Beta Regression with Autoregressive Errors for Interrupted Time Series Analysis of Proportion and Rate Outcomes: A Simulation Study
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中断时间序列中具有自回归误差的贝塔回归
- 研究问题
- 对于比例和比率结局的中断时间序列，如何同时处理有界条件分布与自回归误差，并改善短序列或高持续性情形下的统计推断？
- 方法与思路
- 作者通过递归替换构造带任意阶自回归依赖的条件贝塔似然，联合估计均值、精度和自回归参数，并提供 Stata 实现 betark。
- 材料陈述的贡献
- 摘要称，两种比较方法基本无偏，但 betark 在多数模拟情景中推断校准更好；高持续性三阶自回归下，其自身第一类错误仍偏高。
- 阅读关注点
- 应核对递归似然成立条件、初始化与取值边界处理，并检查干预效应设定；比较时需关注序列长度、自回归阶数和第一类错误表现。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；优势限于所考察模拟，摘要未给出干预的因果识别条件，也未证明推断普遍有效。
原文摘要
Interrupted time series analyses (ITSA) of proportion and rate outcomes are frequently estimated using ordinary least squares regression despite the bounded nature of these outcomes. When methods appropriate for bounded outcomes are used, the standard approach is a quasi-likelihood generalized linear model (GLM) with heteroskedasticity- and autocorrelation-consistent (HAC) standard errors. However, no existing estimator jointly models the beta-distributed conditional density and autoregressive (AR) error structure. We introduce betark, a Stata implementation of a joint conditional maximum likelihood estimator for beta regression with AR(k) errors based on a recursive substitution that yields a closed-form conditional beta likelihood with autoregressive dependence of arbitrary order. Unlike two-stage approaches, betark jointly estimates the mean, precision, and AR(k) coefficients in a single likelihood, so reported standard errors directly account for autocorrelation without separate correction. A Monte Carlo study compared betark with a quasi-binomial GLM using Newey-West HAC standard errors across AR(1)-AR(3) processes, three series lengths, and four effect sizes in a single-group ITSA design. Both methods were essentially unbiased, but betark produced better-calibrated inference than GLM+HAC in most scenarios, with the largest gains under highly persistent autocorrelation, where GLM+HAC Type I error exceeded 60% for short series. Misspecifying the AR order by one lag and varying the starting mean and pre-intervention trend had only modest effects on performance. However, betark's own Type I error remained elevated under highly persistent AR(3) processes even for the longest series examined.