glmregNB: fit a negative binomial model with lasso (or elastic net),...

In mpath: Regularized Linear Models

fit a negative binomial model with lasso (or elastic net), snet and mnet regularization

Description

Fit a negative binomial linear model via penalized maximum likelihood. The regularization path is computed for the lasso (or elastic net penalty), snet and mnet penalty, at a grid of values for the regularization parameter lambda.

Usage

glmregNB(formula, data, weights, offset=NULL, nlambda = 100, lambda=NULL, 
         lambda.min.ratio = ifelse(nobs<nvars,0.05,0.001), alpha=1, gamma=3, 
         rescale=TRUE, standardize = TRUE, penalty.factor = rep(1, nvars), 
         thresh = 0.001, maxit.theta = 10, maxit=1000, eps=.Machine$double.eps,
         trace=FALSE, start = NULL, etastart = NULL, mustart = NULL, 
         theta.fixed=FALSE, theta0=NULL, init.theta=NULL, link=log, 
         penalty=c("enet","mnet","snet"), method="glmreg_fit", model=TRUE, 
         x.keep=FALSE, y.keep=TRUE, contrasts=NULL, convex=FALSE, 
         parallel=TRUE, n.cores=2, ...)

Arguments

formula	formula used to describe a model.
data	argument controlling formula processing via model.frame.
weights	an optional vector of ‘prior weights’ to be used in the fitting process. Should be NULL or a numeric vector. Default is a vector of 1s with equal weight for each observation.
offset	optional numeric vector with an a priori known component to be included in the linear predictor of the model.
nlambda	The number of lambda values - default is 100.
lambda	A user supplied lambda sequence
lambda.min.ratio	Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value (i.e. the smallest value for which all coefficients are zero). The default depends on the sample size nobs relative to the number of variables nvars. If nobs > nvars, the default is 0.001, close to zero. If nobs < nvars, the default is 0.05.
alpha	The L2 penalty mixing parameter, with 0≤α≤ 1. alpha=1 is lasso (mcp, scad) penalty; and alpha=0 the ridge penalty.
gamma	The tuning parameter of the snet or mnet penalty.
rescale	logical value, if TRUE, adaptive rescaling of the penalty parameter for penalty="mnet" or penalty="snet" with family other than "gaussian". See reference
standardize	Logical flag for x variable standardization, prior to fitting the model sequence. The coefficients are always returned on the original scale. Default is standardize=TRUE. If variables are in the same units already, you might not wish to standardize.
penalty.factor	This is a number that multiplies lambda to allow differential shrinkage of coefficients. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is same shrinkage for all variables.
thresh	Convergence threshold for coordinate descent. Defaults value is 1e-6.
maxit.theta	Maximum number of iterations for estimating theta scaling parameter
maxit	Maximum number of coordinate descent iterations for each lambda value; default is 1000.
eps	If a number is less than eps in magnitude, then this number is considered as 0
trace	If TRUE, fitting progress is reported
start, etastart, mustart, ...	arguments for the link{glmreg} function
init.theta	initial scaling parameter theta
theta.fixed	Estimate scale parameter theta? Default is FALSE. Note, the algorithm may become slow. In this case, one may use glmreg function with family="negbin", and a fixed theta

.

theta0	initial scale parameter vector theta, with length nlambda if theta.fixed=TRUE. Default is NULL
convex	Calculate index for which objective function ceases to be locally convex? Default is FALSE and only useful if penalty="mnet" or "snet".
link	link function, default is log
penalty	Type of regularization
method	estimation method
model, x.keep, y.keep	logicals. If TRUE the corresponding components of the fit (model frame, response, model matrix) are returned.
contrasts	the contrasts corresponding to levels from the respective models
parallel, n.cores	a logical value, parallel computing or not for sequence of lambda with the number of CPU cores to use. The lambda loop will attempt to send different lambda off to different cores.

Details

The sequence of models implied by lambda is fit by coordinate descent. This is a lasso (mcp, scad) or elastic net (mnet, snet) regularization path for fitting the negative binomial linear regression paths, by maximizing the penalized log-likelihood. Note that the objective function is

-∑ (weights * loglik) + λ*penalty

if standardize=FALSE and

-\frac{weights}{∑(weights)} * loglik + λ*penalty

if standardize=TRUE.

Value

An object with S3 class "glmreg", "glmregNB" for the various types of models.

call	the call that produced the model fit
b0	Intercept sequence of length length(lambda)
beta	A nvars x length(lambda) matrix of coefficients.
lambda	The actual sequence of lambda values used
resdev	The computed deviance. The deviance calculations incorporate weights if present in the model. The deviance is defined to be 2*(loglike_sat - loglike), where loglike_sat is the log-likelihood for the saturated model (a model with a free parameter per observation).
nulldev	Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)); The NULL model refers to the intercept model.
nobs	number of observations

Author(s)

Zhu Wang <[e-mail]>

References

Zhu Wang, Shuangge Ma, Michael Zappitelli, Chirag Parikh, Ching-Yun Wang and Prasad Devarajan (2014) Penalized Count Data Regression with Application to Hospital Stay after Pediatric Cardiac Surgery, Statistical Methods in Medical Research. 2014 Apr 17. [Epub ahead of print]

See Also

print, predict, coef and plot methods, and the cv.glmregNB function.

Examples

## Not run: 
data("bioChemists", package = "pscl")
system.time(fm_nb1 <- glmregNB(art ~ ., data = bioChemists, parallel=FALSE))
system.time(fm_nb2 <- glmregNB(art ~ ., data = bioChemists, parallel=TRUE, n.cores=2))
coef(fm_nb1)
### ridge regression
fm <- glmregNB(art ~ ., alpha=0, data = bioChemists, lambda=seq(0.001, 1, by=0.01))
fm <- cv.glmregNB(art ~ ., alpha=0, data = bioChemists, lambda=seq(0.001, 1, by=0.01))

## End(Not run)

mpath documentation built on Jan. 7, 2023, 1:17 a.m.