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 ( |

`...` |
this is the argument by means of to pass codeg 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` |
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 | ```
#################################
# Poisson family
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)
``` |

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