Abstract

Latent class analysis (LCA) assigns individuals to mutually exclusive classes based on response patterns to a set of indicators. A primary assumption made is local independence, which suggests class indicators are uncorrelated within each class. When the indicators are correlated and unmodeled, parameter estimates can be severely biased. We provide a comprehensive resource for applied researchers to statistically detect local independence violations and model identified correlated residuals. We explain the local independence assumption and illustrate how to detect and model conditional dependence using maximum likelihood (ML) and Bayesian estimation. For ML, we discuss two detection methods (bivariate residual associations, and the modification index) and one modeling technique (LCA residual associations model). We also demonstrate how to use the restrictive prior strategy to detect and model conditional dependence when using Bayesian estimation. These techniques are illustrated with simulated datasets; code is provided in the online supplemental materials.

摘要

潜在类别分析 (LCA) 根据对一组指标的响应模式将个体分配到相互排斥的类别。所做的主要假设是本地独立性，这表明类指标在每个类中是不相关的。当指标相关且未建模时，参数估计可能会出现严重偏差。我们为应用研究人员提供全面的资源，以统计方式检测局部独立性违规和模型识别的相关残差。我们解释了局部独立性假设，并说明了如何使用最大似然 (ML) 和贝叶斯估计来检测和建模条件依赖性。对于 ML，我们讨论了两种检测方法（双变量残差关联和修正指数）和一种建模技术（LCA 残差关联模型）。我们还演示了在使用贝叶斯估计时如何使用限制性先验策略来检测和建模条件依赖性。这些技术用模拟数据集进行了说明；