alqrfe (version 1.3)

qr: 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)

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.

Arguments

x

Numeric matrix, covariates

y

Numeric vector, outcome.

subj

Numeric vector, identifies the unit to which the observation belongs.

tau

Numeric, identifies the percentile.

method

Factor, "qr" quantile regression, "qrfe" quantile regression with fixed effects, "lqrfe" Lasso quantile regression with fixed effects, "alqrfe" adaptive Lasso quantile regression with fixed effects.

ngrid

Numeric scalar greater than one, number of BIC to test.

inf

Numeric scalar, internal value, small value.

digt

Numeric scalar, internal value greater than one, define "zero" coefficient.

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