SPQR: An R Package for Semi-Parametric Density and Quantile Regression

TL;DR

The paper introduces the SPQR R package that implements a flexible semi-parametric quantile regression method using neural networks and splines, allowing for complex covariate-response relationships and detailed effect visualization.

Contribution

It provides the first implementation of the SPQR method in R, enabling flexible, interpretable quantile regression with non-linear effects and data-driven covariate importance measures.

Findings

Effective modeling of non-linear covariate effects.

Enhanced interpretability through covariate importance visualization.

Successful application to simulated and real datasets.

Abstract

We develop an R package SPQR that implements the semi-parametric quantile regression (SPQR) method in Xu and Reich (2021). The method begins by fitting a flexible density regression model using monotonic splines whose weights are modeled as data-dependent functions using artificial neural networks. Subsequently, estimates of conditional density and quantile process can all be obtained. Unlike many approaches to quantile regression that assume a linear model, SPQR allows for virtually any relationship between the covariates and the response distribution including non-linear effects and different effects on different quantile levels. To increase the interpretability and transparency of SPQR, model-agnostic statistics developed by Apley and Zhu (2020) are used to estimate and visualize the covariate effects and their relative importance on the quantile function. In this article, we detail how this framework is implemented in SPQR and illustrate how this package should be used in practice through simulated and real data examples.