GIC.compCL: Compute information crieteria for the 'compCL' model.
In Compack: Regression with Compositional Covariates

Description Usage Arguments Details Value References See Also Examples

Tune the penalty parameter codelam in the compCGL model by GIC, BIC, or AIC. This function calculates the GIC, BIC, or AIC curve and returns the optimal value of lam.

1	GIC.compCL(y, Z, Zc = NULL, intercept = FALSE, lam = NULL, ...)

`y`	a response vector with length n.
`Z`	a np* design matrix of compositional data or categorical data. If `Z` is categorical data, i.e., row-sums of `Z` differ from 1, the program automatically transforms `Z` into compositional data by dividing each row by its sum. `Z` could NOT include entry of 0's.
`Zc`	a np_c* design matrix of control variables (not penalized). Default is `NULL`.
`intercept`	Boolean, specifying whether to include an intercept. Default is `FALSE`.
`lam`	a user supplied lambda sequence. If `lam` is provided as a scaler and `nlam`>1, `lam` sequence is created starting from `lam`. To run a single value of `lam`, set `nlam`=1. The program will sort user-defined `lambda` sequence in decreasing order.
`...`	other arguments that can be passed to compCL.

The model estimation is conducted through minimizing the following criterion:

\frac{1}{2n}\|y-Zβ\|_2^2 + λ\|β\|_1, s.t. ∑_{j=1}^{p} β_j = 0.

The GIC is defined as:

GIC(λ) = \log{\hat{σ}^2(λ)} + (s(λ) -1) \log{(max(p, n))} * \log{(\log{n})} / n,

where \hat{σ}^2(λ) = \|y - Z\hat{β}(λ)\|_{2}^{2}/n, \hat{β}(λ) is the regularized estimator, and s(λ) is the number of nonzero coefficients in \hat{β}(λ). Because of the zero-sum constraint, the effective number of free parameters is s(λ) - 1 for s(λ) ≥ 2. The optimal λ is selected by minimizing GIC(λ).

an object of S3 class GIC.compCL is returned, which is a list:

`compCL.fit`	a fitted `compCL` object.
`lam`	the sequence of `lam`.
`GIC`	a vector of GIC value(s).
`lam.min`	the `lam` value that minimizes `GIC`(λ).

Lin, W., Shi, P., Peng, R. and Li, H. (2014) Variable selection in regression with compositional covariates, https://academic.oup.com/biomet/article/101/4/785/1775476. Biometrika 101 785-979

Fan, Y., and Tang, C. Y. (2013) Tuning parameter selection in high dimensional penalized likelihood, https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssb.12001 Journal of the Royal Statistical Society. Series B 75 531-552

compCL and cv.compCL, and coef, predict and plot methods for "GIC.compCL" object.

p = 30
n = 50
beta = c(1, -0.8, 0.6, 0, 0, -1.5, -0.5, 1.2)
beta = c(beta, rep(0, times = p - length(beta)))
Comp_data = comp_Model(n = n, p = p, beta = beta, intercept = FALSE)
GICm1 <- GIC.compCL(y = Comp_data$y, Z = Comp_data$X.comp,
                    Zc = Comp_data$Zc, intercept = Comp_data$intercept)
coef(GICm1)
plot(GICm1)
test_data = comp_Model(n = 100, p = p, beta = Comp_data$beta, intercept = FALSE)
y_hat = predict(GICm1, Znew = test_data$X.comp, Zcnew = test_data$Zc)
plot(test_data$y, y_hat, xlab = "Observed value", ylab = "Predicted value")
abline(a = 0, b = 1, col = "red")