Comparing flexible modelling approaches: the varying-thresholds model versus quantile regression

IF 1.3 4区计算机科学 Q2 STATISTICS & PROBABILITY

Advances in Data Analysis and Classification Pub Date : 2025-05-14 DOI:10.1007/s11634-025-00635-8

Niccolò Ducci, Leonardo Grilli, Marta Pittavino

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Abstract

The varying-thresholds model (VTM) is a novel methodology proposed by Tutz ( Flexible predictive distributions from varying-thresholds modelling. https://doi.org/10.48550/arXiv.2103.13324, arXiv:2103.13324 2021) capable of estimating the whole conditional distribution of a response variable in a regression setting. It can be used for continuous, ordinal and count responses. In this study, conditional quantiles and prediction intervals estimated through VTM are compared with those of quantile regression. The comparison is based on a set of data-generating models to assess the performance of the two methodologies regarding the coverage and width of prediction intervals. The simulation study encompasses settings with several functional forms and types of errors. In addition, a discrete version of the continuous ranked probability score is proposed as a tool to choose the best link function for the binary models used in the fitting of VTM. In summary, the varying-thresholds model is a flexible methodology that can be broadly applied with light assumptions; it is advantageous over quantile regression when the conditional quantile function is misspecified.

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比较灵活的建模方法：变阈值模型与分位数回归

变阈值模型（VTM）是由Tutz（可变阈值模型的灵活预测分布）提出的一种新方法。https://doi.org/10.48550/arXiv.2103.13324, arXiv:2103.13324 2021)能够估计回归设置中响应变量的整个条件分布。它可用于连续、有序和计数响应。在本研究中，通过VTM估计的条件分位数和预测区间与分位数回归的结果进行了比较。比较基于一组数据生成模型，以评估两种方法在预测区间的覆盖范围和宽度方面的性能。仿真研究包括具有几种功能形式和错误类型的设置。此外，提出了连续排序概率分数的离散版本，作为选择最佳链接函数的工具，用于VTM拟合中使用的二元模型。总之，变阈值模型是一种灵活的方法，可以广泛应用于较轻的假设；当条件分位数函数指定不当时，它优于分位数回归。

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来源期刊

Advances in Data Analysis and Classification STATISTICS & PROBABILITY-

CiteScore

3.40

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The international journal Advances in Data Analysis and Classification (ADAC) is designed as a forum for high standard publications on research and applications concerning the extraction of knowable aspects from many types of data. It publishes articles on such topics as structural, quantitative, or statistical approaches for the analysis of data; advances in classification, clustering, and pattern recognition methods; strategies for modeling complex data and mining large data sets; methods for the extraction of knowledge from data, and applications of advanced methods in specific domains of practice. Articles illustrate how new domain-specific knowledge can be made available from data by skillful use of data analysis methods. The journal also publishes survey papers that outline, and illuminate the basic ideas and techniques of special approaches.