Kelcey, B., Bai, F., Xie, Y., & Cox, K.
Micro-macro and macro-micro effect estimation in small scale latent variable models with Croon’s method
Psychological theories and research often incorporate and investigate how macro- and micro-level processes cooperate to convey, provision, and envelope effects. A historical challenge in these multilevel contexts has been incorporating micro-macro, bottom-up, or emergent effects alongside the more common top-down or macro-micro effects. Although multilevel structural equation modeling provides a framework for such analyses, a persistent issue is the large sample size requirements necessary to reliably estimate parameters. In this study, we outline extensions to the recently developed Croon-based estimator for multilevel structural equation models. We then evaluate the performance of Croon’s approach under a method-of-moments corrected maximum likelihood estimator to probe models that integrate micro-macro and macro-micro effects. The results suggest that Croon’s method often outperforms maximum likelihood in terms of convergence, bias, and root mean-squared error and represents a useful complementary estimator. We provide R code that applies the estimator to an example using the lavaan package.
Testing, Psychometrics, Methodology in Applied Psychology, 2020, Vol. 27, pp. 477-499, DOI: 10.4473/TPM27.3.9
