Fit a generalized linear model via penalized maximum likelihood. The regularization path is computed for the LEP penalty at a grid of values for the regularization parameter lambda. Fits linear, logistic and Cox regression models.
glmlep(x, y, family = c("gaussian", "binomial"), lambda = NULL,
lambda.min = ifelse(n < p, 0.05, 0.001), nlambda = 100, lambda2 = 0,
kappa = ifelse(n < p, 0.1, 0.05), pen.fac = rep(1, p), tol = 1e-06,
max.ite = 1000)The design matrix, without an intercept.
The response vector. Quantitative for family="gaussian". For family="binomial" should be a vector with two levels.
Response type (see above)
A user supplied lambda sequence. Typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lambda overrides this. WARNING: use with care. Do not supply a single value for lambda. Supply instead a decreasing sequence of lambda values. glmnet relies on its warms starts for speed, and its often faster to fit a whole path than compute a single fit.
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.
The number of lambda values; default is 100.
The tuning parameter for additional L_2 penalty. Use for better grouping effect. The default is 0.
The scale tuning parameter of the LEP penalty. One can specify it to get the desired estimates because of the homotopy of LEP function to the L_0 function. If nobs > nvars, the default is 0.05, close to zero. If nobs < nvars, the default is 0.1.
Separate penalty factors can be applied to each coefficient. This is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables (and implicitly infinity for variables listed in exclude). Note: the penalty factors are internally rescaled to sum to nobs, and the lambda sequence will reflect this change.
Convergence tolerance for MCD. Each inner MCD loop continues until the change in the estimates is less than tol. default is 1E-6.
Maximum number of passes over the data for all lambda values; default is 10^3.
An object of class "glmlep", "*", where "*" is "gaulep" or "binlep" for the two types of models.
A nrow(x) x length(lambda) matrix of estimated coefficient.
The sequence of regularization parameter values used
The degree of freedom for each value of lambda.
The -2*log-likelihood value for each value of lambda.
The EBIC value for each value of lambda. Note tha the EBIC value is defined as
The value of lambda with the minimum EBIC.
The coefficient with the minimum EBIC.
The call that produces this object
The sequence of models implied by lambda is fit by a modified version of coordinate descent (MCD), see reference below. Note that n is the sample size and p is the dimension of variables.
Wen, C., Wang, X., & Wang, S. (2013). Laplace Error Penalty based variable selection in ultra high-dimension. In press.
# NOT RUN {
## generate data
require(mvtnorm)
n = 100;
beta <- c(3,1.5,0,0,2,0,0,0)
set.seed(100)
p=length(beta);
corr_data=diag(rep(1,p));
x=as.matrix(rmvnorm(n,rep(0,p),corr_data))
noise=rnorm(n);
## Gaussian
y <- tcrossprod(x,t(beta)) + noise;
fit <- glmlep(x,y,family="gaussian")
# }
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