# 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

 ```1 2 3``` ```nplbin(y, x, offset, start, 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`. `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 (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 [email protected].

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 May 30, 2017, 2:21 a.m.