Sample Size Requirements for Structural Equation Models: An Evaluation of Power, Bias, and Solution Propriety

Sample Size Requirements for Structural Equation Models: An Evaluation of Power, Bias, and Solution Propriety

2013 December | Erika J. Wolf, Kelly M. Harrington, Shauna L. Clark, and Mark W. Miller
This study evaluates sample size requirements for structural equation models (SEMs) using Monte Carlo simulations. It examines how factors such as the number of indicators, factor loadings, path coefficients, and missing data affect statistical power, parameter bias, and solution propriety. The results show that sample size requirements vary widely, ranging from 30 to 460 cases, depending on model characteristics. Common rules-of-thumb for sample size in SEMs are found to be inadequate as they are not model-specific and may lead to over- or underestimation of required sample sizes. The study highlights the importance of considering statistical power, parameter bias, and solution propriety when determining sample size for SEMs. It also demonstrates that models with more indicators, stronger factor loadings, and fewer factors generally require smaller sample sizes. However, models with more complex structures, such as those with multiple factors or stronger factor correlations, require larger samples. The study also shows that missing data can significantly increase sample size requirements. Additionally, it finds that single-indicator models tend to have higher bias and lower statistical power compared to latent variable models. The study concludes that sample size planning for SEMs should be based on the specific model and its characteristics, rather than relying on general rules-of-thumb. The results emphasize the need for careful evaluation of model parameters and the importance of considering bias, errors, and missing data when determining sample size requirements.This study evaluates sample size requirements for structural equation models (SEMs) using Monte Carlo simulations. It examines how factors such as the number of indicators, factor loadings, path coefficients, and missing data affect statistical power, parameter bias, and solution propriety. The results show that sample size requirements vary widely, ranging from 30 to 460 cases, depending on model characteristics. Common rules-of-thumb for sample size in SEMs are found to be inadequate as they are not model-specific and may lead to over- or underestimation of required sample sizes. The study highlights the importance of considering statistical power, parameter bias, and solution propriety when determining sample size for SEMs. It also demonstrates that models with more indicators, stronger factor loadings, and fewer factors generally require smaller sample sizes. However, models with more complex structures, such as those with multiple factors or stronger factor correlations, require larger samples. The study also shows that missing data can significantly increase sample size requirements. Additionally, it finds that single-indicator models tend to have higher bias and lower statistical power compared to latent variable models. The study concludes that sample size planning for SEMs should be based on the specific model and its characteristics, rather than relying on general rules-of-thumb. The results emphasize the need for careful evaluation of model parameters and the importance of considering bias, errors, and missing data when determining sample size requirements.
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