In multilevel data, cross-classified data structures are common. For example, this occurs when individuals move to different regions in longitudinal data or students go to different secondary schools than their primary school peers. In both cases, the data structure is no longer fully nested. Estimating cross-classified multilevel models is computationally intensive, so researchers have used several shortcuts to decrease run time. We consider how these shortcuts affect parameter estimates. In particular, we compare parameter estimates from fully nested and cross-classified models using a series of Monte Carlo simulations. When the outcome is continuous, we identify systematic differences in estimated standard errors and some differences in the estimated variance components. When the outcome is binary, we also find differences in the estimated coefficients. Accordingly, we caution researchers to avoid fully nested model specifications when cross-classification exists but suggest some limited conditions under which parameter estimates are unlikely to be different.

中文翻译：

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评估嵌套和交叉分类层次​​模型之间的差异

在多级数据中，交叉分类的数据结构很常见。例如，当个人在纵向数据中移动到不同的区域或学生与小学同龄人上不同的中学时，就会发生这种情况。在这两种情况下，数据结构不再完全嵌套。估计交叉分类的多级模型是计算密集型的，因此研究人员使用了几种捷径来减少运行时间。我们考虑这些捷径如何影响参数估计。特别是，我们使用一系列蒙特卡罗模拟比较了完全嵌套和交叉分类模型的参数估计。当结果是连续的时，我们确定估计标准误差的系统差异和估计方差分量的一些差异。当结果是二元的时，我们还发现估计系数的差异。因此，我们提醒研究人员在存在交叉分类时避免完全嵌套的模型规范，但建议在参数估计不太可能不同的一些有限条件下。