Structural Equation Models of Latent Interactions: Clarification of Orthogonalizing and Double-Mean-Centering Strategies

Lin, Ge; Wen, Zefeng; Marsh, Herbert W.; Lin, Huey‐Shyan

doi:10.1080/10705511.2010.488999

Cited by 131 publications

(131 citation statements)

References 13 publications

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“…Fortunately, methodological advancements using structural equation modeling including the "double-mean-centered" approach (Lin, Wen, Marsh, & Lin, 2010) as well as the latent moderated structural model (Klein & Moosebrugger, 2000) and more robust quasi-maximum likelihood estimation (Klein & Muthén, 2007) should help address these issues of measurement error.…”

Section: Discussionmentioning

confidence: 99%

“…Based on the Discussion section, a second useful extension in this field would be simulation studies designed to examine how the use of new techniques in SEM for forming quadratic and interaction terms between continuous latent variables, specifically Lin et al's (2010) "double-mean-centered" approach and Klein and Muthén's (2007) quasimaximum likelihood method, address the reliability issues highlighted in MacCallum and Mar (1995). Similarly, it would be valuable for scholars to study whether these methods are robust when estimating complex linear models including both quadratic terms as well as quadratic-by-linear interactions.…”

Section: Future Research and Conclusionmentioning

confidence: 99%

See 1 more Smart Citation

Extensions of the Johnson-Neyman Technique to Linear Models With Curvilinear Effects: Derivations and Analytical Tools

Miller¹,

Stromeyer²,

Schwieterman³

2013

Multivariate Behavioral Research

143

123

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The past decade has witnessed renewed interest in the use of the Johnson-Neyman (J-N) technique for calculating the regions of significance for the simple slope of a focal predictor on an outcome variable across the range of a second, continuous independent variable. Although tools have been developed to apply this technique to probe 2- and 3-way interactions in several types of linear models, this method has not been extended to include quadratic terms or more complicated models involving quadratic terms and interactions. Curvilinear relations of this type are incorporated in several theories in the social sciences. This article extends the J-N method to such linear models along with presenting freely available online tools that implement this technique as well as the traditional pick-a-point approach. Algebraic and graphical representations of the proposed J-N extension are provided. An example is presented to illustrate the use of these tools and the interpretation of findings. Issues of reliability as well as "spurious moderator" effects are discussed along with recommendations for future research.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Future Research and Conclusionmentioning

confidence: 99%

Extensions of the Johnson-Neyman Technique to Linear Models With Curvilinear Effects: Derivations and Analytical Tools

Miller¹,

Stromeyer²,

Schwieterman³

2013

Multivariate Behavioral Research

143

123

View full text Add to dashboard Cite

show abstract

“…Because moderation analyses involved the interaction of latent variables with different numbers of indicators, the latent variable for the moderator variable was created by first summing scores across the four psychological flexibility indicators. Moderator indicators were then created with indProd in the semtools package and mean-centered without nonlinear constraints (Lin, Wen, Marsh & Lin, 2010).…”

Section: Discussionmentioning

confidence: 99%

The relationship between psychological flexibility, early maladaptive schemas, perceived parenting and psychopathology

Fischer

Smout²,

Delfabbro

2016

Journal of Contextual Behavioral Science

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“…Following Kenny and Judd (1984), several strategies to simplify the specification of the constraints have been devised, for example, by centering the indicators of the latent predictor variables or by using two-step estimation procedures (Algina & Moulder, 2001, Little, Bovaird, & Widaman, 2006, Ping, 1995, 1996. The so-called unconstrained approach (Kelava & Brandt, 2009;Marsh et al, 2004;Marsh, Wen, & Hau, 2006) represents the current end of this development: Marsh et al (2004) showed that only a single constraint is necessary when only a single interaction effect is estimated (see also Lin, Wen, Marsh, & Lin, 2010;Wen, Marsh, & Hau, 2010). Building upon this work, Kelava (2009) and Kelava and Brandt (2009) introduced the extended unconstrained approach (ExUC) and showed how the unconstrained approach can be correctly extended to simultaneously estimate latent quadratic and interDownloaded by [Universitaetsbibliothek Giessen] at 01:37 19 November 2014…”

Section: Non-bayesian Approaches For Estimating Nonlinear Semsmentioning

confidence: 98%

A Bayesian Model For The Estimation Of Latent Interaction And Quadratic Effects When Latent Variables Are Non-Normally Distributed

Kelava

Nagengast²

2012

Multivariate Behavioral Research

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Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent predictor variables are nonnormally distributed. The nonnormal predictor distribution is approximated by a finite mixture distribution. We conduct a simulation study that demonstrates the advantages of the proposed Bayesian model over contemporary approaches (Latent Moderated Structural Equations [LMS], Quasi-Maximum-Likelihood [QML], and the extended unconstrained approach) when the latent predictor variables follow a nonnormal distribution. The conventional approaches show biased estimates of the nonlinear effects; the proposed Bayesian model provides unbiased estimates. We present an empirical example from work and stress research and provide syntax for substantive researchers. Advantages and limitations of the new model are discussed.

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Structural Equation Models of Latent Interactions: Clarification of Orthogonalizing and Double-Mean-Centering Strategies

Cited by 131 publications

References 13 publications

Extensions of the Johnson-Neyman Technique to Linear Models With Curvilinear Effects: Derivations and Analytical Tools

Extensions of the Johnson-Neyman Technique to Linear Models With Curvilinear Effects: Derivations and Analytical Tools

The relationship between psychological flexibility, early maladaptive schemas, perceived parenting and psychopathology

A Bayesian Model For The Estimation Of Latent Interaction And Quadratic Effects When Latent Variables Are Non-Normally Distributed

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