An Empirical Evaluation of Structural Equation Modeling Analysis Based on Composite Variables With Correction for Measurement Errors

• In Event: Composite/Factor Scores Analyses With Bias Correction: Good Alternatives to Full Structural Equation Modeling?

Abstract

Structural equation modeling has been applied in various research fields including education, psychology, and social sciences. Many constructs in these fields are not directly observable from individuals, for example, personality traits, aptitudes, and depression. An important distinction of SEM from classical statistical techniques such as regression analysis is that SEM allows for investigating relationships among latent variables that are free from measurement errors.
Despite of this advantage, an SEM model may become very complex when the number of measurement indicators is large, thus requiring a large sample size in order to obtain accurate and stable parameter estimates, and valid statistical testing. This is particularly concerning when measurement indicators are anchored on a limited number of response options. For studies with small sample size relative to model size, reducing model size and using composite scores (e.g., by summing scores across measurement indicators) as approximation of latent constructs is tempting. However, this approach may yield seriously biased estimates of path coefficients among latent variables. The direction and degree of bias is hard to predict, depending on reliability coefficient of composite scores, complexity of model, and whether the model is correctly or incorrectly specified (Cole & Preacher, 2014).

To correct for bias due to measurement errors while using composite variables, researchers (e.g., Cole & Preacher, 2014; Zhang & Yang, 2020) have suggested correcting for measurement errors by constraining the proportion of measurement error variance for the composite variable as one minus reliability coefficient. This approach has been applied in some empirical studies but pros and cons of such applications have not been discussed.

When applying this approach to an empirical study, a researcher may face the following related questions: how should I determine whether or not one composite variable is sufficient to approximate a latent construct? When measurement indicators are ordinal, which reliability index is appropriate? Would it be problematic if coefficient alpha (the most widely used yet misused index) is used to estimate reliability? How may an inappropriate choice of reliability index and/or estimation method impact accuracy of path coefficient estimation among latent factors? Does this approach perform better than the analysis based on composite scores without correcting for measurement errors in all circumstances?

The proposed study attempts to discuss these issues using data from an empirical study. The sample size was 11831 allowing for analyzing a full SEM model (see Figure 1). The model is specified based on findings from our previous studies. The model consists of 5 latent variables measured by a total of 55 indicators, anchored on 2, 4, or 5-point scales. Results from the full SEM model will be used to evaluate the performance of two approaches based on composite variables: with and without correction for measurement errors. For models based on composite variables, two sets of analyses will be conducted: using the whole sample of 11831 and using subsets of sample with small sizes (e.g., n=100).

Authors

• Yanyun Yang, Florida State University

• Lu Liu, Florida State University

• Zhenzhen Liu, Arizona State University

• Cun-Xian Jia, Shandong University

• Xianchen Liu, The University of Pennsylvania