Type:	Package
Title:	Penalized Quantile Regression with Fixed Effects
Version:	1.1
Date:	2022-12-01
Description:	Quantile regression with fixed effects is a general model for longitudinal data. Here we proposed to solve it by several methods. The estimation methods include three loss functions as check, asymmetric least square and asymmetric Huber functions; and three structures as simple regression, fixed effects and fixed effects with penalized intercepts by LASSO.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Imports:	Rcpp (≥ 1.0.5), MASS (≥ 7.3-49)
LinkingTo:	Rcpp, RcppArmadillo
Suggests:	tinytest (≥ 1.3.1)
RoxygenNote:	7.2.1
NeedsCompilation:	yes
Packaged:	2022-12-01 11:01:53 UTC; ian
Author:	Ian Meneghel Danilevicz [aut, cre], Valderio A Reisen [aut], Pascal Bondon [aut]
Maintainer:	Ian Meneghel Danilevicz <iandanilevicz@gmail.com>
Repository:	CRAN
Date/Publication:	2022-12-01 11:20:02 UTC

Penalized Quantile Regression with Fixed Effects

Description

Quantile regression with fixed effects is a general model for longitudinal data. Here we proposed to solve it by several methods. The estimation methods include three loss functions as check, asymmetric least square and asymmetric Huber functions; and three structures as simple regression, fixed effects and fixed effects with penalized intercepts by LASSO.

Package Content

Index of help topics:

check_lambda            check lambda
choice_p                choice model
clean_data              Clean missings
d_psi_als               D Psi ALS
d_psi_mq                D Psi M-quantile
f_den                   Kernel density
f_tab                   Tabular function
loss_er                 Loss expectile regression
loss_erfe               Loss expectile regression with fixed effects
loss_erlasso            Loss lasso expectile regression with fixed
                        effects
loss_mqr                Loss M-quantile regression
loss_mqrfe              Loss M-quantile regression with fixed effects
loss_mqrlasso           Loss lasso M-quantile regression with fixed
                        effects
loss_qr                 Loss quantile regression
loss_qrfe               Loss quantile regression with fixed effects
loss_qrlasso            Loss lasso quantile regression with fixed
                        effects
mpqr                    Multiple penalized quantile regression
optim_er                optim expectile regression
optim_erfe              optim expectile regression with fixed effects
optim_erlasso           optim expectile regression with fixed effects
                        and LASSO
optim_mqr               optim M-quantile regression
optim_mqrfe             optim quantile regression with fixed effects
optim_mqrlasso          optim M-quantile regression with fixed effects
                        and LASSO
optim_qr                optim quantile regression
optim_qrfe              optim quantile regression with fixed effects
optim_qrlasso           optim quantile regression with fixed effects
                        and LASSO
plot_taus               Plot multiple penalized quantile regression
pqr                     Penalized quantile regression with fixed
                        effects
pqrfe-package           Penalized Quantile Regression with Fixed
                        Effects
print.PQR               Print an PQR
psi_als                 Psi ALS
psi_mq                  Psi M-quantile
q_cov                   Covariance
rho_koenker             Rho Koenker
rho_mq                  Rho M-quantile
sgf                     Identify significance

Maintainer

NA

Author(s)

NA

check lambda

Description

check lambda

Usage

check_lambda(lambda, infb, supb)

Arguments

Value

lambda Numeric, valid value of lambda.

choice model

Description

choice model

Usage

choice_p(effect)

Arguments

Value

penalty Numeric, 1, 2 and 3.

Clean missings

Description

Clean missings

Usage

clean_data(y, x, id)

Arguments

Value

list with the same objects y, x, id, but without missings.

Examples

n = 10
m = 4
d = 3
N = n*m
L = N*d
x = matrix(rnorm(L), ncol=d, nrow=N)
subj = rep(1:n, each=m)
alpha = rnorm(n)
beta = rnorm(d)
eps = rnorm(N)
y = x %*% beta  + matrix(rep(alpha, each=m) + eps)
y = as.vector(y)
x[1,3] = NA
clean_data(y=y, x=x, id=subj)  
 

D Psi ALS

Description

Derivative of Psi asymetric least square

Usage

d_psi_als(x, tau)

Arguments

Value

y vector, linear transformation by derivative ALS psi

D Psi M-quantile

Description

Derivative of psi M-quantile

Usage

d_psi_mq(x, tau, c)

Arguments

Value

y vector, linear transformation by second derivative m-rho

Kernel density

Description

Kernel density

Usage

f_den(x)

Arguments

Value

y vector, kernel density estimation.

Examples

x = rnorm(10)
f_den(x)

Tabular function

Description

Tabular function

Usage

f_tab(N, n, d, theta, sig2, kind)

Arguments

Value

a list with a dataframe Core and a matrix Matx, both display the same information

Loss expectile regression

Description

This function returns the core of expectile regression to be minimized

Usage

loss_er(beta, x, y, tau, N, d)

Arguments

Value

eta Numeric, sum of expectile regression

Loss expectile regression with fixed effects

Description

This function returns the core of expectile regression with fixed effects to be minimized

Usage

loss_erfe(theta, x, y, z, tau, n, d, mm)

Arguments

Value

eta Numeric, sum of expectile regression with fixed effects

Loss lasso expectile regression with fixed effects

Description

This function returns the core of lasso expectile regression with fixed effects to be minimized

Usage

loss_erlasso(theta, x, y, z, tau, n, d, mm, lambda)

Arguments

Value

eta Numeric, sum of lasso expectile regression with fixed effects

Loss M-quantile regression

Description

This function returns the core of M-quantile regression to be minimized

Usage

loss_mqr(beta, x, y, tau, N, d, c)

Arguments

Value

eta Numeric, sum of M-quantile regression

Loss M-quantile regression with fixed effects

Description

This function returns the core of M-quantile regression with fixed effects to be minimized

Usage

loss_mqrfe(theta, x, y, z, tau, n, d, mm, c)

Arguments

Value

eta Numeric, sum of M-quantile regression with fixed effects

Loss lasso M-quantile regression with fixed effects

Description

This function returns the core of lasso M-quantile regression with fixed effects to be minimized

Usage

loss_mqrlasso(theta, x, y, z, tau, n, d, mm, c, lambda)

Arguments

Value

eta Numeric, sum of lasso M-quantile regression with fixed effects

Loss quantile regression

Description

This function returns the core of quantile regression to be minimized

Usage

loss_qr(beta, x, y, tau, N, d)

Arguments

Value

eta Numeric, sum of quantile regression

Loss quantile regression with fixed effects

Description

This function returns the core of quantile regression with fixed effects to be minimized

Usage

loss_qrfe(theta, x, y, z, tau, n, d, mm)

Arguments

Value

eta Numeric, sum of quantile regression with fixed effects

Loss lasso quantile regression with fixed effects

Description

This function returns the core of lasso quantile regression with fixed effects to be minimized

Usage

loss_qrlasso(theta, x, y, z, tau, n, d, mm, lambda)

Arguments

Value

eta Numeric, sum of lasso quantile regression with fixed effects

Multiple penalized quantile regression

Description

Estimate penalized quantile regression for several taus

Usage

mpqr(x, y, subj, tau = 1:9/10, effect = "simple", c = 0)

Arguments

Value

Beta Numeric array, with three dimmensions: 1) tau, 2) coef., lower bound, upper bound, 3) exploratory variables.

Beta array with dimension (ntau, 3, d), where Beta[i,1,k] is the i-th tau estimation of beta_k, Beta[i,2,k] is the i-th tau lower bound 95% confidence of beta_k, and Beta[i,3,k] is the i-th tau lower bound 95% confidence of beta_k.

Examples

n = 10
m = 5
d = 4
N = n*m
L = N*d
x = matrix(rnorm(L), ncol=d, nrow=N)
subj = rep(1:n, each=m)
alpha = rnorm(n)
beta = rnorm(d)
eps = rnorm(N)
y = as.vector(x %*% beta + rep(alpha, each=m) + eps)

Beta = mpqr(x,y,subj,tau=1:9/10, effect="fixed", c = 1.2)
Beta

optim expectile regression

Description

This function solves a expectile regression

Usage

optim_er(beta, x, y, tau, N, d)

Arguments

Value

parametric vector and residuals.

optim expectile regression with fixed effects

Description

This function solves a expectile regression with fixed effects

Usage

optim_erfe(beta, alpha, x, y, z, tau, N, d, n)

Arguments

Value

parametric vector and residuals.

optim expectile regression with fixed effects and LASSO

Description

This function solves a expectile regression with fixed effects and LASSO

Usage

optim_erlasso(beta, alpha, x, y, z, tau, N, d, n)

Arguments

Value

parametric vector and residuals.

optim M-quantile regression

Description

This function solves a M-quantile regression

Usage

optim_mqr(beta, x, y, tau, N, d, c)

Arguments

Value

parametric vector and residuals.

optim quantile regression with fixed effects

Description

This function solves a quantile regression with fixed effects

Usage

optim_mqrfe(beta, alpha, x, y, z, tau, N, d, n, c)

Arguments

Value

parametric vector and residuals.

optim M-quantile regression with fixed effects and LASSO

Description

This function solves a M-quantile regression with fixed effects and LASSO

Usage

optim_mqrlasso(beta, alpha, x, y, z, tau, N, d, n, c)

Arguments

Value

parametric vector and residuals.

optim quantile regression

Description

This function solves a quantile regression

Usage

optim_qr(beta, x, y, tau, N, d)

Arguments

Value

parametric vector and residuals.

optim quantile regression with fixed effects

Description

This function solves a quantile regression with fixed effects

Usage

optim_qrfe(beta, alpha, x, y, z, tau, N, d, n)

Arguments

Value

parametric vector and residuals.

optim quantile regression with fixed effects and LASSO

Description

This function solves a quantile regression with fixed effects and LASSO

Usage

optim_qrlasso(beta, alpha, x, y, z, tau, N, d, n)

Arguments

Value

parametric vector and residuals.

Plot multiple penalized quantile regression

Description

plot penalized quantile regression for several taus

Usage

plot_taus(
  Beta,
  tau = 1:9/10,
  D,
  col = 2,
  lwd = 1,
  lty = 2,
  pch = 16,
  cex.axis = 1,
  cex.lab = 1,
  main = "",
  shadow = "gray90"
)

Arguments

Value

None

Examples

n = 10
m = 5
d = 4
N = n*m
L = N*d
x = matrix(rnorm(L), ncol=d, nrow=N)
subj = rep(1:n, each=m)
alpha = rnorm(n)
beta = rnorm(d)
eps = rnorm(N)
y = as.vector(x %*% beta + rep(alpha, each=m) + eps)

Beta = mpqr(x,y,subj,tau=1:9/10, effect="lasso", c = Inf)
plot_taus(Beta,tau=1:9/10,D=1)

Penalized quantile regression with fixed effects

Description

Estimate parameters and tuning parameter.

Usage

pqr(x, y, subj, tau = 0.5, effect = "simple", c = 1)

Arguments

Value

alpha Numeric vector, intercepts' coefficients.

beta Numeric vector, exploratory variables' coefficients.

lambda Numeric, estimated lambda.

res Numeric vector, percentile residuals.

tau Numeric scalar, the percentile.

penalty Numeric scalar, indicate the chosen effect.

c Numeric scalar, indicate the chosen c.

sig2_alpha Numeric vector, intercepts' standard errors.

sig2_beta Numeric vector, exploratory variables' standard errors.

Tab_alpha Data.frame, intercepts' summary.

Tab_beta Data.frame, exploratory variables' summary.

Mat_alpha Numeric matrix, intercepts' summary.

Mat_beta Numeric matrix, exploratory variables' summary.

References

Koenker, R. (2004) "Quantile regression for longitudinal data", J. Multivar. Anal., 91(1): 74-89, <doi:10.1016/j.jmva.2004.05.006>

Examples

n = 10
m = 5
d = 4
N = n*m
x = matrix(rnorm(d*N), ncol=d, nrow=N)
subj = rep(1:n, each=m)
alpha = rnorm(n)
beta = rnorm(d)
eps = rnorm(N)
y = as.vector(x %*% beta + rep(alpha, each=m) + eps)
m1 = pqr(x=x, y=y, subj=subj, tau=0.75, effect="lasso", c = 0)
m1$Tab_beta

Print an PQR

Description

Define the visible part of the object class PQR

Usage

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

Arguments

Value

None

Psi ALS

Description

Psi asymetric least square

Usage

psi_als(x, tau)

Arguments

Value

y vector, linear transformation by ALS psi

Psi M-quantile

Description

Psi M-quantile

Usage

psi_mq(x, tau, c)

Arguments

Value

y vector, linear transformation by m-rho derivative

Covariance

Description

Estimate Covariance matrix

Usage

q_cov(n, N, d, Z, X, tau, res, penalty, c)

Arguments

Value

a list with two matrices: sig2_alpha (which is the matrix of covariance of estimated alpha) and sig2_beta (which is the matrix of covariance of estimated beta)

Rho Koenker

Description

Rho Koenker

Usage

rho_koenker(x, tau)

Arguments

Value

y vector, linear transformation by rho

Rho M-quantile

Description

Rho M-quantile

Usage

rho_mq(x, tau, c)

Arguments

Value

y vector, linear transformation by m-rho

Identify significance

Description

Identify significance

Usage

sgf(x)

Arguments

Value

y vector Factor, symbol flag of significant p-values.

a vector of Factors, i.e., the symbols to help p-value interpretation

Examples

n = 10
pvalue = rgamma(10,1,10)
sgf(pvalue)