ic.panel.sglfit: Information criteria fit for panel sg-LASSO

In jstriaukas/midasml: Estimation and Prediction Methods for High-Dimensional Mixed Frequency Time Series Data

Information criteria fit for panel sg-LASSO

Description

Does information criteria for panel data sg-LASSO regression model.

The function runs sglfit 1 time; computes the path solution in lambda sequence. Solutions for BIC, AIC and AICc information criteria are returned.

Usage

ic.panel.sglfit(x, y, lambda = NULL, gamma = 1.0, gindex = 1:p, 
                method = c("pooled","fe"), nf = NULL, ...)

Arguments

x	NT by p data matrix, where NT and p respectively denote the sample size of pooled data and the number of regressors.
y	NT by 1 response variable.
lambda	a user-supplied lambda sequence. By leaving this option unspecified (recommended), users can have the program compute its own λ sequence based on nlambda and lambda.factor. It is better to supply, if necessary, a decreasing sequence of lambda values than a single (small) value, as warm-starts are used in the optimization algorithm. The program will ensure that the user-supplied λ sequence is sorted in decreasing order before fitting the model.
gamma	sg-LASSO mixing parameter. γ = 1 gives LASSO solution and γ = 0 gives group LASSO solution.
gindex	p by 1 vector indicating group membership of each covariate.
method	choose between 'pooled' and 'fe'; 'pooled' forces the intercept to be fitted in sglfit, 'fe' computes the fixed effects. User must input the number of fixed effects nf for method = 'fe'. Default is set to method = 'pooled'.
nf	number of fixed effects. Used only if method = 'fe'.
...	Other arguments that can be passed to sglfit.

Details

The sequence of linear regression models implied by λ vector is fit by block coordinate-descent. The objective function is (case method='pooled')

||y - ια - xβ||²_NT + 2λ Ω_γ(β),
where ι∈R^NT and α is common intercept to all N items or (case method='fe')

||y - Bα - xβ||²_NT + 2λ Ω_γ(β),
where B = I_N⊗ι and ||u||²_NT=<u,u>/NT is the empirical inner product. The penalty function Ω_γ(.) is applied on β coefficients and is

Ω_γ(β) = γ |β|₁ + (1-γ)|β|_2,1,
a convex combination of LASSO and group LASSO penalty functions.

Value

ic.panel.sglfit object.

Author(s)

Jonas Striaukas

Examples

 
set.seed(1)
x = matrix(rnorm(100 * 20), 100, 20)
beta = c(5,4,3,2,1,rep(0, times = 15))
y = x%*%beta + rnorm(100)
gindex = sort(rep(1:4,times=5))
ic.panel.sglfit(x = x, y = y, gindex = gindex, gamma = 0.5, 
  standardize = FALSE, intercept = FALSE)

jstriaukas/midasml documentation built on Oct. 5, 2022, 12:18 a.m.