Exploratory.Phase {HCmodelSets}

Perform the Exploratory phase on the hypercube dimension reduction proposed by Cox, D. R. & Battey, H. S. (2017)

Description

This function performs the exploratory phase on the variables retained through the reduction phase, returning any significant squared and interaction terms.

Usage

Exploratory.Phase(X, Y, list.reduction, family=gaussian,
                  signif=0.01, silent=TRUE, Cox.Hazard = FALSE)

Arguments

X

Design matrix.

Y

Response vector.

list.reduction

Indices of retained variables from the reduction phase.

family

A description of the error distribution and link function to be used in the model. For glm this can be a character string naming a family function, a family function or the result of a call to a family function. See family for more details.

signif

Significance level for the assessment of squared and interaction terms. The default is 0.01.

silent

By default, silent=TRUE. If silent=FALSE the user can decide upon the exclusion of individual interaction terms.

Cox.Hazard

If TRUE fits proportional hazards regression model. The family argument will be ignored if Cox.Hazard=TRUE.

Value

mat.select.SQ

Indices of variables with significant squared terms.

mat.select.INTER

Indices of the pairs of variables with significant interaction terms.

Acknowledgement

The work was supported by the UK Engineering and Physical Sciences Research Council under grant number EP/P002757/1.

Author(s)

Hoeltgebaum, H. H.

References

Cox, D. R., and Battey, H. S. (2017). Large numbers of explanatory variables, a semi-descriptive analysis. Proceedings of the National Academy of Sciences, 114(32), 8592-8595.

Battey, H. S. and Cox, D. R. (2018). Large numbers of explanatory variables: a probabilistic assessment. Proceedings of the Royal Society of London, A., 474(2215), 20170631.

Hoeltgebaum, H., & Battey, H. S. (2019). HCmodelSets: An R Package for Specifying Sets of Well-fitting Models in High Dimensions. The R Journal, 11(2), 370-379.

See Also

Reduction.Phase

Examples

## Generates a random DGP
dgp = DGP(s=5, a=3, sigStrength=1, rho=0.9, n=100, intercept=5, noise=1,
          var=1, d=1000, DGP.seed = 2018)

#Reduction Phase using only the first 70 observations
outcome.Reduction.Phase =  Reduction.Phase(X=dgp$X[1:70,],Y=dgp$Y[1:70],
                                           family=gaussian, seed.HC = 1012)

# Exploratory Phase using only the first 70 observations, choosing the variables which
# were selected at least two times in the third dimension reduction

idxs = outcome.Reduction.Phase$List.Selection$`Hypercube with dim 2`$numSelected1
outcome.Exploratory.Phase =  Exploratory.Phase(X=dgp$X[1:70,],Y=dgp$Y[1:70],
                                               list.reduction = idxs,
                                               family=gaussian, signif=0.01)