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An investigation of the influence of sample size and model complexity on point and interval estimates in two-level linear models
Bell, B. A., Morgan, G. B., Schoeneberger, J. A., Kromrey, J. D., & Ferron, J. M. (2014). How low can you go? An investigation of the influence of sample size and model complexity on point and interval estimates in two-level linear models. Methodology, 10(1), 1-11. https://doi.org/10.1027/1614-2241/a000062
Whereas general sample size guidelines have been suggested when estimating multilevel models, they are only generalizable to a relatively limited number of data conditions and model structures, both of which are not very feasible for the applied researcher. In an effort to expand our understanding of two-level multilevel models under less than ideal conditions, Monte Carlo methods, through SAS/IML, were used to examine model convergence rates, parameter point estimates (statistical bias), parameter interval estimates (confidence interval accuracy and precision), and both Type I error control and statistical power of tests associated with the fixed effects from linear two-level models estimated with PROC MIXED. These outcomes were analyzed as a function of: (a) level-1 sample size, (b) level-2 sample size, (c) intercept variance, (d) slope variance, (e) collinearity, and (f) model complexity. Bias was minimal across nearly all conditions simulated. The 95% confidence interval coverage and Type I error rate tended to be slightly conservative. The degree of statistical power was related to sample sizes and level of fixed effects; higher power was observed with larger sample sizes and level-1 fixed effects.