正交化無限制潛在交互效果模式之修正策略的評估

The Evaluation of the Modified Strategies for Orthogonalizing Approach for Unconstrained Structural Equation Models

Little、Bovaird 和Widaman(2006)提出的處理潛在交互效果模式的乘積指標正交化策略(orthogonalizing strategy)，在三階動差(third-order moments)不為零時，會有結構不一致性問題，因此對常態假設不具穩健性(robustness)（林冠群、溫忠麟、Marsh、林惠賢，2008；Lin， Wen， Marsh， & Lin， 2010）。本文介紹了三種修正此問題的策略，並將它們與Lin等人(2010)的雙重均心化策略(double-mean-centering strategy)一同進行比較。結果顯示先針對潛在交互項進行正交化，然後再尋找適合潛在交互項的指標的修正方式（修正策略1），在四種分布條件下其偏差大都在5%左右或是更小，為三種修正策略中表現最佳的估計方式。然而，不論哪一種修正策略的表現，皆不如指標建立過程較為容易的雙重均心化策略。本文建議如果要估計潛在交互效果，最好不要採用正交化策略及其修正策略，而應採用雙重均心化策略。

As the third-order moments is not equal to 0， the orthogonalizing strategy for unconstrained latent interaction models proposed by Little， Bovaird， & Widaman (2006) will produce the inconsistency problem of structure， leading to substantial bias of estimated interaction effect (Lin， Wen， Marsh， & Lin， 2010). This paper introduced three modified strategies to solve the problem， and compared them with the double-mean-centering strategy (Lin et al.， 2010). The results showed that the best one of the three modified strategies is to orthogonalize the latent interaction term and then create proper indicators for it (modified strategy 1). This strategy is approximately 5% or even smaller bias under four different kinds of distribution conditions. However， this strategy is not as good as the double-mean-centering strategy in terms of less bias of estimated interaction effect. More importantly， the double-mean-centering strategy is much easier to be applied. As the result， the double-mean-centering strategy w as recommended.