带有多重分类变量的潜变量模型的可识别性

Identification of Latent Variable Model with Multiple Categorical Variables

潜变量模型是一种广泛应用于表征多个观察变量之间相关性的统计方法.在刻画多重分类数据关联性方面,这类模型通常假定每个分类变量都与一个潜在连续变量或向量相联系,通过潜变量或向量在窗口部分的观察值来确定分类变量的值,从而达到对类别界定.然而该方法存在一个弱点:观察似然或模型存在确定性问题.模型缺乏识别性必然会对估计构成影响.本文对带有多重二分、有序和/或无序分数据的潜变量模型的模型识别问题,提出一种基于模型的识别方法,给出了一些有用的结果,特别是在建立因子分析模型和/或结构方程模型解释多重响应变量之间的相关性时.这些条件利用模型结构并保持了不同类型参数的相互分离性,这从理论和应用角度来看都较为方便.

Latent variable model is a widely appreciated statistical method in characterizing the item-dependence of multiple observed responses.In characterizing the association among multiple categorical data,such model typically assumes that each categorical variable is related to a latent continuous variable or vector of which their realizations are partially observed through windows to index the category under consideration.An underlying drawback is that the observed likelihood often suffers from the model inter-determinacy.Lack of model identification may be problematic when the interests are focused on the estimation issue.In this paper,we attempt to address the model identification problem when the latent variable models are suggested to model the multiple binary,ordered categorical and/or unordered categorical data.We present some useful results to ensure the model identification especially when the factor analysis model and/or structural equation model are presented to interpret the correlation of the multiple responses.These conditions are more convenient both from the theoretical and practical viewpoints since they utilize the model structure and maintain the separateness of different types of parameters.