Title:	Penalized Regression with Second-Generation P-Values
Version:	1.0.0
Date:	2021-08-06
Maintainer:	Yi Zuo <yi.zuo@vanderbilt.edu>
Description:	Implementation of penalized regression with second-generation p-values for variable selection. The algorithm can handle linear regression, GLM, and Cox regression. S3 methods print(), summary(), coef(), predict(), and plot() are available for the algorithm. Technical details can be found at Zuo et al. (2021) <doi:10.1080/00031305.2021.1946150>.
Depends:	R (≥ 3.5.0), glmnet, brglm2
Imports:	MASS, survival
License:	GPL-3
Encoding:	UTF-8
URL:	https://github.com/zuoyi93/ProSGPV
BugReports:	https://github.com/zuoyi93/ProSGPV/issues
LazyData:	true
RoxygenNote:	7.1.1
Suggests:	rmarkdown, knitr
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2021-08-06 16:27:07 UTC; Buzzzuoyi
Author:	Yi Zuo [aut, cre], Thomas Stewart [aut], Jeffrey Blume [aut]
Repository:	CRAN
Date/Publication:	2021-08-06 21:40:02 UTC

coef.sgpv: Extract coefficients from the model fit

Description

S3 method coef for an S3 object of class sgpv

Usage

## S3 method for class 'sgpv'
coef(object, ...)

Arguments

Value

Coefficients in the OLS model

Examples

# prepare the data
x <- t.housing[, -ncol(t.housing)]
y <- t.housing$V9

# run one-stage algorithm
out.sgpv <- pro.sgpv(x = x, y = y)

# get coefficients
coef(out.sgpv)

gen.sim.data: Generate simulation data

Description

This function can be used to generate autoregressive simulation data

Usage

gen.sim.data(
  n = 100,
  p = 50,
  s = 10,
  family = c("gaussian", "binomial", "poisson", "cox"),
  beta.min = 1,
  beta.max = 5,
  rho = 0,
  nu = 2,
  sig = 1,
  intercept = 0,
  scale = 2,
  shape = 1,
  rateC = 0.2
)

Arguments

Value

A list of following components:

X

The generated explanatory variable matrix

Y

A vector of outcome. If family is ⁠\code{cox}⁠, a two-column object is returned where the first column is the time and the second column is status (0 is censoring and 1 is event)

index

The indices of true signals

beta

The true coefficient vector of length p

Examples

# generate data for linear regression
data.linear <- gen.sim.data(n = 20, p = 10, s = 4)

# extract x
x <- data.linear[[1]]

# extract y
y <- data.linear[[2]]

# extract the indices of true signals
index <- data.linear[[3]]

# extract the true coefficient vector
true.beta <- data.linear[[4]]

# generate data for logistic regression
data.logistic <- gen.sim.data(n = 20, p = 10, s = 4, family = "binomial")

# extract x
x <- data.logistic[[1]]

# extract y
y <- data.logistic[[2]]

# extract the indices of true signals
index <- data.logistic[[3]]

# extract the true coefficient vector
true.beta <- data.logistic[[4]]

get.candidate: Get candidate set

Description

Get the indices of the candidate set in the first stage

Usage

get.candidate(xs, ys, family)

Arguments

Value

A list of following components:

candidate.index

A vector of indices of selected variables in the candidate set

lambda

The lambda selected by generalized information criterion

get.coef: Get coefficients at each lambda

Description

Get the coefficients and confidence intervals from regression at each lambda as well as the null bound in SGPVs

Usage

get.coef(xs, ys, lambda, lasso, family)

Arguments

Value

A vector that contains the point estimates, confidence intervals and the null bound

get.var: Get indices

Description

Get the indices of the variables selected by the algorithm

Usage

get.var(candidate.index, xs, ys, family, gvif)

Arguments

Value

A list of following components:

out.sgpv

A vector of indices of selected variables

null.bound.p

Null bound in the SGPV screening

pe

Point estimates in the candidate set

lb

Lower bounds of effect estimates in the candidate set

ub

Upper bounds of effect estimates in the candidate set

gvif: Get GVIF for each variable

Description

Get generalized variance inflation factor (GVIF) for each variable. See Fox (1992) doi: 10.1080/01621459.1992.10475190 for more details on how to calculate GVIF.

Usage

gvif(mod, family)

Arguments

Value

A vector of GVIF for each variable in the model

plot.sgpv: Plot variable selection results

Description

S3 method plot for an object of class sgpv. When the two-stage algorithm is used, this function plots the fully relaxed lasso solution path on the standardized scale and the final variable selection results. When the one-stage algorithm is used, a histogram of all coefficients with selected effects is shown.

Usage

## S3 method for class 'sgpv'
plot(x, lpv = 3, lambda.max = NULL, short.label = T, ...)

Arguments

Examples

# prepare the data
x <- t.housing[, -ncol(t.housing)]
y <- t.housing$V9

# one-stage algorithm
out.sgpv.1 <- pro.sgpv(x = x, y = y, stage = 1)

# plot the selection result

plot(out.sgpv.1)

# two-stage algorithm
out.sgpv.2 <- pro.sgpv(x = x, y = y)

# plot the fully relaxed lasso solution path and final solution
plot(out.sgpv.2)

# zoom in a little bit
plot(out.sgpv.2, lambda.max = 0.01)

# only plot one confidence bound
plot(out.sgpv.2, lpv = 1, lambda.max = 0.01)

predict.sgpv: Prediction using the fitted model

Description

S3 method predict for an object of class sgpv

Usage

## S3 method for class 'sgpv'
predict(object, newdata, type, ...)

Arguments

Value

Predicted values

Examples

# prepare the data
x <- t.housing[, -ncol(t.housing)]
y <- t.housing$V9

# run one-stage algorithm
out.sgpv <- pro.sgpv(x = x, y = y)

predict(out.sgpv)

print.sgpv: Print variable selection results

Description

S3 method print for an S3 object of class sgpv

Usage

## S3 method for class 'sgpv'
print(x, ...)

Arguments

Value

Variable selection results

Examples

# prepare the data
x <- t.housing[, -ncol(t.housing)]
y <- t.housing$V9

# run one-stage algorithm
out.sgpv.1 <- pro.sgpv(x = x, y = y, stage = 1)

out.sgpv.1

pro.sgpv function

Description

This function outputs the variable selection results from either one-stage algorithm or two-stage algorithm.

Usage

pro.sgpv(
  x,
  y,
  stage = c(1, 2),
  family = c("gaussian", "binomial", "poisson", "cox"),
  gvif = F
)

Arguments

Value

A list of following components:

var.index

A vector of indices of selected variables

var.label

A vector of labels of selected variables

lambda

lambda selected by generalized information criterion in the two-stage algorithm. NULL for the one-stage algorithm

x

Input data x

y

Input data y

family

family from the input

stage

stage from the input

null.bound

Null bound in the SGPV screening

pe.can

Point estimates in the candidate set

lb.can

Lower bounds of CI in the candidate set

ub.can

Upper bounds of CI in the candidate set

See Also

• print.sgpv() prints the variable selection results

• coef.sgpv() extracts coefficient estimates

• summary.sgpv() summarizes the OLS outputs

• predict.sgpv() predicts the outcome

• plot.sgpv() plots variable selection results

Examples

# prepare the data
x <- t.housing[, -ncol(t.housing)]
y <- t.housing$V9

# run ProSGPV in linear regression
out.sgpv <- pro.sgpv(x = x, y = y)

# More examples at https://github.com/zuoyi93/ProSGPV/tree/master/vignettes

Spine data

Description

Lower back pain can be caused by a variety of problems with any parts of the complex, interconnected network of spinal muscles, nerves, bones, discs or tendons in the lumbar spine. This dataset contains 12 biomechanical attributes from 310 patients, of whom 100 are normal and 210 are abnormal (Disk Hernia or Spondylolisthesis). The goal is to differentiate the normal patients from the abnormal using those 12 variables.

Usage

spine

Format

pelvic_incidence

pelvic incidence

pelvic_tilt

pelvic tilt

lumbar_lordosis_angle

lumbar lordosis angle

sacral_slope

sacral slope

pelvic_radius

pelvic radius

degree_spondylolisthesis

degree of spondylolisthesis

pelvic_slope

pelvic slope

direct_tilt

direct tilt

thoracic_slope

thoracic slope

cervical_tilt

cervical tilt

sacrum_angle

sacrum angle

scoliosis_slope

scoliosis slope

outcome

1 is abnormal (Disk Hernia or Spondylolisthesis) and 0 is normal

Source

http://archive.ics.uci.edu/ml/datasets/vertebral+column

summary.sgpv: Summary of the final model

Description

S3 method summary for an S3 object of class sgpv

Usage

## S3 method for class 'sgpv'
summary(object, ...)

Arguments

Value

Summary of a model

Examples

# prepare the data
x <- t.housing[, -ncol(t.housing)]
y <- t.housing$V9

# run one-stage algorithm
out.sgpv <- pro.sgpv(x = x, y = y)

# get regression summary
summary(out.sgpv)

Tehran housing data

Description

A dataset containing Tehran housing data. The data set has 372 observations. There are 26 explanatory variables at baseline, including 7 project physical and financial features (V2-V8) and 19 economic variables and indices (V11-V29). The outcome (V9) is the sales price of a real estate single-family residential apartment.

Usage

t.housing

Format

V9

Actual sales price

V2

Total floor area of the building

V3

Lot area

V4

Total Preliminary estimated construction cost based on the prices at the beginning of the project

V5

Preliminary estimated construction cost based on the prices at the beginning of the project

V6

Equivalent preliminary estimated construction cost based on the prices at the beginning of the project in a selected base year

V7

Duration of construction

V8

Price of the unit at the beginning of the project per square meter

V11

The number of building permits issued

V12

Building services index for preselected base year

V13

Wholesale price index of building materials for the base year

V14

Total floor areas of building permits issued by the city/municipality

V15

Cumulative liquidity

V16

Private sector investment in new buildings

V17

Land price index for the base year

V18

The number of loans extended by banks in a time resolution

V19

The amount of loans extended by banks in a time resolution

V20

The interest rate for loan in a time resolution

V21

The average construction cost by private sector at the completion of construction

V22

The average cost of buildings by private sector at the beginning of construction

V23

Official exchange rate with respect to dollars

V24

Nonofficial (street market) exchange rate with respect to dollars

V25

Consumer price index (CPI) in the base year

V26

CPI of housing, water, fuel & power in the base year

V27

Stock market index

V28

Population of the city

V29

Gold price per ounce

Source

http://archive.ics.uci.edu/ml/datasets/Residential+Building+Data+Set