Description Usage Arguments Details Value Author(s) References See Also Examples

`AIC.dglars`

is used to compute the Akaike's ‘An Information Criterion’ for the sequence of models estimated by “`dglars`

”.

1 2 3 4 5 6 |

`object` |
a fitted |

`phi` |
a description of the estimator of the dispersion parameter (see below for more details). |

`k` |
non negative value used to weight the complexity of the fitted dglars model (see below for more details). |

`complexity` |
argument used to specify the method to measure the complexity of a fitted dglars model, i.e. the number of non-zero estimates ( |

`g` |
vector of values of the tuning parameter. |

`...` |
further arguments passed to the function |

The values returned by `AIC.dglars`

are computed according to the following formula of a generic measure of Goodness-of-Fit (GoF):

*-2 * log-likelihood + k * comp,*

where “comp” represents the term used to measure the complexity of the fitted model, and *k* is the ‘weight’ of the complexity in the previous formula.

For binomial and Poisson family, the log-likelihood function is evaluated assuming that the dispersione parameter is known and equal to one while for the remaining families the dispersion parameter is estimated by the method specified by `phi`

(see `phihat`

for more details).

According to the results given in Augugliaro et. al. (2013), the complexity of a model fitted by dglars method can be measured by the classical notion of ‘Degrees-of-Freedom’ (`complexity = "df"`

), i.e., the number of non-zero estimated, or by the notion of ‘Generalized Degrees-of-Freedom’ (`complexity = "gdf"`

).

By the previous formula, it is easy to see that the standard AIC-values are obtained setting `k = 2`

and `complexity = "df"`

(default values for the function `AIC.dglars`

) while the so-called BIC-values (Schwarz's Bayesian criterion) are obtained setting `k = log(n)`

, where *n* denotes the sample size, and `complexity = "df"`

(default values for the function `BIC.dglars`

).

The optional argument `g`

is used to specify the values of the tuning parameter; if not specified (default), the values of the measure of goodness-of-fit are computed for the sequence of models storage in `object`

otherwise `predict.dglars`

is used to compute the estimate of the parameters needed to evaluate the log-likelihood function (see the example below).

`AIC.dglars`

and `BIC.dglars`

return a named list with class “`gof_dglars`

” and components:

`val` |
the sequence of AIC/BIC-values; |

`g` |
the sequence of |

`loglik` |
the sequence of log-likelihood values used to compute the AIC or BIC; |

`k` |
the non negative value used to weight the complexity of the fitted dglars model; |

`comp` |
the measures of model complexity used to compute the measure of goodness-of-fit. It is equal to |

`npar` |
the seqeunce of the number of non-zero estimates |

`phi` |
a description of the estimator used to estimate the dispersion pamater; |

`phih` |
the vector of penalized estimate of the dispersion parameter used to evaluate the log-likelihood function; |

`complexity` |
character specifying the method to measure the complexity of a fitted dglars model; |

`object` |
the fitted |

`type` |
character specifying the type of used measure-of-goodness of fit, i.e., AIC, BIC or GoF. |

In order to summarize the information about the AIC-valuse, a `print`

method is available for an object with class “`gof_dglars`

”.

Luigi Augugliaro

Maintainer: Luigi Augugliaro [email protected]

Augugliaro L., Mineo A.M. and Wit E.C. (2013)
*dgLARS: a differential geometric approach to sparse generalized linear models*,
*Journal of the Royal Statistical Society. Series B.*, Vol 75(3), 471-498.

Sakamoto, Y., Ishiguro, M., and Kitagawa G. (1986).
*Akaike Information Criterion Statistics*.
D. Reidel Publishing Company.

`logLik.dglars`

, `predict.dglars`

, `dglars`

and `summary.dglars`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | ```
#################################
# y ~ Pois
library("dglars")
set.seed(123)
n <- 100
p <- 5
X <- matrix(abs(rnorm(n*p)),n,p)
eta <- 1 + X[, 1] + X[, 2]
mu <- poisson()$linkinv(eta)
y <- rpois(n, mu)
out <- dglars(y ~ X, poisson)
out
AIC(out)
AIC(out, g = seq(2, 1, by = -0.1))
AIC(out, complexity = "gdf")
AIC(out, k = log(n)) #BIC-values
BIC(out)
#################################
# y ~ Gamma
n <- 100
p <- 50
X <- matrix(abs(rnorm(n*p)),n,p)
eta <- 1 + 2 * X[, 1L]
mu <- drop(Gamma()$linkinv(eta))
shape <- 0.5
phi <- 1 / shape
y <- rgamma(n, scale = mu / shape, shape = shape)
out <- dglars(y ~ X, Gamma("log"))
AIC(out, phi = "pearson")
AIC(out, phi = "deviance")
AIC(out, phi = "mle")
AIC(out, phi = "grcv")
``` |

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