In multilevel data, units at level 1 are nested in clusters at level 2, which in turn may be nested in even larger clusters at level 3, and so on. For continuous data, several authors have shown how to model multilevel data in a ‘wide’ or ‘multivariate’ format approach. We provide a general framework to analyze random intercept multilevel SEM in the ‘wide format’ (WF) and extend this approach for discrete data. In a simulation study, we vary response scale (binary, four response options), covariate presence (no, between-level, within-level), design (balanced, unbalanced), model misspecification (present, not present), and the number of clusters (small, large) to determine accuracy and efficiency of the estimated model parameters. With a small number of observations in a cluster, results indicate that the WF approach is a preferable approach to estimate multilevel data with discrete response options.

中文翻译：

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具有离散数据的“宽格式”方法中的多级建模：小集群规模的解决方案

在多级数据中，级别 1 的单元嵌套在级别 2 的集群中，而级别又可能嵌套在级别 3 的更大集群中，依此类推。对于连续数据，几位作者已经展示了如何以“宽”或“多元”格式方法对多级数据进行建模。我们提供了一个通用框架来分析“宽格式”（WF）中的随机拦截多级 SEM，并将这种方法扩展到离散数据。在模拟研究中，我们改变响应尺度（二元、四个响应选项）、协变量存在（否、水平之间、水平内）、设计（平衡、不平衡）、模型错误指定（存在、不存在）和数量集群（小，大）来确定估计模型参数的准确性和效率。集群中的少量观察，