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‘qrcmNP’ extends quantile regression coefficients modeling (QRCM, Frumento and Bottai, 2016; package ‘qrcm’) in two directions:
piqr(): penalized QRCM for covariate
selection using the information on all quantiles simultaneously
(Sottile, Frumento, Chiodi and Bottai, 2020), with lasso and group lasso
penalties;niqr(): nonlinear parametric quantile
models, nonlinear in the parameters, in the covariates, or both (Bottai
and Cilluffo, 2020).# CRAN version
install.packages("qrcmNP")
# development version
# install.packages("remotes")
remotes::install_github("gianluca-sottile/qrcmNP")library(qrcmNP)
set.seed(1234)
n <- 300
d <- data.frame(x1 = rexp(n), x2 = runif(n, 0, 5), x3 = rnorm(n), x4 = runif(n))
u <- runif(n)
d$y <- 1 + qnorm(u) + (1 + 2 * u) * d$x1 + d$x2 # x3 and x4 are irrelevant
fit <- piqr(y ~ x1 + x2 + x3 + x4, formula.p = ~ slp(p, 2), data = d, nlambda = 30)
best <- gof.piqr(fit, method = "BIC", plot = FALSE)
best
#>
#> Selection of lambda by BIC
#>
#> Selected lambda: 9.051 (position 7 )
#> Degrees of freedom: 8
#>
#> Coefficients:
#> (Intercept) slp1 slp2
#> (Intercept) 0.17508 1.57385 0.42889
#> x1 0.32843 0.93906 -0.38235
#> x2 0.89827 NA -0.07583
#> x3 NA NA NA
#> x4 NA NA NA
# unpenalized re-estimation of the selected model, with standard errors
m <- refit_piqr(fit, pos.lambda = best$posMinLambda)
summary(m)
#>
#> Call: qrcm::iqr(formula = y ~ x1 + x2 + x3 + x4, formula.p = ~slp(p,
#> 2), data = d, s = structure(c(1, 1, 1, 0, 0, 1, 1, 1, 0,
#> 0, 1, 1, 1, 0, 0), dim = c(5L, 3L)))
#>
#> converged: TRUE
#> n. of iterations: 8
#> n. of free parameters: 9
#> n. of observations: 300
#>
#> ######################
#> ######################
#>
#> Coefficients:
#> (Intercept) slp1 slp2
#> (Intercept) -0.63231 1.67534 0.18250
#> x1 0.94257 0.81220 -0.16305
#> x2 1.03363 -0.01867 -0.05563
#> x3 NA NA NA
#> x4 NA NA NA
#>
#> Standard errors:
#> (Intercept) slp1 slp2
#> (Intercept) 0.44946 0.24757 0.24323
#> x1 0.27067 0.15583 0.14521
#> x2 0.10498 0.07303 0.06567
#> x3 NA NA NA
#> x4 NA NA NA
#>
#> ######################
#> ######################
#>
#> Wald test for x:
#> chi-square df P(> chi)
#> (Intercept) 75.11 3 3.43e-16 ***
#> x1 442.62 3 < 2e-16 ***
#> x2 343.33 3 < 2e-16 ***
#> x3 NA 0 NA
#> x4 NA 0 NA
#>
#>
#> Wald test for b(p):
#> chi-square df P(> chi)
#> (Intercept) 555.687 3 <2e-16 ***
#> slp1 528.039 3 <2e-16 ***
#> slp2 2.719 3 0.437
#>
#> Minimized loss function: 128.1989set.seed(1234)
x <- runif(n)
fun <- function(theta, p) cbind(theta[1] + exp(theta[2] * p), theta[3] + theta[4] * p)
b <- fun(c(1, 1, 1, 1), runif(n))
dn <- data.frame(y = b[, 1] + b[, 2] * x, x = x)
m2 <- niqr(y ~ x, data = dn, fun = fun, x0 = rep(0.5, 4))
summary(m2)
#>
#> Call: niqr(formula = y ~ x, data = dn, fun = fun, x0 = rep(0.5, 4))
#>
#> n. of observations: 300 n. of iterations: 5
#> Standard errors: sandwich
#>
#> Estimate Std. Error z value Pr(>|z|)
#> theta0 1.05523 0.06841 15.426 < 2e-16 ***
#> theta1 1.00759 0.03903 25.816 < 2e-16 ***
#> theta2 1.02334 0.14501 7.057 1.70e-12 ***
#> theta3 1.04106 0.20787 5.008 5.49e-07 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Minimized loss function: 0.1852556
#> AIC = 63.5767 BIC = 78.3918 AIC* = -1.67269 BIC* = -1.64799These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.