Type:	Package
Title:	Penalized Quantile Regression with Fixed Effects
Version:	1.3
Date:	2025-12-08
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
Encoding:	UTF-8
Suggests:	testthat (≥ 3.0.0), tinytest (≥ 1.3.1)
RoxygenNote:	7.3.3
NeedsCompilation:	yes
Packaged:	2025-12-08 13:27:26 UTC; idanilevicz
Author:	Ian Meneghel Danilevicz [aut, cre], Valderio A Reisen [aut], Pascal Bondon [aut]
Maintainer:	Ian Meneghel Danilevicz <iandanilevicz@gmail.com>
Repository:	CRAN
Config/testthat/edition:	3
Date/Publication:	2025-12-08 13:50:02 UTC

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 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

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 regression parameters and tuning parameters for quantile, expectile, or M-quantile regression.

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 ‘effect' is '"fixed"' or '"lasso"', 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

pqr(x, y, subj, tau = 0.5, effect = "fixed", c = 0)

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

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

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