get.GIC: GIC criterion selection for FuncompCGL
In jiji6454/Rpac_compReg: Compositional Data Regression

Description Usage Arguments Details Value

Calculate GIC for GIC.FuncompCGL, select beta coefficients vector and df via BIC, AIC, GIC criterion

get.GIC(p, df_list, GIC_obj, GIC_arg, cut_type = c("Strict", "Matrix",
  "Curve"), lower_tri = 0.01, GIC_type = c("GIC1", "GIC2", "GIC3", "GIC4",
  "AIC", "BIC"), method_type = c("cgl", "naive", "base"), y = NULL,
  Zc = NULL, refit = FALSE)

`p`	number of compositional predictors
`df_list`	vector of df's used in `GIC_obj`
`GIC_obj`	an object of `GIC.FuncompCGL`
`GIC_arg`	argument list used to fit `GIC.FuncompCGL`, need to at least provide information for basis generation, including `basis_fun`, `degree` and `sseq`.
`cut_type`	cut method for none zero group - default value is `Strict` which is no cut-off. Other two methods are `Matrix` and `Curve`. See details.
`lower_tri`	lower percentage boundary used in cut none zero groups.
`GIC_type`	variations of GIC's, AIC and BIC. See details.
`method_type`	mehod used to fitted `GIC.FuncompCGL` `cgl` - constrained group lasso `base` - log contract group lasso `naive` - do not consider the fact of compositional.
`y, Zc`	when `refit=TRUE`, need to privde `y` and `Zc` to re-calcualte likelihood.
`refit`	logical, whehter refit likelihood when small magnitude groups are cut to zeros' Default value is `FALSE`.

$$GIC(λ) = log(MSE) + Selection * alpha$$, for normal error. If include linear constraints, like in log contract and constraints group lasso model, selection = None zero group - 1; otherwise in naive method without consideration of linear constraints, selection = None zero group.

alpha_GIC1 = log(max(p*df, n)) * df / n
alpha_GIC2 = log(max(p*df, n)) * df * log(log(n)) / n
alpha_GIC3 = log(p*df) *df /n
alpha_GIC4 = log(p*df) * df * log(log(n)) / n
alpha_BIC = log(n) * df / n
alpha_AIC = 2 * df / n.

cut_off = 'Curve', calculate L2 function norm for curves for each compositional covariates , across df and lambda. Consider those betas' with L2 curve norm smaller than sum(L2_j)*lower_tri as none-selected.

cut_off = 'Matrix' calculate L2 norm for coefficient matrix by rows, across df and lambda, condiser these betas' with vector L2 norm that is smaller than srqt(sum(L2_j^2)) * lower_tri.

cut_off = 'Strict', strict none zero group, whenever there is none zero entries considered as selected.

`beta`	selected beta vector.
`k_opt`	selected `df`.
`GIC_curve`	a `length(df_list)` by `nlam` matrix of GIC values
`N_zero`	a matrix of numbers of none zero groups selected.