We propose a two-step estimator for multilevel latent class analysis (LCA) with covariates. The measurement model for observed items is estimated in its first step, and in the second step covariates are added in the model, keeping the measurement model parameters fixed. We discuss model identification, and derive an Expectation Maximization algorithm for efficient implementation of the estimator. By means of an extensive simulation study we show that (i) this approach performs similarly to existing stepwise estimators for multilevel LCA but with much reduced computing time, and (ii) it yields approximately unbiased parameter estimates with a negligible loss of efficiency compared to the one-step estimator. The proposal is illustrated with a cross-national analysis of predictors of citizenship norms.

翻译：我们提出了一种含协变量的多层次潜类分析（LCA）的两步估计法。该方法第一步估计观测项目的测量模型，第二步在保持测量模型参数固定的前提下将协变量纳入模型。我们讨论了模型可识别性，并推导出期望最大化算法以实现该估计量的高效计算。通过大规模模拟研究，我们证明：（i）该方法在性能上与现有的多层次LCA逐步估计法相近，但计算时间大幅缩短；（ii）与一步估计法相比，该方法能产生近似无偏的参数估计，且效率损失可忽略不计。最后，我们通过一项关于公民规范预测因素的跨国分析对上述方法进行了实例展示。