Rizopoulos Dimitris, Moustaki Irini
Erasmus University Medical Center, Rotterdam, The Netherlands.
Br J Math Stat Psychol. 2008 Nov;61(Pt 2):415-38. doi: 10.1348/000711007X213963. Epub 2007 May 24.
Until recently, item response models such as the factor analysis model for metric responses, the two-parameter logistic model for binary responses and the multinomial model for nominal responses considered only the main effects of latent variables without allowing for interaction or polynomial latent variable effects. However, non-linear relationships among the latent variables might be necessary in real applications. Methods for fitting models with non-linear latent terms have been developed mainly under the structural equation modelling approach. In this paper, we consider a latent variable model framework for mixed responses (metric and categorical) that allows inclusion of both non-linear latent and covariate effects. The model parameters are estimated using full maximum likelihood based on a hybrid integration-maximization algorithm. Finally, a method for obtaining factor scores based on multiple imputation is proposed here for the non-linear model.
直到最近，诸如用于计量反应的因子分析模型、用于二元反应的两参数逻辑模型以及用于名义反应的多项模型等项目反应模型仅考虑了潜在变量的主效应，而不允许存在交互作用或多项式潜在变量效应。然而，在实际应用中，潜在变量之间的非线性关系可能是必要的。用于拟合具有非线性潜在项模型的方法主要是在结构方程建模方法下开发的。在本文中，我们考虑了一个用于混合反应（计量和分类）的潜在变量模型框架，该框架允许同时纳入非线性潜在效应和协变量效应。基于混合积分最大化算法，使用完全最大似然估计模型参数。最后，本文针对非线性模型提出了一种基于多次填补的因子得分获取方法。
