潜变量交互效应建模:告别均值结构

Structural Equation Modeling of Latent Interactions Without Using the Mean Structure

潜变量交互效应建模研究近年来有了长足的发展,但模型中被认为不可缺少的均值结构往往让实际应用工作者却步。本文首先分析了潜变量交互效应模型中均值结构产生的根源;然后讨论了指标变换与均值结构的关系;接着提出了一个均值为零的潜变量交互结构,所建立的模型不需要均值结构,却不会改变主效应和交互效应等参数;最后用模拟例子对无均值结构和有均值结构的两种模型的参数估计进行了比较,结果符合理论预期,困扰人们多年的均值结构问题从此可以终结。

Estimating the interaction between variables is a particularly important theoretical,substantive,and empirical issue in psychology,as well as in many other social and behavioral sciences. Interactions between （multiple indicator） latent variables are rarely used because of the implementation complexity especially when the mean structure is known as a necessary part of any latent interaction model. There are four types of parameters related to the mean structure,which are namely,the intercepts of the y-measurement equations,the intercepts of the x-measurement equations,the intercepts of the structural equations,and the means of the exogenous latent variables. In this article,it is shown that the mean structure in the latent interaction model comes from the non-zero mean of the latent interaction construct ξ1ξ2 （the product of the two first terms）. Thus,the means of the exogenous latent variables and the intercepts of the y-measurement equations are always necessary even if all indicators are mean-centered when the traditional latent interaction construct is used. By building a new latent interaction construct so that its mean is zero,we obtain a structural equation model of latent interaction in which the mean structure is no longer necessary and the parameters of main and interaction effects are unchanged. A simulation study comparing the estimated parameters and goodness of fit indices of the two latent interaction models with and without the mean structure by using the matched-pair product indicators and the unconstrained approach is demonstrated. The simulation results are consistent with the theoretical predictions. This research unambiguously shows that the mean structure problem which has unduly deterred the applied researchers for a long time can now be solved.