grcv {dglars} | R Documentation

## General Refitted Cross-Validation Estimator

### Description

`grcv` computes the estimate of the dispersion parameter using the general refitted cross-validation method.

### Usage

    grcv(object, type = c("BIC", "AIC"), nit = 10L, trace = FALSE,
         control = list(), ...)

### Arguments

`object` | fitted `dglars` object.
`type` | the measure of goodness-of-fit used in Step 2 to select the two set of variables (see section Description for more details). Default is `type = BIC`.
`control` | a list of control parameters passed to the function `dglars`.
`nit` | integer specifying the number of times that the general refitted cross-validation method is repeated (see section Description for more details). Default is `nit = 10L`.
`trace` | flag used to print out information about the algorithm. Default is `trace = FALSE`.
`...` | further arguments passed to the functions `AIC.dglars` or `BIC.dglars`.

### Details

The general refitted cross-validation (grcv) estimator (Pazira et al., 2018) is an estimator of the dispersion parameter of the exponential family based on the following four stage procedure:

Step | Description
1. | randomly split the data set D = (y, X) into two even datasets, denoted by D_1 and D_2.
2. | fit dglars model to the dataset D_1 to select a set of variables A_1.
| fit dglars model to the dataset D_2 to select a set of variables A_2.
3. | fit the glm model to the dataset D_1 using the variables that are in A_2; then estimate the
| disporsion parameter using the Pearson method. Denote by hat{phi}_1(A_2) the resulting estimate.
| fit the glm model to the dataset D_2 using the variables that are in A_1; then estimate the
| disporsion parameter using the Pearson method. Denote by hat{phi}_2(A_1) the resulting estimate.
4. | estimate phi using the following estimator: \hat{phi}_{grcv} = (hat{phi}_1(A_2) + hat{phi}_2(A_1)) / 2.

In order to reduce the random variabilty due to the splitting of the dataset (Step 1), the previous procedure is repeated ‘`nit`’-times; the median of the resulting estimates is used as final estimate of the dispersion parameter. In Step 3, the two sets of variables are selected using the `AIC.dglars` and `BIC.dglars`; in this step, the Pearson method is used to obtain a first estimate of the dispersion parameter. Furthermore, if the function `glm` does not converge the function `dglars` is used to compute the maximum likelihood estimates.

### Value

`grcv` returns the estimate of the dispersion parameter.

### Author(s)

Luigi Augugliaro and Hassan Pazira
Maintainer: Luigi Augugliaro luigi.augugliaro@unipa.it

### References

Pazira H., Augugliaro L. and Wit E.C. (2018) <DOI: 10.1007/s11222-017-9761-7> Extended differential-geometric LARS for high-dimensional GLMs with general dispersion parameter, Statistics and Computing, Vol 28(4), 753-774.

### See Also

`phihat`, `AIC.dglars` and `BIC.dglars`.

### Examples

    ############################
    # y ~ Gamma
    set.seed(321)
    n <- 100
    p <- 50
    X <- matrix(abs(rnorm(n*p)),n,p)
    eta <- 1 + 2 * X[,1]
    mu <- drop(Gamma()$linkinv(eta))
    shape <- 0.5
    phi <- 1 / shape
    y <- rgamma(n, scale = mu / shape, shape = shape)
    fit <- dglars(y ~ X, Gamma("log"))

    phi
    grcv(fit, type = "AIC")
    grcv(fit, type = "BIC")

[Package dglars version 2.1.2 Index]