The analysis of longitudinal income data is often made challenging for several reasons. For example, in a national Australian survey on income over time, a non-negligible proportion of responses are missing, and it is believed the missingness mechanism is non-ignorable. Also, there are a large number of reported zero incomes, some of which may be true zeros (corresponding to individuals who legitimately do not earn an income), while some may be false zeros (corresponding to individuals choosing to round their income to zero). We propose a new shared parameter mixture (SPM) model for analysing semi-continuous longitudinal income data, which addresses the two challenges of income non-response and zero rounding. This is accomplished by jointly modelling an individual's underlying income together with the probability of missingness and rounding to zero, where both probabilities are permitted to vary in a smooth manner with their underlying non-zero income. Applying the SPM model to the Australian income survey reveals that on average, older female individuals and individuals with a long-term health condition are considerably less likely to earn an income, while income tended to be highest for male individuals on fixed-term/permanent job contracts between ages 50 and 60. Furthermore there is evidence of both zero rounding, and conditional on the assumed missingness mechanism, individuals with incomes at the higher and lower ends are more likely to not report their income.

中文翻译：

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具有缺失响应和零舍入的纵向收入数据共享参数混合模型

由于多种原因，纵向收入数据的分析通常具有挑战性。例如，在澳大利亚一项关于收入随时间变化的全国调查中，有不可忽视的比例缺失，并且认为缺失机制是不可忽略的。此外，还有大量报告的零收入，其中一些可能是真零（对应于合法没有收入的个人），而有些可能是假零（对应于个人选择将收入四舍五入为零） . 我们提出了一种新的共享参数混合 (SPM) 模型来分析半连续纵向收入数据，该模型解决了收入无响应和零舍入这两个挑战。这是通过对个体进行联合建模来实现的 s 基础收入以及缺失概率和四舍五入到零的概率，其中允许两种概率随其基础非零收入以平滑方式变化。将 SPM 模型应用于澳大利亚收入调查显示，平均而言，老年女性个人和长期健康状况不佳的个人赚取收入的可能性要低得多，而定期/永久的男性个人的收入往往最高。 50 至 60 岁之间的工作合同。此外，有证据表明，无论是零舍入还是假设缺失机制，收入较高和较低的个人更有可能不报告其收入。