drop1SignifReg {SignifReg}

Drop a predictor to a (generalized) linear regression model using the backward step in the Significance Controlled Variable Selection method

Description

drop1SignifReg removes from the model the predictor, out of the current predictors, which minimizes the criterion (AIC, BIC, r-ajd, PRESS, max p-value) when a) the p-values of the predictors in the current model do not pass the multiple testing correction (Bonferroni, FDR, None, etc) or b) when the p-values of both current and prospective models pass the correction but the criterion of the prospective model is smaller.

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 to be added to the model 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

drop1SignifReg(fit, scope, alpha = 0.05, criterion = "p-value", 
  adjust.method = "fdr", override = FALSE, print.step = FALSE)

Arguments

fit

an lm or glm object representing a model.

scope

defines the range of models examined in the stepwise search. This should be either a single formula, or a list containing components upper and lower, both formulae. See the details for how to specify the formulae and how they are used.

alpha

Significance level. Default value is 0.05.

criterion

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

adjust.method

Correction for multiple testing accumulation of error. See p.adjust.

override

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

print.step

If true, information is printed for each step of variable selection. Default is FALSE.

Value

drop1SifnifReg returns an object of the class lm or glm for a generalized regression model with the additional component steps.info, which shows the steps taken during the variable selection and model metrics: Deviance, Resid.Df, Resid.Dev, AIC, BIC, adj.rsq, PRESS, max_pvalue, max.VIF, and whether it passed the chosen p-value correction.

Author(s)

Jongwook Kim <[e-mail]>

Adriano Zanin Zambom <[e-mail]>

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, add1SignifReg, drop1summary,

Examples

##mtcars data is used as an example.

data(mtcars)

fit <- lm(mpg~., mtcars)
drop1SignifReg(fit, print.step = TRUE)