无均值结构的潜变量交互效应模型的标准化估计

Appropriate Standardized Estimates of Latent Interaction Models without the Mean Structure

潜变量交互效应建模研究近年来有两项重要进展,一是提出了潜变量交互效应模型的标准化估计及其计算公式;二是发现无均值结构模型可以取代传统的有均值结构模型,建模大为简化。但标准化估计是在传统的有均值结构模型中建立的,在简化的模型中同样适用吗?本文在无均值结构模型的框架内,给出了潜变量交互效应模型的标准化形式、计算公式和建模步骤,并通过模拟研究比较了极大似然和广义最小二乘两种估计方法、配对乘积指标和全部乘积指标两种指标类型,结果表明,在计算交互效应的标准化估计时,应当使用配对乘积指标建模,并且首选极大似然估计。

There are two important lines of progress in the recent research on latent interaction modeling. First, the appropriate ‘standardized’ parameter estimates have been proposed and formulated using parameter estimates routinely available from existing SEM software packages （see, e.g., Wen, Marsh, Hau, 2010）. Second, it has been found that the mean structure is not necessary in the structural equation models of latent interaction, as the parameters of the main and interaction effects remain theoretically unchanged both with and without the mean structure （see, e.g., Lin, Wen, Marsh, Lin, 2010）. Although the appropriate standardized parameter estimates have been established under the framework of the traditional latent interaction models with the mean structure, it is unknown whether the same concepts and the formulae for standardized parameter estimates remain applicable under the framework of the simplified latent interaction models without the mean structure. To answer this question, we deduced the appropriate standardized form of the structural equation for latent interaction models, and formulated the appropriate standardized estimations of main and interaction effects without the mean structure in the models. Furthermore, through a simulation study, we compared two estimation methods—maximum likelihood （ML） versus generalized least squares （GLS）, and two strategies for forming the product indicators—matched-pair product indicators versus all possible cross product indicators. Results showed that matched-pair product indicators had an advantage over all possible cross product indicators, and that ML estimates were preferable to GLS estimates when calculating the appropriate standardized estimates of main and interaction effects. It is therefore recommended that matched-pair product indicators should be adopted. The ML method is the preferred choice in estimating the latent interaction.