Individual-specific, time-constant, random effects are often used to model dependence and/or to account for omitted covariates in regression models for longitudinal responses. Longitudinal studies have known a huge and widespread use in the last few years as they allow to distinguish between so-called age and cohort effects; these relate to differences that can be observed at the beginning of the study and stay persistent through time, and changes in the response that are due to the temporal dynamics in the observed covariates. While there is a clear and general agreement on this purpose, the random effect approach has been frequently criticized for not being robust to the presence of correlation between the observed (i.e. covariates) and the unobserved (i.e. random effects) heterogeneity. Starting from the so-called correlated effect approach, we argue that the random effect approach may be parametrized to account for potential correlation between observables and unobservables. Specifically, when the random effect distribution is estimated non-parametrically using a discrete distribution on finite number of locations, a further, more general, solution is developed. This is illustrated via a large scale simulation study and the analysis of a benchmark dataset.

翻译：个体特异性、时间恒定的随机效应常用于建模纵向响应回归模型中的依赖性，并/或用于解释遗漏协变量。纵向研究在过去几年中得到了广泛而大量的应用，因为它们能够区分所谓的年龄效应和队列效应；这些效应涉及研究开始时可观察到并随时间持续存在的差异，以及由观测协变量的时间动态引起的响应变化。尽管在这一目的上存在明确且普遍的共识，但随机效应方法常因对观测（即协变量）与未观测（即随机效应）异质性之间相关性的存在缺乏稳健性而受到批评。从所谓的相关效应方法出发，我们认为随机效应方法可以通过参数化来考虑可观测变量与不可观测变量之间的潜在相关性。具体而言，当使用有限位置上的离散分布非参数地估计随机效应分布时，我们提出了一种更进一步的通用解决方案。这一方法通过大规模模拟研究和基准数据集分析得到了验证。