Multivariate Behav Res. 2006 Dec 1;41(4):499-532. doi: 10.1207/s15327906mbr4104_4.
Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an underlying latent variable is continuous or categorical, and (b) to quantify the effect of sample size and class proportions on making this distinction. Latent variable models with categorical, continuous, or both types of latent variables are fitted to simulated data generated under different types of latent variable models. If an analysis is restricted to fitting continuous latent variable models assuming a homogeneous population and data stem from a heterogeneous population, overextraction of factors may occur. Similarly, if an analysis is restricted to fitting latent class models, overextraction of classes may occur if covariation between observed variables is due to continuous factors. For the data-generating models used in this study, comparing the fit of different exploratory factor mixture models usually allows one to distinguish correctly between categorical and/or continuous latent variables. Correct model choice depends on class separation and within-class sample size.
潜变量模型存在连续型、类别型或这两种类型的潜变量。潜变量的作用是解释观测响应中的系统模式。本文有两个目标:(a) 根据观测响应,确定潜在的潜变量是连续型还是类别型;(b) 量化样本量和类别比例对做出这种区分的影响。类别型、连续型或这两种类型的潜变量的潜变量模型拟合于在不同类型的潜变量模型下生成的模拟数据。如果分析仅限于拟合连续潜变量模型,且假设总体同质,而数据来源于异质总体,则可能会过度提取因子。同样,如果分析仅限于拟合潜在类别模型,那么如果观测变量之间的协变是由于连续因素,则可能会过度提取类别。对于本研究中使用的数据生成模型,比较不同探索性因子混合模型的拟合情况通常可以正确区分类别型和/或连续型潜变量。正确的模型选择取决于类别分离和类别内样本量。