LINEAR LOGISTIC LATENT CLASS ANALYSIS FOR POLYTOMOUS DATA
LINEAR LOGISTIC LATENT CLASS ANALYSIS FOR POLYTOMOUS DATA
复制标题
DOI：
10.2307/2290280
复制
发表时间：
1992-06-01
影响因子：
3.7
通讯作者：
FORMANN, AK
中科院分区：
文献类型：
--
作者：
FORMANN, AK
对于潜在类别分析，一种广为人知的统计方法，用于将观察到的频率表分解为几个不可观察到的频率表，提出了一种灵活的模型，以限制未知的类别大小（混合权重）和未知的潜在响应概率。陈述了两个基本方程组，使得它们同时允许参数固定、某些参数的相等性以及每个原始参数的线性逻辑约束。给出了“线性逻辑潜在类分析”参数的最大似然方程，并描述了通过 EM 算法对其进行估计。此外，概述了其局部可识别性和拟合优度的统计检验（Pearson 和似然比-chi-2）的标准。线性逻辑潜在类别分析的实际适用性通过三个示例来证明：混合逻辑回归、用于与关系配对比较的混合 Bradley-Terry 模型，以及局部依赖潜在类别模型，其中每个类别的单个附加参数涵盖了随机独立性的偏离。
For latent class analysis, a widely known statistical method for the unmixing of an observed frequency table into several unobservable ones, a flexible model is presented in order to restrain the unknown class sizes (mixing weights) and the unknown latent response probabilities. Two systems of basic equations are stated such that they simultaneously allow parameter fixations, the equality of certain parameters as well as linear logistic constraints of each of the original parameters. The maximum likelihood equations for the parameters of this "linear logistic latent class analysis" are given, and their estimation by means of the EM algorithm is described. Further, the criteria for their local identifiability and statistical tests (Pearson- and likelihood-ratio-chi-2) for goodness of fit are outlined. The practical applicability of linear logistic latent class analysis is demonstrated by three examples: mixed logistic regression, a mixed Bradley-Terry model for paired comparisons with ties, and a local dependence latent class model in which the departure from stochastic independence is covered by a single additional parameter per class.