This paper focuses on the substantive application of multilevel LCA to the evolution of citizenship norms in a diverse array of democratic countries. To do so, we present a two-stage approach to fit multilevel latent class models: in the first stage (measurement model construction), unconditional class enumeration is done separately on both low and high level latent variables, estimating only a part of the model at a time -- hence keeping the remaining part fixed -- and then updating the full measurement model; in the second stage (structural model construction), individual and/or group covariates are included in the model. By separating the two parts -- first stage and second stage of model building -- the measurement model is stabilized and is allowed to be determined only by it's indicators. Moreover, this two-step approach makes the inclusion/exclusion of a covariate a relatively simple task to handle. Our proposal amends common practice in applied social science research, where simple (low-level) LCA is done to obtain a classification of low-level unit, and this is then related to (low- and high-level) covariates simply including group fixed effects. Our analysis identifies latent classes that score either consistently high or consistently low on all measured items, along with two theoretically important classes that place distinctive emphasis on items related to engaged citizenship, and duty-based norms.

翻译：本文聚焦于多水平潜类分析（多水平LCA）在多样化民主国家公民规范演变中的实质性应用。为此，我们提出一种两阶段方法来拟合多水平潜类模型：在第一阶段（测量模型构建），分别对低层和高层潜变量进行无条件的类别枚举，每次仅估计模型的一部分（其余部分保持固定），随后更新完整的测量模型；在第二阶段（结构模型构建），将个体和/或群体协变量纳入模型。通过将模型构建的第一阶段与第二阶段相分离，测量模型得以稳定，且仅由其指标变量决定。此外，这种两步法使得协变量的纳入/排除成为相对简单的操作。我们的方法修正了应用社会科学研究中的常见做法——即仅通过简单（低层）LCA获取低层单元分类，随后仅通过纳入组别固定效应来关联（低层与高层）协变量。分析结果识别出两类在所有测量项目上持续高分或持续低分的潜类，以及两个具有理论意义的类别——它们分别对"参与型公民"相关项目和"义务型规范"赋予显著不同的权重。