R: Gives the GAIC for a GAMLSS Object

IC {gamlss} | R Documentation

## Gives the GAIC for a GAMLSS Object

### Description

The function `GAIC()` calculates the Generalised Akaike information criterion (GAIC) for a given penalty `k` for a fitted GAMLSS object.

The function `AIC.gamlss()` is the method associated with a GAMLSS object of the generic function `AIC()`. Note that `GAIC()` is a synonymous of the function `AIC.gamlss`.

The function `IC()` is an old version of `GAIC()`.

The function `GAIC.table()` produces a table with different models as rows and different penalties, `k`, as columns.

The function `GAIC.scaled()` produces, [for a given set of different fitted models or for a table produced by `chooseDist()`], the scaled Akaike values (see Burnham and Anderson (2002) section 2.9 for a similar concept the GAIC weights. The scaled Akaike should not be interpreted as posterior probabilities of models given the data but for model selection purpose they produce a scaled ranking of the model using their relative importance i.e. from the worst to the best model.

The function `extractAIC` is a the method associated a GAMLSS object of the generic function `extractAIC` and it is mainly used in the `stepAIC` function.

The function `Rsq` compute a generalisation of the R-squared for not normal models.

### Usage

    IC(object, k = 2)
    ## S3 method for class 'gamlss'
    AIC(object, ..., k = 2, c = FALSE)
    GAIC(object, ..., k = 2, c = FALSE )
    GAIC.table(object, ..., k = c(2, 3.84, round(log(length(object$y)), 2)),
               text.to.show=NULL)
    GAIC.scaled(object,..., k = 2, c = FALSE, plot = TRUE,
                  text.cex = 0.7, which = 1, diff.dev = 1000,
                  text.to.show = NULL, col = NULL, horiz = FALSE)
    ## S3 method for class 'gamlss'
    extractAIC(fit, scale, k = 2, c = FALSE, ...)

### Arguments

`object` | an gamlss fitted model(s) [or for `GAIC.scaled()` a table produced by `chooseDist()`].
`fit` | an gamlss fitted model
`...` | allows several GAMLSS object to be compared using a GAIC
`k` | the penalty with default `k=2.5`
`c` | whether the corrected AIC, i.e. AICc, should be used, note that it applies only when `k=2`
`scale` | this argument is not used in gamlss
`plot` | whether to plot the ranking in `GAIC.scaled()`.
`text.cex` | the size of the models/famlies in the text of the plot of `GAIC.scaled()`.
`diff.dev` | this argument prevents models with a difference in deviance greater than `diff.dev` from the ‘best’ model to be considered (or plotted).
`which` | which column of GAIC scaled to plot in `GAIC.scaled()`.
`text.to.show` | if NULL, `GAIC.scaled()` shows the model names otherwise the character in this list
`col` | The colour of the bars in `GAIC.scaled()`
`horiz` | whether to plot the bars vertically (default) or horozontaly

### Value

The function `IC()` returns the GAIC for given penalty k of the GAMLSS object. The function `AIC()` returns a matrix contains the df's and the GAIC's for given penalty k. The function `GAIC()` returns identical results to `AIC`. The function `GAIC.table()` returns a table which its rows showing different models and its columns different `k`'s. The function `extractAIC()` returns vector of length two with the degrees of freedom and the AIC criterion.

### Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk

### References

Burnham K. P. and Anderson D. R (2002). Model Selection and Multimodel Inference A Practical Information-Theoretic Approach, Second Edition, Springer-Verlag New York, Inc.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, https://www.jstatsoft.org/v23/i07/.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

(see also https://www.gamlss.com/).

### See Also

`gamlss`

### Examples

    data(abdom)
    m1 <-  gamlss(y~x, family=NO, data=abdom)
    IC(m1)
    extractAIC(m1,k=2)
    m2 <-  gamlss(y~x, sigma.fo=~x, family=NO, data=abdom)
    m3 <-  gamlss(y~pb(x), sigma.fo=~x, family=NO, data=abdom)
    m4 <-  gamlss(y~pb(x), sigma.fo=~pb(x), family=NO, data=abdom)
    AIC(m1,m2, m3, m4)
    AIC(m1,m2, m3, m4, c=TRUE)
    AIC(m1,m2, m3, m4, k=3)
    GAIC.table(m1,m2, m3, m4)
    GAIC.scaled(m1,m2, m3, m4)
    ## Not run:
    MT <- chooseDist(m3)
    GAIC.scaled(MT)
    GAIC.scaled(MT, which=2)
    ## End(Not run)

[Package gamlss version 5.3-2 Index]