stepAICmle.fun: Choose the best PP model by AIC in a stepwise algorithm
In NHPoisson: Modelling and Validation of Non Homogeneous Poisson Processes

Description Usage Arguments Details Value References See Also Examples

Performs stepwise model selection by AIC for Poisson proces models estimated by maximum likelihood.

It calls the auxiliary function checkdim (not intended for the users).

1 2	stepAICmle.fun(ImlePP, covariatesAdd = NULL, startAdd = NULL, direction = "forward", ...)

`ImlePP`	A `mlePP`-class object; usually the output from `fitPP.fun`. It defines the initial model of the stepwise algorithm. The fitted model cannot include fixed parameters.
`covariatesAdd`	Matrix of the potential covariates to be added to the model; each column must contain a covariate. In the 'forward' and the 'both' directions, it is compulsory to assign a matrix to this argument. It is advisable to give names to the columns of this matrix (using `dimnames`) since, they will be used in the output. Otherwise the default names 'New Covariate i' are used.
`startAdd`	Optional. The vector of initial values for the estimation of the coefficients of each potential covariate. If it is NULL, initial values equal to 0 are used.
`direction`	Label indicating the direction of the algortihm: 'forward' (the default), 'backward' or 'both'.
`...`	Further arguments to pass to `addAIC.fun` and `dropAIC.fun`, for example the constant k for the AIC calculation

Three directions, forward, backward and both, are implemented. The initial model is given by ImlePP and the algorithm stops when none of the covariates eliminated from the model or added from the potential covariates set (argument covariatesAdd ) improves the model fitted in the previous step, according to the AIC. For the 'both' and 'forward' directions, the argument covariatesADD is compulsary, and the default NULL leads to an error.

In the 'both' direction, 'forward' and 'backward' steps are carried out alternatively. In the 'forward' direction, the initial model usually contains only the intercept.

A mlePP-class object, the fit of the final PP model selectecd by the algorithm.

Casella, G. and Berger, R.L., (2002). Statistical inference. Brooks/Cole.

Cebrian, A.C., Abaurrea, J. and Asin, J. (2015). NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes. Journal of Statistical Software, 64(6), 1-24.

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

addAIC.fun, dropAIC.fun, testlik.fun

data(BarTxTn)

BarEv<-POTevents.fun(T=BarTxTn$Tx,thres=318, 
	date=cbind(BarTxTn$ano,BarTxTn$mes,BarTxTn$dia))

#The initial model contains only the inercept
 mod1Bind<-fitPP.fun(covariates=NULL, posE=BarEv$Px, inddat=BarEv$inddat,
	tit='BAR  Intercept ', 	start=list(b0=1))
#the potential covariates
covB<-cbind(cos(2*pi*BarTxTn$dia/365), sin(2*pi*BarTxTn$dia/365), 
	BarTxTn$TTx,BarTxTn$Txm31,BarTxTn$Txm31**2)
dimnames(covB)<-list(NULL,c('cos','sin','TTx','Txm31', 'Txm31**2'))

bb<-stepAICmle.fun(ImlePP=mod1Bind, covariates=covB, startAdd=c(1,-1,0,0,0), 
direction='both')