MLM/lme4 内的聚类标准错误
是否可以同时使用聚类标准误差和多级模型？如何在 R 中实现这一点？
在我的设置中，我正在 26 个国家/地区进行联合实验，每个国家/地区有 2000 名参与者。与任何联合实验一样，每个参与者都会看到两个小插图，并要求对每个小插图进行选择/评分。然后向相同的参与者展示两个新的小插图进行比较，并要求他们重复该任务。在这种情况下，每个参与者都会进行两次比较。因此，层次结构是嵌套在国家内个人内部的比较。我目前正在运行一个多级模型，每次比较都在 1 级，国家/地区是 2 级单位。显然，个体内部的比较可能是相关的，所以我也想在个体层面上对标准误差进行聚类。为此在 MLM 中添加另一个级别似乎有点矫枉过正，因为我的集群的大小非常小 (n=2)，并且在个人级别上进行分析更有意义（更不用说自 2000 年以来不必要地使模型复杂化）个人*26个国家参数空间变得疯狂巨大）。这可能吗？如果是这样，如何在 R 中同时设置多级模型来做到这一点？
Is it possible to use both cluster standard errors and multilevel models together and how does one implement this in R?
In my set up I am running a conjoint experiment in 26 countries with 2000 participants per country. Like any conjoint experiment each participant is shown two vignettes and asked to choose/rate each vignette. The same participants is then shown two fresh vignettes for comparison and asked to repeat the task. In this case each participant performs two comparisons. The hierarchy is thus comparisons nested within individuals nested within countries. I am currently running a multilevel model with each comparison at level 1 and country is the level 2 unit. Obviously comparisons within individuals are likely to be correlated so I'd like to cluster standard errors at the individual level as well. It seems overkill to add another level in the MLM for this since the size of my clusters are extremely small (n=2) and it makes more sense to do my analysis at the individual level (not to mention unnecessarily complicating the model since with 2000 individuals*26 countries the parameter space becomes crazy huge). Is this possible? If so how does one do this in R together with a multilevel model set up?
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簇大小 2 不是问题，而且我也没有看到参数空间有任何问题。如果您对参与者和国家进行随机截距，这些将被估计为潜在的正态分布变量。诸如以下的模型：
这将处理集群内的依赖关系（在参与者级别和国家级别），因此无需使用集群标准错误。
The cluster size of 2 is not an issue, and I don't see any issue with the parameter space either. If you fit random intercepts for participants, and countries, these are estimated as latent normally distributed variables. A model such as:
This will handle the dependencies within clusters (at the participant level and the country level) so there will be no need to use cluster standard errors.