Package 'lzrq'

Quantile regression for logarithmic relationships with non-positive outcome values

Description

lzrq fits a quantile regression model where the raw dependent variable is transformed with a calibrated extensive margin (CEM) transformation of the form

$y^* = \ln(y) \quad \text{if } y > 0$

$y^* = -\psi \quad \text{if } y \leq 0$

lzrq is a wrapper for rq. If all fitted values from a quantile regression on the CEM-transformed outcome are greater than $-\psi$, results are returned. The resulting coefficients can be interpreted as logarithmic intensive-margin relationships between the outcome and the independent variables, even when the outcome contains non-positive values. If the condition does not hold, lzrq iteratively increases $\psi$ and re-checks. After ten failed iterations, lzrq returns an error and suppresses results. This is an automated adaptation of the algorithm described by Liu & Kaplan (2025).

All methods supported by rq are available, including coef(), residuals(), fitted(), predict(), summary(), AIC(), and logLik().

Usage

lzrq(formula, data, tau = 0.5, psi_init = -1e35, ...)

Arguments

formula	A formula with the raw (untransformed) outcome on the left-hand side.
data	Optional data frame containing the variables in the model.
tau	Quantile level. Numeric scalar strictly between 0 and 1. Defaults to 0.5.
psi_init	Initial lower bound constant used in the bisection algorithm. Defaults to -1e35 to mirror Stata's lzqreg convention.
...	Additional arguments passed to rq, such as weights or method.

Value

An object of class c("lzrq", "rq"). This is the fitted rq object with two additional fields:

lb_constant	The lower bound constant $-\psi$ used to replace non-positive outcomes in the final iteration.
n_nonpos	Number of non-positive outcome values in the estimation sample.

All rq fields are preserved, so the full suite of rq postestimation methods works automatically.

Author(s)

David Valenta ([email protected]) and Jack Fitzgerald ([email protected])

References

Fitzgerald, J., Adema, J., Fiala, L., Kujansuu, E., & Valenta, D. (2026). Non-Robustness in Log-Like Specifications. MetaArXiv. doi:10.31222/osf.io/juda7_v1

Liu, X., & Kaplan, D. M. (2025). Quantile Regression with Log(0) Outcomes. https://drive.google.com/file/d/1F3dnhm8MrlO5aRrGt48rBWAEaBqdCBH-/view

See Also

rq, summary.rq

Examples

library(MASS)

# The 'epil' dataset records epileptic seizure counts.
# The outcome 'y' is zero for about 10% of observations.
table(epil$y == 0)

# Because the median of 'y', conditional on 'trt', is above zero for
# both treatment groups, lzrq returns results at quantile 0.5.
result <- lzrq(y ~ trt + age, data = epil, tau = 0.5)
print(result)
summary(result)

# However, the tenth percentile of 'y' is zero for some treatment groups,
# so lzrq suppresses results and returns an error at quantile 0.1.
tryCatch(
  lzrq(y ~ trt + age, data = epil, tau = 0.1),
  error = function(e) message(e$message)
)

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