HCmodelSets (version 1.1.3)

Exploratory.Phase: 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)

Value

mat.select.SQ

Indices of variables with significant squared terms.

mat.select.INTER

Indices of the pairs of variables with significant interaction terms.

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.

Author

Hoeltgebaum, H. H.

Acknowledgement

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

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

# \donttest{
## 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)
# }

# \dontshow{
dgp = DGP(s=5, a=3, sigStrength=1, rho=0.9, n=20, intercept=5, noise=1,
          var=1, d=50, DGP.seed = 2019)

#Reduction Phase using only the first 70 observations
outcome.Reduction.Phase =  Reduction.Phase(X=dgp$X[1:10,],Y=dgp$Y[1:10],
                                           dmHC = 2, family=gaussian, seed.HC = 1093)

# 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`$numSelected2
outcome.Exploratory.Phase =  Exploratory.Phase(X=dgp$X[1:10,],Y=dgp$Y[1:10],
                                               list.reduction = idxs,
                                               family=gaussian, signif=0.01)

# }