TY - JOUR

T1 - Unconstrained structural equation models of latent interactions

T2 - Contrasting residual- and mean-centered approaches

AU - Marsh, Herbert W.

AU - Wen, Zhonglin

AU - Hau, Kit Tai

AU - Little, Todd D.

AU - Bovaird, James A.

AU - Widaman, Keith F.

PY - 2007

Y1 - 2007

N2 - Little, Bovaird and Widaman (2006) proposed an unconstrained approach with residual centering for estimating latent interaction effects as an alternative to the mean-centered approach proposed by Marsh, Wen, and Hau (2004, 2006). Little et al. also differed from Marsh et al. in the number of indicators used to infer the latent interaction factor and how they were represented, but this issue is separate from the mean versus residual centering distinction that was their primary focus. However, their implementation of the Marsh et al. mean-centered approach failed to incorporate the mean structure that Marsh et al. argued was necessary to obtain unbiased estimates. One might suppose that their new approach would suffer this same problem, an issue not addressed by Little et al. However, we demonstrate here why the Little et al. approach obviates this requirement that heretofore was thought to be necessary for all constrained, partially constrained, and unconstrained approaches. Both the Marsh et al. and Little et al. unconstrained approaches typically result in similar results and are much easier to implement than traditional constrained approaches. They differ primarily in that the Little et al. approach is a 2-step approach involving a potentially large number of separate analyses prior to estimating the structural equation model that apparently does not require the estimation of a mean structure, whereas the Marsh et al. approach is a 1-step approach that includes a mean structure.

AB - Little, Bovaird and Widaman (2006) proposed an unconstrained approach with residual centering for estimating latent interaction effects as an alternative to the mean-centered approach proposed by Marsh, Wen, and Hau (2004, 2006). Little et al. also differed from Marsh et al. in the number of indicators used to infer the latent interaction factor and how they were represented, but this issue is separate from the mean versus residual centering distinction that was their primary focus. However, their implementation of the Marsh et al. mean-centered approach failed to incorporate the mean structure that Marsh et al. argued was necessary to obtain unbiased estimates. One might suppose that their new approach would suffer this same problem, an issue not addressed by Little et al. However, we demonstrate here why the Little et al. approach obviates this requirement that heretofore was thought to be necessary for all constrained, partially constrained, and unconstrained approaches. Both the Marsh et al. and Little et al. unconstrained approaches typically result in similar results and are much easier to implement than traditional constrained approaches. They differ primarily in that the Little et al. approach is a 2-step approach involving a potentially large number of separate analyses prior to estimating the structural equation model that apparently does not require the estimation of a mean structure, whereas the Marsh et al. approach is a 1-step approach that includes a mean structure.

UR - http://www.scopus.com/inward/record.url?scp=38049152866&partnerID=8YFLogxK

U2 - 10.1080/10705510701303921

DO - 10.1080/10705510701303921

M3 - Article

AN - SCOPUS:38049152866

VL - 14

SP - 570

EP - 580

JO - Structural Equation Modeling

JF - Structural Equation Modeling

SN - 1070-5511

IS - 4

ER -