## Data-Generating Mechanisms Versus Constructively Defined Latent Variables in Multitrait–Multimethod Analysis: A Comment on Castro-Schilo, Widaman, and Grimm (2013)

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**Data-Generating Mechanisms Versus Constructively Defined Latent Variables in Multitrait–Multimethod Analysis: A Comment on Castro-Schilo, Widaman, and Grimm (2013).**/ Geiser, Christian; Koch, Tobias; Eid, Michael.

In: Structural Equation Modeling: A Multidisciplinary Journal, Vol. 21, No. 4, 02.10.2014, p. 509-523.

Research output: Journal contributions › Journal articles › Research › peer-review

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*Structural Equation Modeling: A Multidisciplinary Journal*, vol. 21, no. 4, pp. 509-523. https://doi.org/10.1080/10705511.2014.919816

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*Structural Equation Modeling: A Multidisciplinary Journal*,

*21*(4), 509-523. https://doi.org/10.1080/10705511.2014.919816

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### Bibtex

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### RIS

TY - JOUR

T1 - Data-Generating Mechanisms Versus Constructively Defined Latent Variables in Multitrait–Multimethod Analysis:

T2 - A Comment on Castro-Schilo, Widaman, and Grimm (2013)

AU - Geiser, Christian

AU - Koch, Tobias

AU - Eid, Michael

PY - 2014/10/2

Y1 - 2014/10/2

N2 - In a recent article, Castro-Schilo, Widaman, and Grimm (2013) compared different approaches for relating multitrait–multimethod (MTMM) data to external variables. Castro-Schilo et al. reported that estimated associations with external variables were in part biased when either the correlated traits–correlated uniqueness (CT-CU) or correlated traits–correlated (methods–1) [CT-C(M–1)] models were fit to data generated from the correlated traits–correlated methods (CT-CM) model, whereas the data-generating CT-CM model accurately reproduced these associations. Castro-Schilo et al. argued that the CT-CM model adequately represents the data-generating mechanism in MTMM studies, whereas the CT-CU and CT-C(M–1) models do not fully represent the MTMM structure. In this comment, we question whether the CT-CM model is more plausible as a data-generating model for MTMM data than the CT-C(M–1) model. We show that the CT-C(M–1) model can be formulated as a reparameterization of a basic MTMM true score model that leads to a meaningful and parsimonious representation of MTMM data. We advocate the use confirmatory factor analysis MTMM models in which latent trait, method, and error variables are explicitly and constructively defined based on psychometric theory.

AB - In a recent article, Castro-Schilo, Widaman, and Grimm (2013) compared different approaches for relating multitrait–multimethod (MTMM) data to external variables. Castro-Schilo et al. reported that estimated associations with external variables were in part biased when either the correlated traits–correlated uniqueness (CT-CU) or correlated traits–correlated (methods–1) [CT-C(M–1)] models were fit to data generated from the correlated traits–correlated methods (CT-CM) model, whereas the data-generating CT-CM model accurately reproduced these associations. Castro-Schilo et al. argued that the CT-CM model adequately represents the data-generating mechanism in MTMM studies, whereas the CT-CU and CT-C(M–1) models do not fully represent the MTMM structure. In this comment, we question whether the CT-CM model is more plausible as a data-generating model for MTMM data than the CT-C(M–1) model. We show that the CT-C(M–1) model can be formulated as a reparameterization of a basic MTMM true score model that leads to a meaningful and parsimonious representation of MTMM data. We advocate the use confirmatory factor analysis MTMM models in which latent trait, method, and error variables are explicitly and constructively defined based on psychometric theory.

KW - Sociology

KW - constructively defined latent variables

KW - CT-CM model

KW - CT-C(M-1) model

UR - http://www.scopus.com/inward/record.url?scp=84927564218&partnerID=8YFLogxK

U2 - 10.1080/10705511.2014.919816

DO - 10.1080/10705511.2014.919816

M3 - Journal articles

C2 - 25419098

VL - 21

SP - 509

EP - 523

JO - Structural Equation Modeling: A Multidisciplinary Journal

JF - Structural Equation Modeling: A Multidisciplinary Journal

SN - 1532-8007

IS - 4

ER -