Varriale Roberta, Vermunt Jeroen K
a Italian National Statistical Institute (ISTAT).
b Tilburg University.
Multivariate Behav Res. 2012 Mar 30;47(2):247-75. doi: 10.1080/00273171.2012.658337.
Factor analysis is a statistical method for describing the associations among sets of observed variables in terms of a small number of underlying continuous latent variables. Various authors have proposed multilevel extensions of the factor model for the analysis of data sets with a hierarchical structure. These Multilevel Factor Models (MFMs) have in common that-as in multilevel regression analysis-variation at the higher level is modeled using continuous random effects. In this article, we present an alternative multilevel extension of factor analysis which we call the Multilevel Mixture Factor Model (MMFM). It is based on the assumption that higher level units belong to latent classes that differ in terms of the parameters of the factor model specified for the lower level units. We demonstrate the added value of MMFM compared with MFM, both from a theoretical and applied perspective, and we illustrate the complementarity of the two approaches with an empirical application on students' satisfaction with the University of Florence. The multilevel aspect of this application is that students are nested within study programs, which makes it possible to cluster these programs based on their differences in students' satisfaction.
因子分析是一种统计方法,用于根据少量潜在的连续变量来描述观测变量集之间的关联。许多作者提出了因子模型的多层次扩展,用于分析具有层次结构的数据集。这些多层次因子模型(MFM)的共同之处在于,与多层次回归分析一样,使用连续随机效应来对较高层次的变异进行建模。在本文中,我们提出了因子分析的另一种多层次扩展,我们称之为多层次混合因子模型(MMFM)。它基于这样一种假设,即较高层次的单元属于潜在类别,这些潜在类别在为较低层次单元指定的因子模型参数方面存在差异。我们从理论和应用的角度展示了MMFM相对于MFM的附加值,并通过对佛罗伦萨大学学生满意度的实证应用来说明这两种方法的互补性。该应用的多层次方面在于,学生嵌套在学习项目中,这使得可以根据学生满意度的差异对这些项目进行聚类。