Croon’s Bias-Corrected Factor Score Path Analysis for Small- to Moderate-Sample Multilevel Structural Equation Models

Abstract

Maximum likelihood estimation of multilevel structural equation model (MLSEM) parameters is a preferred approach to probe theories involving latent variables in multilevel settings. Although maximum likelihood has many desirable properties, a major limitation is that it often fails to converge and can incur significant bias when implemented in studies with a small to moderate multilevel sample (e.g., fewer than 100 organizations with 10 or less individuals/organization). To address similar limitations in single-level SEM, literature has developed Croon’s bias-corrected factor score path analysis estimator that converges more regularly than maximum likelihood and delivers less biased parameter estimates with small to moderate sample sizes. We derive extensions to this framework for MLSEMs and probe the degree to which the estimator retains these advantages with small to moderate multilevel samples. The estimator emerges as a useful alternative or complement to maximum likelihood because it often outperforms maximum likelihood in small to moderate multilevel samples in terms of convergence, bias, error variance, and power. The proposed estimator is implemented as a function in R using lavaan and is illustrated using a multilevel mediation example.