Package 'ProSGPV' reference manual

Title:	Penalized Regression with Second-Generation P-Values
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>.
Authors:	Yi Zuo [aut, cre] , Thomas Stewart [aut], Jeffrey Blume [aut]
Maintainer:	Yi Zuo <[email protected]>
License:	GPL-3
Version:	1.0.1
Built:	2025-01-25 03:33:43 UTC
Source:	https://github.com/zuoyi93/prosgpv

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

Arguments

`object`	An `sgpv` object
`...`	Other `coef` 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)
# 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
)
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

`n`	Number of observations. Default is 100.
`p`	Number of explanatory variables. Default is 50.
`s`	Number of true signals. It can only be an even number. Default is 10.
`family`	A description of the error distribution and link function to be used in the model. It can take the value of `⁠\code{gaussian}⁠`, `⁠\code{binomial}⁠`, `⁠\code{poisson}⁠`, and `⁠\code{cox}⁠`. Default is `⁠\code{gaussian}⁠`
`beta.min`	The smallest effect size in absolute value. Default is 1.
`beta.max`	The largest effect size in absolute value. Default is 5.
`rho`	Autocorrelation level. A numerical value between -1 and 1. Default is 0.
`nu`	Signal to noise ratio in linear regression. Default is 2.
`sig`	Standard deviation in the design matrix. Default is 1.
`intercept`	Intercept of the linear predictor in the GLM. Default is 0.
`scale`	Scale parameter in the Weibull distribution. Default is 2.
`shape`	Shape parameter in the Weibull distribution. Default is 1.
`rateC`	Rate of censoring in the survival data. Default is 0.2.

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]]
# 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)
get.candidate(xs, ys, family)

Arguments

`xs`	Standardized independent variables
`ys`	Standardized dependent variable
`family`	A description of the error distribution and link function to be used in the model. It can take the value of `⁠\code{gaussian}⁠`, `⁠\code{binomial}⁠`, `⁠\code{poisson}⁠`, and `⁠\code{cox}⁠`.

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

Arguments

`xs`	Standardized design matrix
`ys`	Standardized outcome
`lambda`	`lambda` in the lasso
`lasso`	An `glmnet` object
`family`	A description of the error distribution and link function to be used in the model. It can take the value of `⁠\code{gaussian}⁠`, `⁠\code{binomial}⁠`, `⁠\code{poisson}⁠`, and `⁠\code{cox}⁠`.

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

Arguments

`candidate.index`	Indices of the candidate set
`xs`	Standardized independent variables
`ys`	Standardized dependent variable
`family`	A description of the error distribution and link function to be used in the model. It can take the value of `⁠\code{gaussian}⁠`, `⁠\code{binomial}⁠`, `⁠\code{poisson}⁠`, and `⁠\code{cox}⁠`.
`gvif`	A logical operator indicating whether a generalized variance inflation factor-adjusted null bound is used. Default is FALSE.

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)
gvif(mod, family)

Arguments

`mod`	A model object with at least two explanatory variables
`family`	A description of the error distribution and link function to be used in the model. It can take the value of `⁠\code{gaussian}⁠`, `⁠\code{binomial}⁠`, `⁠\code{poisson}⁠`, and `⁠\code{cox}⁠`.

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

Arguments

`x`	An `sgpv` object
`lpv`	Lines per variable. It can take the value of 1 meaning that only the bound that is closest to the null will be plotted, or the value of 3 meaning that point estimates as well as 95% confidence interval will be plotted. Default is 3.
`lambda.max`	The maximum lambda on the plot. Default is `NULL`.
`short.label`	An indicator if a short label is used for each variable for better visualization. Default is `TRUE`
`...`	Other `plot` 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)
# 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, ...)
## S3 method for class 'sgpv'
predict(object, newdata, type, ...)

Arguments

`object`	An `sgpv` objectect
`newdata`	Prediction data set
`type`	The type of prediction required. Can take the value of `link`, `response`, and `terms`. Default is `response`.
`...`	Other `predict` 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)
# 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, ...)
## S3 method for class 'sgpv'
print(x, ...)

Arguments

`x`	An `sgpv` object
`...`	Other `print` 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
# 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
)
pro.sgpv(
  x,
  y,
  stage = c(1, 2),
  family = c("gaussian", "binomial", "poisson", "cox"),
  gvif = F
)

Arguments

`x`	Independent variables, can be a `matrix` or a `data.frame`
`y`	Dependent variable, can be a `vector` or a column from a `data.frame`
`stage`	Algorithm indicator. 1 denotes the one-stage algorithm and 2 denotes the two-stage algorithm. Default is 2. When `n` is less than `p`, only the two-stage algorithm is available.
`family`	A description of the error distribution and link function to be used in the model. It can take the value of `⁠\code{gaussian}⁠`, `⁠\code{binomial}⁠`, `⁠\code{poisson}⁠`, and `⁠\code{cox}⁠`. Default is `⁠\code{gaussian}⁠`
`gvif`	A logical operator indicating whether a generalized variance inflation factor-adjusted null bound is used. Default is FALSE. See Fox (1992) doi:10.1080/01621459.1992.10475190 for more details on how to calculate GVIF

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

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

Arguments

`object`	An `sgpv` object
`...`	Other 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)
# 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
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

Package 'ProSGPV'

Help Index

coef.sgpv: Extract coefficients from the model fit

Description

Usage

Arguments

Value

Examples

gen.sim.data: Generate simulation data

Description

Usage

Arguments

Value

Examples

get.candidate: Get candidate set

Description

Usage

Arguments

Value

get.coef: Get coefficients at each lambda

Description

Usage

Arguments

Value

get.var: Get indices

Description

Usage

Arguments

Value

gvif: Get GVIF for each variable

Description

Usage

Arguments

Value

plot.sgpv: Plot variable selection results

Description

Usage

Arguments

Examples

predict.sgpv: Prediction using the fitted model

Description

Usage

Arguments

Value

Examples

print.sgpv: Print variable selection results

Description

Usage

Arguments

Value

Examples

pro.sgpv function

Description

Usage

Arguments

Value

See Also

Examples

Spine data

Description

Usage

Format

Source

summary.sgpv: Summary of the final model

Description

Usage

Arguments

Value

Examples

Tehran housing data

Description

Usage

Format

Source

`coef.sgpv`: Extract coefficients from the model fit

`gen.sim.data`: Generate simulation data

`get.candidate`: Get candidate set

`get.coef`: Get coefficients at each `lambda`

`get.var`: Get indices

`gvif`: Get GVIF for each variable

`plot.sgpv`: Plot variable selection results

`predict.sgpv`: Prediction using the fitted model

`print.sgpv`: Print variable selection results

`pro.sgpv` function

`summary.sgpv`: Summary of the final model