RAMP (version 1.0)

RAMP: Regularization Algorithm under Marginality Principle (RAMP) for high dimensional generalized quadratic regression.

Description

RAMP

Usage

RAMP(X, y, family = "gaussian", penalty = "LASSO", gamma, inter = TRUE,
 eps = 1e-15, tune = "EBIC", lam.list, lambda.min.ratio, max.iter = 100, 
 max.num, n.lambda = 100, ebic.gamma = 1, refit = TRUE, trace = FALSE)

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. Default is "gaussian".

penalty

Currently, only LASSO is implemented.

gamma

concavity parameter. Experimental feature.

inter

whether to select interaction effects. Default is TRUE.

eps

the precision used to test the convergence. Default is 1e-15.

tune

tuning parameter selection method. "AIC", "BIC" and "EBIC" are available options. Default is EBIC.

lam.list

a user supplied $\lambda$ 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 $\lambda$ 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 >

max.iter

maximum number of iteration in the computation. Default is 100.

max.num

optional input. maximum number of nonzero coefficients.

n.lambda

the number of lambda values. Default is 100.

ebic.gamma

the gamma parameter value in the EBIC criteria. Default is 1.

refit

whether to perform a MLE refit on the selected model. Default is TRUE.

trace

whether to trace the fitting process. Default is FALSE.

Value

• a0
  intercept vector of length(lambda).
• beta
  nvar x length(lambda) matrix of coefficients.

See Also

predict.RAMP

Examples

set.seed(0)
n = 500
p = 100 #Can be changed to a much larger number say 100000
x = matrix(rnorm(n*p),n,p)
eta = 1 * x[,1] + 2 * x[,3]  + 3*x[,6]  + 4*x[,1]*x[,3] + 5*x[,1]*x[,6]
y =  eta + rnorm(n)

fit1 = RAMP(x, y)
fit1    ###examine the results


y = rbinom(n, 1, 1/(1+exp(-eta)))
fit2 = RAMP(x, y, family='binomial')  ###for binary response