IC: 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 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) 
# S3 method for 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

the penalty with default k=2.5

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.table() shows the model names otherwise the character in this list

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.

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.

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.com/).

Examples

Run this code

# NOT RUN {
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)
# }