R: Gives the GAIC for a GAMLSS Object

IC {gamlss} | R Documentation

## Gives the GAIC for a GAMLSS Object

### Description

`IC` is a function to calculate 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`. The function `GAIC` is a synonymous of the function `AIC.gamlss`. 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 )
    ## S3 method for class 'gamlss'
    extractAIC(fit, scale, k = 2, c = FALSE, ...)

### Arguments

`object` | an gamlss fitted model
`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

### 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 `extractAIC` returns vector of length two with the degrees of freedom and the AIC criterion.

### Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org

### References

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.

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, http://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 http://www.gamlss.org/).

### See Also

`gamlss`

### Examples

    data(abdom)
    mod1<-gamlss(y~pb(x),sigma.fo=~pb(x),family=BCT, data=abdom)
    IC(mod1)
    mod2<-gamlss(y~pb(x),sigma.fo=~x,family=BCT, data=abdom)
    AIC(mod1,mod2,k=3)
    GAIC(mod1,mod2,k=3)
    extractAIC(mod1,k=3)
    rm(mod1,mod2)

[Package gamlss version 5.0-2 Index]