On the merits of orthogonalizing powered and product terms: Implications for modeling interactions among latent variables
On the merits of orthogonalizing powered and product terms: Implications for modeling interactions among latent variables
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DOI：
10.1207/s15328007sem1304_1
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发表时间：
2006-01-01
影响因子：
6
通讯作者：
Widaman, Keith F.
中科院分区：
文献类型：
--
作者：
Little, Todd D.;Bovaird, James A.;Widaman, Keith F.
本文的目标有两个：(a) 简要强调残差中心化在标准回归上下文中表示交互作用和幂项的优点（例如，Lance，1988），以及 (b) 扩展残差中心化过程以表示潜在变量交互作用。所提出的表示潜在变量相互作用的方法比现有程序具有潜在优势。首先，潜在变量交互作用是从所有可能的交互作用指标之间观察到的协变模式得出的。其次，不需要对特定的估计参数施加限制。第三，不需要重新计算参数。第四，模型估计是稳定且可解释的。我们认为，正交化方法在技术上和概念上都很简单，可以使用任何结构方程建模软件包进行估计，并且对参数估计具有直接的实际解释。它在模型拟合和估计标准误差方面的行为非常合理，并且可以很容易地推广到涉及非线性或共线性的其他类型的潜在变量（例如，幂变量）。
The goals of this article are twofold: (a) briefly highlight the merits of residual centering for representing interaction and powered terms in standard regression contexts (e.g., Lance, 1988), and (b) extend the residual centering procedure to represent latent variable interactions. The proposed method for representing latent variable interactions has potential advantages over extant procedures. First, the latent variable interaction is derived from the observed covariation pattern among all possible indicators of the interaction. Second, no constraints on particular estimated parameters need to be placed. Third, no recalculations of parameters are required. Fourth, model estimates are stable and interpretable. In our view, the orthogonalizing approach is technically and conceptually straightforward, can be estimated using any structural equation modeling software package, and has direct practical interpretation of parameter estimates. Its behavior in terms of model fit and estimated standard errors is very reasonable, and it can be readily generalized to other types of latent variables where nonlinearity or collinearity are involved (e.g., powered variables).