gamlss (version 4.2-4)

stepGAIC: Choose a model by GAIC in a Stepwise Algorithm

Description

The function stepGAIC() performs stepwise model selection using a Generalized Akaike Information Criterion. The function stepGAIC() calls one of the two functions stepGAIC.VR() or stepGAIC.CH() depending on the argument additive. The function stepGAIC.VR() is based on the function stepAIC() given in the library MASS of Venables and Ripley (2002). The function stepGAIC.CH is based on the S function step.gam() (see Chambers and Hastie (1991)) and it is more suited for model with smoothing additive terms, (see below comments for the additive function pb()). Both functions have been adapted to work with gamlss objects. The main difference for the user is the scope argument, see below. If the stepGAIC() is called with the argument additive=FALSE then the stepGAIC.VR() is called else the stepGAIC.CH().

While the functions stepGAIC.VR() and stepGAIC.CH() are used to build models for individual parameters of the distribution of the response variable, the functions stepGAICAll.A() and stepGAICAll.A() are building a model for all the parameters. Both the functions stepGAICAll.A() and stepGAICAll.B() are based on stepGAIC.VR(). The use two different strategies for selecting a appropriate final model. stepGAICAll.A() has the following strategy: Stategy A:

i) build a model for mu using a forward approach.

ii) given the model for mu build a model for sigma (forward)

iii) given the models for mu and sigma build a model for nu (forward)

iv) given the models for mu, sigma and nu build a model for tau (forward)

v) given the models for mu, sigma, nu and tau check whether the terms for nu are needed using backward elimination.

vi) given the models for mu, sigma, nu and tau check whether the terms for sigma are needed (backward).

vii) given the models for mu, sigma, nu and tau check whether the terms for mu are needed (backward).

Note for this strategy to work the scope argument should be set appropriately.

stepGAICAll.B() uses the same procedure as the function stepGAIC.VR() but each term in the scope is fitted to ALL the parameters of the distribution, rather than the one specified by the argument what of stepGAIC.VR().

Usage

stepGAIC.VR(object, scope, direction = c("both", "backward", "forward"), 
         trace = T, keep = NULL, steps = 1000, scale = 0, 
         what = c("mu", "sigma", "nu", "tau"), k = 2, ...)
stepGAIC.CH(object, scope = gamlss.scope(model.frame(object)), 
            direction = c("both", "backward", "forward"), trace = T, keep = NULL, 
            steps = 1000, what = c("mu", "sigma", "nu", "tau"), k = 2, ...)

stepGAIC(object, scope = gamlss.scope(model.frame(object)), 
          direction = c("both", "backward", "forward"), 
          trace = T, keep = NULL, steps = 1000, 
          what = c("mu", "sigma", "nu", "tau"), k = 2, 
          additive = FALSE, ...)
stepGAICAll.A(object, scope = NULL, sigma.scope = NULL, nu.scope = NULL, 
              tau.scope = NULL, mu.try = TRUE, sigma.try = TRUE, 
              nu.try = TRUE, tau.try = TRUE, ...)

stepGAICAll.B(object, scope, direction = c("both", "backward", "forward"), 
               trace = T, keep = NULL, steps = 1000, scale = 0, k = 2, ...)
               
stepTGD(object, scope, newdata, direction = c("both", "backward", "forward"), 
              trace = T, keep = NULL, steps = 1000, 
              what = c("mu", "sigma", "nu", "tau"), ...)

Arguments

object

an gamlss object. This is used as the initial model in the stepwise search.

scope

defines the range of models examined in the stepwise search. For the function stepAIC() this should be either a single formula, or a list containing components upper and lower, both formulae.

direction

the mode of stepwise search, can be one of both, backward, or forward, with a default of both. If the scope argument is missing the default for direction

trace

if positive, information is printed during the running of stepAIC. Larger values may give more information on the fitting process.

keep

a filter function whose input is a fitted model object and the associated 'AIC' statistic, and whose output is arbitrary. Typically 'keep' will select a subset of the components of the object and return them. The default is n

steps

the maximum number of steps to be considered. The default is 1000 (essentially as many as required). It is typically used to stop the process early.

scale

scale is nor used in gamlss

what

which distribution parameter is required, default what="mu"

k

the multiple of the number of degrees of freedom used for the penalty. Only 'k = 2' gives the genuine AIC: 'k = log(n)' is sometimes referred to as BIC or SBC.

additive

if additive=TRUE then stepGAIC.CH is used else stepGAIC.CH, default value is FALSE

sigma.scope

scope for sigma if different to scope in stepGAICAll.A()

nu.scope

scope for nu if different to scope in stepGAICAll.A()

tau.scope

scope for tau if different to scope in stepGAICAll.A()

mu.try

The default value is is TRUE, set to FALSE if no model for mu is needed

sigma.try

The default value is TRUE, set to FALSE if no model for sigma is needed

nu.try

The default value is TRUE, set to FALSE if no model for nu is needed

tau.try

The default value is TRUE, set to FALSE if no model for tau is needed

newdata

The new data set where the Test Global Deviance (TGD) will be evaluated

...

any additional arguments to 'extractAIC'. (None are currently used.)

Value

• the stepwise-selected model is returned, with up to two additional components. There is an '"anova"' component corresponding to the steps taken in the search, as well as a '"keep"' component if the 'keep=' argument was supplied in the call. The '"Resid. Dev"' column of the analysis of deviance table refers to a constant minus twice the maximized log likelihood The function stepGAICAll.A() returns with a component "anovaAll" containing all the different anova tables used in the process.

Details

The set of models searched is determined by the scope argument.

For the function stepGAIC.VR() the right-hand-side of its lower component is always included in the model, and right-hand-side of the model is included in the upper component. If scope is a single formula, it specifies the upper component, and the lower model is empty. If scope is missing, the initial model is used as the upper model.

Models specified by scope can be templates to update object as used by update.formula.

For the function stepGAIC.CH() each of the formulas in scope specifies a "regimen" of candidate forms in which the particular term may enter the model. For example, a term formula might be

~ x1 + log(x1) + cs(x1, df=3)

This means that x1 could either appear linearly, linearly in its logarithm, or as a smooth function estimated non-parametrically. Every term in the model is described by such a term formula, and the final model is built up by selecting a component from each formula.

The function gamlss.scope similar to the S gam.scope() in Chambers and Hastie (1991) can be used to create automatically term formulae from specified data or model frames.

The supplied model object is used as the starting model, and hence there is the requirement that one term from each of the term formulas of the parameters be present in the formula of the distribution parameter. This also implies that any terms in formula of the distribution parameter not contained in any of the term formulas will be forced to be present in every model considered.

When the smoother used in gamlss modeling belongs to the new generation of smoothers allowing the determination of the smoothing parameters automatically (i.e. pb(), cy()) then the function stepGAIC.VR() can be used for model selection (see example below).

The function stepTGD is a clone function of stepGAIC.VR() where the selection criterion is not anymore a GAIC but the Test Global Deviance, that is, the deviance (-2log(Likelihood)) evaluated at the test data rather than the training ones.

References

Chambers, J. M. and Hastie, T. J. (1991). Statistical Models in S, Chapman and Hall, London.

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. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

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.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

gamlss.scope

Examples

data(usair)
# Note default of additive=FALSE
# fitting all variables linearly 
mod1<-gamlss(y~., data=usair, family=GA)
# find the best subset for the mu
mod2<-stepGAIC(mod1)
mod2$anova
# find the best subset for sigma
mod3<-stepGAIC(mod2, what="sigma", scope=~x1+x2+x3+x4+x5+x6)
mod3$anova
# find the best model using pb() smoother 
#only three variables are used here for simplicity
mod10 <-gamlss(y~1, data=usair, family=GA)
mod20<-stepGAIC(mod10, scope=list(lower=~1, upper=~pb(x1)+pb(x2)+pb(x5)))
edf(mod20)
# x1 and x2 enter linearly
# now use the stepGAIC.CH function
# creating a scope from the usair model frame 
gs<-gamlss.scope(model.frame(y~x1+x2+x3+x4+x5+x6, data=usair))
gs 
mod4<-gamlss(y~1, data=usair, family=GA)
mod5<-stepGAIC(mod4,gs, additive=TRUE)
mod5$anova
mod6<-stepGAIC(mod5, what="sigma", scope=~x1+x2+x3+x4+x5+x6)
mod6$anova
mod6
# now stepGAICAll.A    
mod7<-stepGAICAll.A(mod4, scope=list(lower=~1,upper=~x1+x2+x3+x4+x5+x6)) 
# now  stepGAICAll.B
mod8<-stepGAICAll.B(mod4, scope=list(lower=~1,upper=~x1+x2+x3+x4+x5+x6))
# now stepTGD()
data(aep)
# sampling from the data
rand <- sample(2, dim(aep)[1], replace=TRUE, prob=c(0.6,0.4))
# the proportions in the sample
table(rand)/dim(aep)[1]
oldaep<-aep[rand==1,]
newaep<-aep[rand==2,] 
m0<-gamlss(y~ward+year+loglos, data=oldaep, family=BB)
#checking mu
m1 <- stepTGD(m0, newdata=newaep) 
#checking sigma 
m2 <- stepTGD(m0,scope=~ward+year, newdata=newaep, what="sigma")