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 |

`Zc` |
a |

`intercept` |
Boolean, specifying whether to include an intercept.
Default is |

`lam` |
a user supplied lambda sequence.
If |

`...` |
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 |

`lam` |
the sequence of |

`GIC` |
a vector of GIC value(s). |

`lam.min` |
the |

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
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")
``` |

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