School of Business and Economics, Humboldt-Universität zu Berlin, Berlin, Germany.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain.
Stat Med. 2019 Sep 30;38(22):4404-4422. doi: 10.1002/sim.8306. Epub 2019 Jul 29.
Underreporting in gender-based violence data is a worldwide problem leading to the underestimation of the magnitude of this social and public health concern. This problem deteriorates the data quality, providing poor and biased results that lead society to misunderstand the actual scope of this domestic violence issue. The present work proposes time series models for underreported counts based on a latent integer autoregressive of order 1 time series with Poisson distributed innovations and a latent underreporting binary state, that is, a first-order Markov chain. Relevant theoretical properties of the models are derived, and the moment-based and maximum-based methods are presented for parameter estimation. The new time series models are applied to the quarterly complaints of domestic violence against women recorded in some judicial districts of Galicia (Spain) between 2007 and 2017. The models allow quantifying the degree of underreporting. A comprehensive discussion is presented, studying how the frequency and intensity of underreporting in this public health concern are related to some interesting socioeconomic and health indicators of the provinces of Galicia (Spain).
基于性别暴力数据的漏报是一个全球性问题，这导致了对这一社会和公共卫生问题严重程度的低估。这一问题恶化了数据质量，提供了不完善和有偏见的结果，导致社会对这一家庭暴力问题的实际范围产生误解。本研究提出了基于一阶滞后整数自回归的具有泊松分布创新和潜在漏报二元状态的时间序列模型，即一阶马尔可夫链。推导出了模型的相关理论性质，并提出了基于矩和基于极大似然的参数估计方法。新的时间序列模型应用于 2007 年至 2017 年间加利西亚（西班牙）部分司法区记录的季度家庭暴力妇女投诉。该模型可量化漏报程度。进行了全面的讨论，研究了加利西亚（西班牙）各省与这一公共卫生关注相关的漏报频率和强度与一些有趣的社会经济和健康指标之间的关系。
