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.
nplbin(y, x, offset, start, Amat = diag(ncol(x)), control = logbin.control(),
accelerate = c("em", "squarem", "pem", "qn"),
control.accelerate = list(list()))A list containing the following components
the constrained non-positive 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 binomial(log).
the linear fit on link scale.
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.
the number of trials associated with each binomial response.
the residual degrees of freedom.
the residual degrees of freedom for the null model.
the y vector used.
logical. Did the EM algorithm converge?
logical. Is the MLE on the boundary of the parameter
space --- i.e. are any of the coefficients < control$bound.tol?
the maximised log-likelihood.
the non-negative x matrix used.
binomial response. May be a single column of 0/1 or two columns, giving the number of successes and failures.
non-negative covariate matrix.
non-positive additive offset vector. The default is a vector of zeros.
starting values for the parameter estimates. All elements must be less than
or equal to -control$bound.tol.
matrix that parameter estimates are left-multiplied by before testing for convergence (e.g. to check reduced version of expanded parameter vector).
a logbin.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.
Mark W. Donoghoe markdonoghoe@gmail.com.
This function is based on code from Marschner and Gillett (2012) written by Alexandra Gillett.
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.
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.