SignifReg {SignifReg}

Significance Controlled Variable Selection in (Generalized) Linear Regression

Description

Significance controlled variable selection selects variables in a generalized linear regression model with different directions of the algorithm (forward, backward, stepwise) based on a chosen criterion (AIC, BIC, adjusted r-square, PRESS or p-value). The algorithm selects a final model with only significant variables based on a correction choice of False Discovery Rate, Bonferroni, etc from the p.adjust().

Usage

SignifReg(fit, scope, alpha = 0.05, direction = "forward",
  criterion = "p-value", adjust.method = "fdr", trace=FALSE)

Arguments

fit

an lm or glm object representing a model. It is an initial model for the variable selection.

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.

direction

Direction in variable selection: direction = "both",

direction = "forward", and

direction = "backward" are available. direction = "both" is a stepwise selection. Default is direction = "forward".

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.

trace

If true, information is printed for each step of variable selection. Default is FALSE. Offers summaries of prospective models as each predictor in the scope is added to or removed from the model. max_pvalue indicates the maximum p-value from the multiple t-tests for each predictor in the model.

Details

SignifReg selects only significant predictors according to a designated criterion. A model with the best criterion, for example, the smallest AIC, will not be considered if it includes insignificant predictors based on the chosen correction. When the criterion is "p-value", a predictor can be droped only if the current model has an insignificant pedictor, and a predictor can be added as long as the prospective model has all predictors significant (including the one to be added). The predictor to be added or removed is the one that generates a model having the smallest maximum p-value of the t-tests in the prospective models. This step is repeated as long as every predictor is significant according to the correction criterion. In the case that the criterion is "AIC", and "BIC", SignifReg selects, at each step, the model having the smallest value of the criterion among models having only significant predictors according to the chosen correction.

Value

SifnifReg 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

add1SignifReg, drop1SignifReg, add1summary, drop1summary

Examples

##mtcars data is used as an example.

data(mtcars)
nullmodel = lm(mpg~1, mtcars)
fullmodel = lm(mpg~., mtcars)
scope = list(lower=formula(nullmodel),upper=formula(fullmodel))


fit1 <- lm(mpg~1, mtcars)
select.fit = SignifReg(fit1, scope = scope, direction = "forward", trace = TRUE)
select.fit$steps.info

fit = lm(mpg ~cyl + hp + am + gear, data = mtcars)
select.fit = SignifReg(fit,scope=scope, alpha = 0.05,direction = "backward",
  criterion = "p-value",adjust.method = "fdr",trace=TRUE)
select.fit$steps.info



fit = lm(mpg ~ cyl + hp + am + gear + disp, data = mtcars)
select.fit = SignifReg(fit,scope=scope, alpha = 0.5,direction = "both",
  criterion = "AIC",adjust.method = "fdr",trace=TRUE)
select.fit$steps.info