Title:	Adaptive Lasso Quantile Regression with Fixed Effects
Version:	1.3
Description:	Quantile regression with fixed effects solves longitudinal data, considering the individual intercepts as fixed effects. The parametric set of this type of problem used to be huge. Thus penalized methods such as Lasso are currently applied. Adaptive Lasso presents oracle proprieties, which include Gaussianity and correct model selection. Bayesian information criteria (BIC) estimates the optimal tuning parameter lambda. Plot tools are also available.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends:	R (≥ 4.4.0)
Imports:	Rcpp (≥ 1.0.5), MASS (≥ 7.3-49), stats
LinkingTo:	Rcpp, RcppArmadillo
Encoding:	UTF-8
RoxygenNote:	7.3.3
NeedsCompilation:	yes
Packaged:	2025-12-08 14:59:42 UTC; idanilevicz
Author:	Ian Meneghel Danilevicz [aut, cre], Pascal Bondon [aut], Valderio A. Reisen [aut]
Maintainer:	Ian Meneghel Danilevicz <iandanilevicz@gmail.com>
Repository:	CRAN
Date/Publication:	2025-12-08 15:20:02 UTC
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	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)

multiple penalized quantile regression

Description

Estimate QR for several taus

Usage

mqr(x, y, subj, tau = 1:9/10, method = "qr", ngrid = 20, inf = 1e-08, digt = 4)

Arguments

Value

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

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 = x %*% beta  + matrix(rep(alpha, each=m) + eps)
y = as.vector(y)

Beta = mqr(x,y,subj,tau=1:9/10, method="qr", ngrid = 10)
Beta

multiple penalized quantile regression - alpha

Description

Estimate QR intercepts for several taus

Usage

mqr_alpha(
  x,
  y,
  subj,
  tau = 1:9/10,
  method = "qr",
  ngrid = 20,
  inf = 1e-08,
  digt = 4
)

Arguments

Value

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

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 = x %*% beta  + matrix(rep(alpha, each=m) + eps)
y = as.vector(y)

Alpha = mqr(x,y,subj,tau=1:9/10, method="qr", ngrid = 10)
Alpha

plot multiple penalized quantile regression - alpha

Description

plot QR intercepts for several taus

Usage

plot_alpha(
  Beta,
  tau = 1:9/10,
  D,
  ylab = expression(alpha[1]),
  col = 2,
  lwd = 1,
  lty = 2,
  pch = 1,
  cex.axis = 1,
  cex.lab = 1,
  main = ""
)

Arguments

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 = x %*% beta  + matrix(rep(alpha, each=m) + eps)
y = as.vector(y)

Beta = mqr_alpha(x,y,subj,tau=1:9/10, method="qr", ngrid = 10)
plot_alpha(Beta,tau=1:9/10,D=1)

plot multiple penalized quantile regression

Description

plot QR for several taus

Usage

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

Arguments

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 = x %*% beta  + matrix(rep(alpha, each=m) + eps)
y = as.vector(y)

Beta = mqr(x,y,subj,tau=1:9/10, method="qr", ngrid = 10)
plot_taus(Beta,tau=1:9/10,D=1)

quantile regression

Description

Estimate quantile regression parameters for any quantile.

Remarks:

1. If the first column of 'x' is entirely equal to 1, then the first element of 'beta' represents the common intercept. Otherwise, there is no default common intercept (unlike the default behavior in 'lm').

2. If there is a common intercept and ‘method' is '"qrfe"', '"lqrfe"' or '"alqrfe"', a ’sum-to-zero constraint' is applied on the 'alpha' parameters:

\sum_{i=1}^{n} \alpha_i = 0

This follows the approach in Danilevicz (2025).

Usage

qr(x, y, subj, tau = 0.5, method = "qrfe", ngrid = 20, inf = 1e-08, digt = 4)

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.

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.

method Factor, method applied.

References

Danilevicz, I.M., Bondon, P., Reisen, V.A. (2025) "Adaptive LASSO Quantile Regression with Fixed Effects", Appl. Math. Model., xx (xx), <doi:10.1016/j.apm.2025.116600>

Danilevicz, I.M., Reisen, V.A., Bondon, P. (2024) "Expectile and M-quantile regression for panel data", Stat. Comput., 34 (97), <doi:10.1007/s11222-024-10396-7>

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

Examples

# Example 1
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 = x %*% beta  + matrix(rep(alpha, each=m) + eps)
y = as.vector(y)
m1 = qr(x,y,subj,tau=0.75, method="qrfe")
m1
m2 = qr(x,y,subj,tau=0.3, method="lqrfe", ngrid = 10)
m2

# Example 2, from MASS package
Rabbit = MASS::Rabbit
Rabbit$Treatment = ifelse(Rabbit$Treatment=="Control",0,1)
Rabbit$Animal = ifelse(Rabbit$Animal == "R1",1,ifelse(Rabbit$Animal == "R2",2,
ifelse(Rabbit$Animal == "R3",3,ifelse(Rabbit$Animal == "R4",4,5))))
X = matrix(cbind(Rabbit$Dose,Rabbit$Treatment), ncol=2)
m3 = qr(x=X, y=Rabbit$BPchange, subj=Rabbit$Animal,tau=0.5, method="alqrfe", ngrid = 10)
m3