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Modeling Measurement Errors of the Exogenous Composites From Congeneric Measures in Interaction Models
Yu-Yu Hsiao1, Oi-Man Kwok2, Mark H C Lai3
1Department of Individual, Family, and Community Education, University of New Mexico.
Structural Equation Modeling : a Multidisciplinary Journal
|July 9, 2021
Summary
This study compared methods for testing interaction effects using congeneric measures. Four reliability estimates performed similarly well when adjusting for measurement errors in latent moderated structural equation (LMS) and reliability-adjusted product indicator (RAPI) models.
Area of Science:
- Psychometrics
- Structural Equation Modeling
- Statistical Methods
Background:
- Testing interaction effects in structural equation models (SEM) is crucial for understanding complex relationships.
- Congeneric measures, which vary in factor loadings and error variances, present unique challenges in SEM analyses.
- Accurate adjustment for measurement error is essential for reliable estimation of interaction effects.
Purpose of the Study:
- To evaluate the performance of two single indicator methods, latent moderated structural equation (LMS) and reliability-adjusted product indicator (RAPI), for testing interaction effects with congeneric measures.
- To compare the effectiveness of four reliability estimates (Cronbach's alpha, omega composite, Coefficient H, and greatest lower bound [GLB]) in adjusting for measurement errors of exogenous composites.
Main Methods:
- A simulation study was conducted to assess the performance of LMS and RAPI methods.
- Four different reliability estimation methods were applied to adjust for measurement errors.
- The study manipulated sample sizes and population reliability conditions.
Main Results:
- The four reliability estimates demonstrated comparable performance when adjusting for measurement errors in the context of interaction effects with congeneric measures.
- Both LMS and RAPI methods showed effectiveness in estimating interaction effects under the simulated conditions.
- The choice between LMS and RAPI may depend on specific sample size and reliability conditions.
Conclusions:
- The selection of reliability estimation methods does not significantly impact the estimation of interaction effects when using congeneric measures with either LMS or RAPI.
- Practical recommendations are provided regarding the choice of reliability estimates and methods based on study characteristics.
- This research contributes to best practices in SEM for analyzing interaction effects with imperfectly measured constructs.
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