Forward stepwise selection procedure for penalized logistic regression

Description

This function fits a series of L2 penalized logistic regression models selecting variables through the forward stepwise selection procedure.

Usage

1
2
3
4
  step.plr(x, y, weights = rep(1,length(y)), fix.subset = NULL,
           level = NULL, lambda = 1e-4, cp = "bic", max.terms = 5,
           type = c("both", "forward", "forward.stagewise"),
           trace = FALSE)  

Arguments

x

matrix of features

y

binary response

weights

optional vector of weights for observations

fix.subset

vector of indices for the variables that are forced to be in the model

level

list of length ncol(x). The j-th element corresponds to the j-th column of x. If the j-th column of x is discrete, level[[j]] is the set of levels for the categorical factor. If the j-th column of x is continuous, level[[j]] = NULL. level is automatically generated in the function; however, if any levels of the categorical factors are not observed, but still need to be included in the model, then the user must provide the complete sets of the levels through level. If a numeric column needs to be considered discrete, it can be done by manually providing level as well.

lambda

regularization parameter for the L2 norm of the coefficients. The minimizing criterion in plr is -log-likelihood+λ*\|β\|^2. Default is lambda=1e-4.

cp

complexity parameter to be used when computing the score. score=deviance+cp*df. If cp="aic" or cp="bic", these are converted to cp=2 or cp=log(sample size), respectively. Default is cp="bic".

max.terms

maximum number of terms to be added in the forward selection procedure. Default is max.terms=5.

type

If type="both", forward selection is followed by a backward deletion. If type="forward", only a forward selection is done. If type="forward.stagewise", variables are added in the forward-stagewise method. Default is "both".

trace

If TRUE, the variable selection procedure prints out its progress.

Details

This function implements an L2 penalized logistic regression along with the stepwise variable selection procedure, as described in "Penalized Logistic Regression for Detecting Gene Interactions (2008)" by Park and Hastie.

If type="forward", max.terms terms are sequentially added to the model, and the model that minimizes score is selected as the optimal fit. If type="both", a backward deletion is done in addition, which provides a series of models with a different combination of the selected terms. The optimal model minimizing score is chosen from the second list.

Value

A stepplr object is returned. anova, predict, print, and summary functions can be applied.

fit

plr object for the optimal model selected

action

list that stores the selection order of the terms in the optimal model

action.name

list of the names of the sequentially added terms - in the same order as in action

deviance

deviance of the fitted model

df

residual degrees of freedom of the fitted model

score

deviance + cp*df, where df is the model degrees of freedom

group

vector of the counts for the dummy variables, to be used in predict.stepplr

y

response variable used

weight

weights used

fix.subset

fix.subset used

level

level used

lambda

lambda used

cp

complexity parameter used when computing the score

type

type used

xnames

column names of x

Author(s)

Mee Young Park and Trevor Hastie

References

Mee Young Park and Trevor Hastie (2008) Penalized Logistic Regression for Detecting Gene Interactions

See Also

cv.step.plr, plr, predict.stepplr

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
n <- 100

p <- 3
z <- matrix(sample(seq(3),n*p,replace=TRUE),nrow=n)
x <- data.frame(x1=factor(z[ ,1]),x2=factor(z[ ,2]),x3=factor(z[ ,3]))
y <- sample(c(0,1),n,replace=TRUE)
fit <- step.plr(x,y)
# 'level' is automatically generated. Check 'fit$level'.

p <- 5
x <- matrix(sample(seq(3),n*p,replace=TRUE),nrow=n)
x <- cbind(rnorm(n),x)
y <- sample(c(0,1),n,replace=TRUE)
level <- vector("list",length=6)
for (i in 2:6) level[[i]] <- seq(3)
fit1 <- step.plr(x,y,level=level,cp="aic")
fit2 <- step.plr(x,y,level=level,cp=4)
fit3 <- step.plr(x,y,level=level,type="forward")
fit4 <- step.plr(x,y,level=level,max.terms=10)
# This is an example in which 'level' was input manually.
# level[[1]] should be either 'NULL' or 'NA' since the first factor is continuous.