glmregNB function

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

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.

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 $0\le\alpha\le 1$. 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

if standardize=FALSE and

if standardize=TRUE.

Returns

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

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]

Author(s)

Zhu Wang zwang145@uthsc.edu

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)