This paper is motivated by the panel surveys, called Statistics on Income and Living Conditions (SILC), conducted annually on (randomly selected) country-representative households to monitor EU 2020 aims on poverty reduction. We particularly consider the surveys conducted in Turkey, within the scope of integration to the EU, between 2010 and 2013. Our main interests are on health aspects of economic and living conditions. The outcome is {\it self-reported health} that is clustered longitudinal ordinal, since repeated measures of it are nested within individuals and individuals are nested within families. Economic and living conditions were measured through a number of individual- and family-level explanatory variables. The questions of interest are on the marginal relationships between the outcome and covariates that are addressed using a polytomous logistic regression with Bridge distributed random-effects. This choice of distribution allows one to {\it directly} obtain marginal inferences in the presence of random-effects. Widely used Normal distribution is also considered as the random-effects distribution. Samples from the joint posterior density of parameters and random-effects are drawn using Markov Chain Monte Carlo. Interesting findings from public health point of view are that differences were found between sub-groups of employment status, income level and panel year in terms of odds of reporting better health.

中文翻译：

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土耳其收入和生活条件数据的贝叶斯分析，使用具有桥分布随机效应的集群纵向序数模型

本文由名为“收入和生活条件统计数据 (SILC)”的小组调查推动，该调查每年对（随机选择的）国家代表家庭进行，以监测欧盟 2020 年减贫目标。我们特别考虑了 2010 年至 2013 年在土耳其在融入欧盟的范围内进行的调查。我们的主要兴趣是经济和生活条件的健康方面。结果是 {\it self-reported health} 是聚集的纵向序数，因为它的重复测量嵌套在个人内部，而个人又嵌套在家庭中。经济和生活条件是通过一些个人和家庭层面的解释变量来衡量的。感兴趣的问题是结果与协变量之间的边际关系，这些关系使用具有 Bridge 分布式随机效应的多分逻辑回归来解决。这种分布选择允许人们在随机效应存在的情况下 {\it direct} 获得边际推断。广泛使用的正态分布也被认为是随机效应分布。使用马尔可夫链蒙特卡罗从参数和随机效应的联合后验密度中抽取样本。从公共卫生的角度来看，有趣的发现是，就业状况、收入水平和小组年份的子组之间在报告更好健康的几率方面存在差异。这种分布选择允许人们在随机效应存在的情况下 {\it direct} 获得边际推断。广泛使用的正态分布也被认为是随机效应分布。使用马尔可夫链蒙特卡罗从参数和随机效应的联合后验密度中抽取样本。从公共卫生的角度来看，有趣的发现是，就业状况、收入水平和小组年份的子组之间在报告更好健康的几率方面存在差异。这种分布选择允许人们在随机效应存在的情况下 {\it direct} 获得边际推断。广泛使用的正态分布也被认为是随机效应分布。使用马尔可夫链蒙特卡罗从参数和随机效应的联合后验密度中抽取样本。从公共卫生的角度来看，有趣的发现是，就业状况、收入水平和小组年份的子组之间在报告更好健康的几率方面存在差异。