive Log-Binomial Regression

In logbin: Relative Risk Regression Using the Log-Binomial Model

Description

Finds the maximum likelihood estimate of a log-link binomial GLM using an EM algorithm, where each of the coefficients in the linear predictor is restricted to be non-positive.

Usage

nplbin(y, x, offset, start, Amat = diag(ncol(x)), control = logbin.control(),
       accelerate = c("em", "squarem", "pem", "qn"),
       control.accelerate = list(list()))

Arguments

y	binomial response. May be a single column of 0/1 or two columns, giving the number of successes and failures.
x	non-negative covariate matrix.
offset	non-positive additive offset vector. The default is a vector of zeros.
start	starting values for the parameter estimates. All elements must be less than or equal to -control$bound.tol.
Amat	matrix that parameter estimates are left-multiplied by before testing for convergence (e.g. to check reduced version of expanded parameter vector).
control	a logbin.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.accelerate	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 logbin, and runs the EM algorithm to find the constrained non-positive MLE associated with a log-link binomial GLM. See Marschner and Gillett (2012) for full details.

Value

A list containing the following components

coefficients	the constrained non-positive maximum likelihood estimate of the parameters.
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 binomial(log).
linear.predictors	the linear fit on link scale.
deviance	up to a constant, minus twice the maximised log-likelihood.
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	the number of trials associated with each binomial response.
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 EM algorithm converge?
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].

This function is based on code from Marschner and Gillett (2012) written by Alexandra Gillett.

References

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.

Marschner, I. C. and A. C. Gillett (2012). Relative risk regression: reliable and flexible methods for log-binomial models. Biostatistics 13(1): 179–192.

logbin documentation built on Aug. 10, 2021, 1:06 a.m.