Replication Data for Ordered Beta Regression: A Parsimonious, Well-Fitting Model for Continuous Data with Lower and Upper Bounds

I propose a new model, ordered Beta regression, for continuous distributions with both lower and upper bounds, such as data arising from survey slider scales, visual analog scales, and dose-response relationships. This model employs the cutpoint technique popularized by ordered logit to fit a single linear model to both continuous (0,1) and degenerate [0,1] responses. The model can be estimated with or without observations at the bounds, and as such is a general solution for this type of data. Employing a Monte Carlo simulation, I show that the model is noticeably more efficient than ordinary least squares regression, zero-and-one-inflated Beta regression, re-scaled Beta regression and fractional logit while fully capturing nuances in the outcome. I apply the model to a replication of the Aidt and Jensen (2012) study of suffrage extensions in Europe. The model can be fit with the R package `ordbetareg` to facilitate hierarchical, dynamic and multivariate modeling.

本研究提出一种面向同时具有上下界的连续分布数据的新型模型——有序Beta回归（ordered Beta regression），此类数据常见于调查滑块量表、视觉模拟量表以及剂量-反应关系的观测场景中。该模型借鉴了有序logit回归（ordered logit）所推广的切点技术，可针对连续型(0,1)与退化型[0,1]响应变量拟合单一线性模型。该模型可在包含或不包含边界观测值的情况下进行参数估计，因此可作为这类数据的通用建模方案。通过开展蒙特卡洛模拟（Monte Carlo simulation）实验，本研究证实该模型的效率显著优于普通最小二乘回归（ordinary least squares regression）、零一膨胀Beta回归（zero-and-one-inflated Beta regression）、重缩放Beta回归（re-scaled Beta regression）以及分数logit回归（fractional logit），且可完整捕捉响应变量的细微变化特征。本研究将该模型应用于对Aidt与Jensen（2012）关于欧洲普选权扩张的研究的复刻分析中。用户可通过R包`ordbetareg`拟合该模型，以便捷开展分层、动态及多变量建模工作。