A Structural Equation Modeling Approach to Canonical Correlation Analysis

Lu, Zhenqiu; Gu, Fei

doi:10.1007/978-3-319-77249-3_22

Cited by 2 publications

(4 citation statements)

References 9 publications

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“…Consequently, current software implementations do not produce standard errors of the weight estimates. To address this issues, it was proposed to apply the delta method (Dorfman, 1938;Gu et al, 2019;Lu & Gu, 2018).…”

Section: Estimating Structural Models Containing Compositesmentioning

confidence: 99%

“…Considering the H-O specification, the weight estimates were calculated based on Equation 4; that is, they were obtained from the estimated loadings. Although, the standard errors for the weight estimates can be generally obtained via the delta method (Gu et al, 2019;Lu & Gu, 2018), they are not reported in the following. The IGSCA results were copied from the original study of Hwang et al (2021; see Tables 6 and 7 of their study).…”

Section: K ¼mentioning

confidence: 99%

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The Henseler-Ogasawara specification of composites in structural equation modeling: A tutorial.

Schuberth¹

2023

Psychological Methods

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Structural equation modeling (SEM) is a versatile statistical method that should theoretically be able to emulate all other methods that are based on the general linear model. In practice, however, researchers using SEM encounter problems incorporating composites into their models. In this tutorial article, I present a specification for SEM that was recently sketched by Henseler ( 2021) to incorporate composites in structural models. It draws from the same idea that was proposed in the c`ontext of canonical correlation analysis to express a set of observed variables forming a composite by a set of synthetic variables (Ogasawara, 2007), which were labeled by Henseler (2021) as emergent and excrescent variables. An emergent variable is a linear combination of variables that is related to other variables in the structural model, whereas an excrescent variable is a linear combination of variables that is unrelated to all other variables in the structural model. This approach is advantageous over existing approaches, as it allows drawing on all existing developments in SEM, such as testing parameter estimates, testing for overall model fit and dealing with missing values. To demonstrate the presented approach, I conduct a small scenario analysis. Moreover, SEM applying the presented specification is used to reestimate an empirical example from Hwang et al. (2021). Finally, this article discusses avenues for future research opened by this approach for SEM to study composites.

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Section: Estimating Structural Models Containing Compositesmentioning

confidence: 99%

Section: K ¼mentioning

confidence: 99%

The Henseler-Ogasawara specification of composites in structural equation modeling: A tutorial.

Schuberth¹

2023

Psychological Methods

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“…Similarly, the standard errors of the weights can be obtained using the delta method ([34], Chapter 2). Since the weights are functions of the composite loadings, their standard errors can generally be obtained as follows (see also [36]):…”

Section: The Refined H-o Specificationmentioning

confidence: 99%

\operatorname{var}\left(\mathbf{w}\right)=\operatorname{var}\left(\mathbf{f}\left(\boldsymbol{\uplambda} \right)\right)=\frac{\partial \mathbf{f}\left(\boldsymbol{\uplambda} \right)}{\partial \boldsymbol{\uplambda}}\operatorname{var}\left(\boldsymbol{\uplambda} \right){\left(\frac{\partial \mathbf{f}\left(\boldsymbol{\uplambda} \right)}{\partial \boldsymbol{\uplambda}}\right)}^{\prime },

where w = vec( W ), λ = vec( Λ ), and f ( λ ) are the functions producing the vectorized inverse of Λ , that is, the weights, and ∂ f ( λ )/∂ λ is the Jacobian matrix of f . Note that standard errors of the weight estimates are not produced by default in SEM software because only composite loadings are specified and their standard errors are thereby reported.…”

Section: The Refined H–o Specificationmentioning

confidence: 99%

Specifying composites in structural equation modeling: A refinement of the Henseler–Ogasawara specification

Schuberth

Henseler

2023

Statistical Analysis

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Structural equation modeling (SEM) plays an important role in business and social science and so do composites, that is, linear combinations of variables. However, existing approaches to integrate composites into structural equation models still have limitations. A major leap forward has been the Henseler–Ogasawara (H–O) specification, which for the first time allows for seamlessly integrating composites into structural equation models. In doing so, it relies on emergent variables, that is, the composite of interest, and one or more orthogonal excrescent variables, that is, composites that have no surplus meaning but just span the remaining space of the emergent variable's components. Although the H–O specification enables researchers to flexibly model composites in SEM, it comes along with several practical problems: (i) The H–O specification is difficult to visualize graphically; (ii) its complexity could create difficulties for analysts, and (iii) at times SEM software packages seem to encounter convergence issues with it. In this paper, we present a refinement of the original H–O specification that addresses these three problems. In this new specification, only two components load on each excrescent variable, whereas the excrescent variables are allowed to covary among themselves. This results in a simpler graphical visualization. Additionally, researchers facing convergence issues of the original H–O specification are provided with an alternative specification. Finally, we illustrate the new specification's application by means of an empirical example and provide guidance on how (standardized) weights including their standard errors can be calculated in the R package lavaan. The corresponding Mplus model syntax is provided in the Supplementary Material.

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A Structural Equation Modeling Approach to Canonical Correlation Analysis

Cited by 2 publications

References 9 publications

The Henseler-Ogasawara specification of composites in structural equation modeling: A tutorial.

The Henseler-Ogasawara specification of composites in structural equation modeling: A tutorial.

Specifying composites in structural equation modeling: A refinement of the Henseler–Ogasawara specification

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