selection {envlpaster} R Documentation

## selection

### Description

Finds the envelope eigenspace or dimension that is favored using AIC, BIC, or the LRT at a specified size.

### Usage

  selection(parm, index, model, data = NULL, alpha = 0.05,
type = c("canonical","mean-value"), method = c("eigen","1d"))


### Arguments

 parm The MLE of the parameter of interest. index The indices denoting which components of the canonical parameter vector are parameters of interest. model An aster model object. data An asterdata object. alpha The desired size of the LRT. type The parameterization of the aster model in which envelope methods are being applied. method The procedure used to obtain envelope estimators.

### Details

This function provides the user with the envelope model dimension or indices of the eigenspace favored by AIC, BIC, and the likelihood ratio test of size alpha. There are four possible combinations of outputs. They are:

1. [1.] The specification of method = "eigen" and type = "mean-value" provides the user with the indices of the eigenspace of estimated Fisher information used to construct an envelope estimator for \tau favored by AIC, BIC, and the LRT of size alpha.

2. [2.] The specification of method = "eigen" and type = "canonical" provides the user with the indices of the eigenspace of estimated Fisher information used to construct an envelope estimator for \beta favored by AIC, BIC, and the LRT of size alpha.

3. [3.] The specification of method = "1d" and type = "mean-value" provides the user with the envelope model dimension used to construct an envelope estimator for \tau favored by AIC, BIC, and the LRT of size alpha.

4. [4.] The specification of method = "1d" and type = "canonical" provides the user with the envelope model dimension used to construct an envelope estimator for \beta favored by AIC, BIC, and the LRT of size alpha.

When one is interested in envelope model dimensions or eigenspaces with respect to \beta, then an asterdata object does not need to be specified. On the other hand, an asterdata is needed in order to map the estimated \tau to its corresponding \beta value. This is necessary because of the interface (or lack thereof) between current aster and aster2 software. The way in which aster model log likelihoods are evaluated is incorporated in aster software and changing parameterizations is carried out using aster2 software.

### Value

 aic The eigenspace or envelope model dimension favored using AIC. bic The eigenspace or envelope model dimension favored using BIC. LRT The eigenspace or envelope model dimension favored using the LRT of size alpha. out The output table of all model selection criteria for all envelope estimators considered.

### References

Cook, R.D. and Zhang, X. (2014). Foundations for Envelope Models and Methods. JASA, In Press.

Cook, R.D. and Zhang, X. (2015). Algorithms for Envelope Estimation. Journal of Computational and Graphical Statistics, Published online. doi: 10.1080/10618600.2015.1029577.

Eck, D. J., Geyer, C. J., and Cook, R. D. (2016). Enveloping the aster model. in prep.

### Examples

## Not run:
set.seed(13)
library(envlpaster)
library(aster2)
data(generateddata)
m.null <- aster(resp ~ 0 + varb, fam = fam, pred = pred,
varvar = varb, idvar = id, root = root, data = redata)
m1 <- aster(resp ~ 0 + varb + mass + timing,
fam = fam, pred = pred, varvar = varb, idvar = id,
root = root, data = redata)
m2 <- aster(resp ~ 0 + varb + mass + timing +
I(mass^2) + I(timing^2) + I(mass*timing),
fam = fam, pred = pred, varvar = varb, idvar = id,
root = root, data = redata)
anova.table <- anova(m.null,m1,m2); anova.table
beta <- m1$coef a <- grepl( "offsp", names(beta)) a <- a + grepl( "surviv", names(beta)) b <- which(a == 1) target <- c(1:length(beta))[-b] nnode <- ncol(m1$x)
data.aster <- asterdata(data, vars, pred, rep(0,nnode),
fam, families = list("bernoulli", "poisson",
fam.zero.truncated.poisson()))
selection(parm  = beta, index = target, model = m1,
data = data.aster, alpha = 0.05, type = "canonical",
method = "eigen")

## End(Not run)


[Package envlpaster version 0.1-2 Index]