Description Usage Arguments Value References Examples
This function implements Kfold crossvalidation for groupregularized negative binomial regression with a known size parameter α and the log link. For a description of groupregularized negative binomial regression, see the description for the grpreg.nb
function.
Our implementation is based on the least squares approximation approach of Wang and Leng (2007), and hence, the function does not allow the total number of covariates p to be greater than \frac{K1}{K} \times sample size, where K is the number of folds.
1 2 3  cv.grpreg.nb(y, X, groups, nb.size=1, penalty=c("gLASSO","gSCAD","gMCP"),
nfolds=10, weights, taper, nlambda=100, lambda, max.iter=10000,
tol=1e4)

y 
n \times 1 vector of responses. 
X 
n \times p design matrix, where the jth column of 
groups 
pdimensional vector of group labels. The jth entry in 
nb.size 
known size parameter α in NB(α,μ_i) distribution for the responses. Default is 
penalty 
group regularization method to use on the groups of coefficients. The options are 
nfolds 
number of folds K to use in Kfold crossvalidation. Default is 
weights 
groupspecific, nonnegative weights for the penalty. Default is to use the square roots of the group sizes. 
taper 
tapering term γ in group SCAD and group MCP controlling how rapidly the penalty tapers off. Default is 
nlambda 
number of regularization parameters L. Default is 
lambda 
grid of L regularization parameters. The user may specify either a scalar or a vector. If the user does not provide this, the program chooses the grid automatically. 
max.iter 
maximum number of iterations in the algorithm. Default is 
tol 
convergence threshold for algorithm. Default is 
The function returns a list containing the following components:
lambda 
L \times 1 vector of regularization parameters 
cve 
L \times 1 vector of mean crossvalidation error across all K folds. The kth entry in 
cvse 
L \times 1 vector of standard errors for crossvalidation error across all K folds. The kth entry in 
lambda.min 
value of 
Breheny, P. and Huang, J. (2015). "Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors." Statistics and Computing, 25:173187.
Wang, H. and Leng, C. (2007). "Unified LASSO estimation by least squares approximation." Journal of the American Statistical Association, 102:10391048.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  ## Generate data
set.seed(1234)
X = matrix(runif(100*16), nrow=100)
n = dim(X)[1]
groups = c(1,1,1,2,2,2,2,3,4,5,5,6,7,8,8,8)
true.beta = c(2,2,2,0,0,0,0,0,0,1.5,1.5,0,0,2,2,2)
## Generate count responses from negative binomial regression
eta = crossprod(t(X), true.beta)
y = rnbinom(n,size=1, mu=exp(eta))
## 10fold crossvalidation for groupregularized negative binomial
## regression with the group SCAD penalty
nb.cv = cv.grpreg.nb(y,X,groups,penalty="gMCP")
## Plot crossvalidation curve
plot(nb.cv$lambda, nb.cv$cve, type="l", xlab="lambda", ylab="CVE")
## lambda which minimizes mean CVE
nb.cv$lambda.min

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