使用非线性计数回归模型估计波兰境内非正常外国人的人数
Estimation of the number of irregular foreigners in Poland using non-linear count regression models
摘要：
种群规模估计需要获得单位级数据，以便正确应用捕获-再捕获方法。遗憾的是，出于保密的原因，对这些数据的获取可能受到限制。为了克服这个问题，我们应用并扩展了Zhang（2008）提出的分层泊松-伽马模型，该模型最初用于估计挪威非正常外国人的数量。该模式是现行捕获-再捕获办法的替代办法，因为它不需要连接多个来源，仅以汇总的行政数据为基础，其中包括：（1）被逮捕的非正常外国人人数;（2）面临刑事指控的外国人人数;（3）在中央人口登记处登记的外国人人数。该模型明确假定未经许可的人口和登记人口之间的关系，这是由这两个群体之间的相互联系所激发的。这使得估计有条件地依赖于正常人口的规模，提供了与注册人口类似的解释，并使估计的参数随时间推移更加稳定。在本文中，我们修改了原来的想法，允许协变量和灵活的计数分布，以估计2019年波兰的非正常外国人的数量。我们还提出了一个参数自助估计的标准误的估计。根据扩展模型，我们得出结论，截至2019年3月31日和2019年9月30日，约有15，000和20，000名外国人在没有有效许可证的情况下居住在波兰。这意味着被波兰边防军逮捕的人约占总数的15-20%。
英文摘要：
Population size estimation requires access to unit-level data in order to correctly apply capture-recapture methods. Unfortunately, for reasons of confidentiality access to such data may be limited. To overcome this issue we apply and extend the hierarchical Poisson-Gamma model proposed by Zhang (2008), which initially was used to estimate the number of irregular foreigners in Norway. The model is an alternative to the current capture-recapture approach as it does not require linking multiple sources and is solely based on aggregated administrative data that include (1) the number of apprehended irregular foreigners, (2) the number of foreigners who faced criminal charges and (3) the number of foreigners registered in the central population register. The model explicitly assumes a relationship between the unauthorized and registered population, which is motivated by the interconnection between these two groups. This makes the estimation conditionally dependent on the size of regular population, provides interpretation with analogy to registered population and makes the estimated parameter more stable over time. In this paper, we modify the original idea to allow for covariates and flexible count distributions in order to estimate the number of irregular foreigners in Poland in 2019. We also propose a parametric bootstrap for estimating standard errors of estimates. Based on the extended model we conclude that in as of 31.03.2019 and 30.09.2019 around 15,000 and 20,000 foreigners and were residing in Poland without valid permits. This means that those apprehended by the Polish Border Guard account for around 15-20% of the total.
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