Maraun M D
Multivariate Behav Res. 1996 Oct 1;31(4):517-38. doi: 10.1207/s15327906mbr3104_6.
The issue of indeterminacy in the factor analysis model has been the source of a lengthy and on-going debate. This debate can be seen as featuring two relevant interpretations of indeterminacy. The alternative solution position considers the latent common factor to be a random variate whose properties are determined by functional constraints inherent in the model. When the model fits the data, an infinity of random variates are criterially latent common factors to the set of manifest variates analyzed. The posterior moment position considers the latent common factor to be a single random entity with a non-point posterior distribution, given the manifest variables. It is argued here that: (a) The issue of indeterminacy centres on the criterion for the claim "X is a latent common factor to Y"; (b) the alternative solution position is correct, the posterior moment position representing a conflation of the criterion, which is provided by the equations of the model, with metaphors, analogies, and senses of "factor" that are external to the model. A number of implications for applied work involving factor analysis are discussed.
因子分析模型中的不确定性问题一直是一场漫长且仍在进行的辩论的根源。这场辩论可以被视为以对不确定性的两种相关解释为特征。替代解决方案立场认为潜在公共因子是一个随机变量，其属性由模型中固有的功能约束决定。当模型拟合数据时，对于所分析的一组显变量而言，存在无穷多个随机变量是符合标准的潜在公共因子。后验矩立场认为，给定显变量，潜在公共因子是一个具有非点后验分布的单一随机实体。本文认为：(a) 不确定性问题集中在 “X 是 Y 的潜在公共因子” 这一主张的标准上；(b) 替代解决方案立场是正确的，后验矩立场代表了由模型方程提供的标准与模型外部的 “因子” 的隐喻、类比和含义的混合。文中讨论了对涉及因子分析的应用工作的一些影响。
