ic.panel.sglfit {midasml}

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 \lambda 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 \lambda sequence is sorted in decreasing order before fitting the model.

gamma

sg-LASSO mixing parameter. \gamma = 1 gives LASSO solution and \gamma = 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)