SignifReg (version 3.0)

add1SignifReg: Add a predictor to a linear regression model using the forward step in the Significance Controlled Variable Selection method

Description

add1SignifReg includes in the model the predictor, out of the available predictors, which minimizes the criterion (AIC, BIC, r-ajd, PRESS, max p-value) as long as all the p-values of the predictors in the prospective model (including the prospective predictor) are below the chosen correction method (Bonferroni, FDR, None). The function provides a summary table of the prospective models.

max_pvalue indicates the maximum p-value from the multiple t-tests for each predictor. More specifically, the algorithm computes the prospective models with each predictor included, and all p-values of this prospective model. Then, the predictor selected is the one whose generating model has the smallest p-values, in fact, the minimum of the maximum p-values in each prospective model.

Usage

add1SignifReg(fit, scope, alpha = 0.05, criterion = "p-value",
 correction = "FDR", override = FALSE)

Arguments

fit

an lm object representing a linear regression model.

scope

The range of models examined in regression. It should be either a data.frame or formula containing predictors. When scope is data.frame, all variables except the response variable in the data.frame are considered.

alpha

Significance level. Default value is 0.05.

criterion

Criterion to select predictor variables. criterion = "AIC", criterion = "BIC", criterion = "r-adj" (adjusted r-square), and criterion = "p-value" are available. Default is p-value.

correction

Correction criterion to reduce multiple testing error. correction = "FDR" (False Discovery Rate), correction = "Bonferroni", and

correction = "None" (no correction) are available. Default is

correction = "FDR" . For Bonferroni correction,

either correction = "Bonferroni" or correction = "Bonf" can be used.

override

If override = TRUE, it returns a new lm object that adds a new variable according to criterion even if the new model does not pass the multiple testing p-value correction.

References

Zambom A Z, Kim J. Consistent significance controlled variable selection in high-dimensional regression. Stat.2018;7:e210. https://doi.org/10.1002/sta4.210

See Also

SignifReg, add1summary, drop1summary, drop1SignifReg

Examples

# NOT RUN {
##mtcars data is used as an example.

data(mtcars)

fit1 <- lm(mpg~1, mtcars)
add1SignifReg(fit1)

fit2 <- lm(mpg~disp+cyl+wt+qsec, mtcars)
add1SignifReg(fit2, criterion="AIC", override="TRUE")
# }