apple: Approximate Path for Penalized Likelihood Estimator

In apple: Approximate Path for Penalized Likelihood Estimators

Description

Fit a generalized linear model via penalized maximum likelihood. The regularization path is computed for the LASSO or MCP penalty at a grid of values for the regularization parameter lambda. Can deal all shapes of data, including very large sparse data matrices. Fits binomial-logistic and poisson regression models.

Usage

apple(X, y, family="binomial", penalty = "LASSO", gamma, cha.poi = 1, 
eps = 1e-15, lam.list, lambda.min.ratio, max.iter = 100, max.num, 
n.lambda = 100)

Arguments

X	input matrix, of dimension nobs x nvars; each row is an observation vector.
y	response variable, of dimension nobs x 1. non-negative counts for family="poisson", binary for family="binomial".
family	response type.
penalty	LASSO and MCP are provided.
gamma	the MCP concavity parameter.
cha.poi	the value used to change from Newton Raphson correction to Coordinate Descent correction, which is the α in the following inequality, k> α√{n}, where k is the size of current active set. when this inequality holds, the correction method changes from Newton Raphson to Coordinate Descent.
eps	the precision used to test the convergence.
lam.list	a user supplied λ sequence. typical usage is to have the program compute its own lambda sequence based on lambda.min.ratio and n.lambda. supplying a value of λ overrides this.
lambda.min.ratio	optional input. smallest value for lambda, as a fraction of max.lam, the (data derived) entry value. the default depends on the sample size n relative to the number of variables p. if n > p, the default is 0.0001. otherwise, the default is 0.01.
max.iter	maximum number of iteration in the computation.
max.num	optional input. maximum number of nonzero coefficients.
n.lambda	the number of lambda values.

Value

a0	intercept vector of length(lambda).
beta	nvar x length(lambda) matrix of coefficients.
lambda	the list of lambda derived the solution path.
ebic	the list of EBIC values.
ebic.loc	the location of the EBIC selected solution in the path.
family	the family of the supplied dataset.

Author(s)

Yi Yu and Yang Feng

References

Yi Yu and Yang Feng, APPLE: Approximate Path for Penalized Likelihood Estimator, manuscript.

See Also

plot.apple, cv.apple and predict.apple

Examples

p=10
n=200
d=5
coefs=c(3,1.5,0,0,2)
intercept=0
beta=rep(0,p)
beta[1:d]=coefs
X=matrix(rnorm(p*n), nrow=n)
mu=1/(1+exp(-X %*% beta-intercept))
y=rbinom(n,1,mu)
	

fit.apple=apple(X, y, family= "binomial")


plot(fit.apple)

apple documentation built on May 2, 2019, 3:23 a.m.