Reliability Estimation in a Multilevel Confirmatory Factor Analysis Framework

• Published in: Psychological methods 2014-03, Vol.19 (1), p.72-91
• Main Authors: Geldhof, G. John, Preacher, Kristopher J., Zyphur, Michael J.
• Format: Article
• Language: English
• Subjects: Bayes Theorem; Bias; Confidence Limits (Statistics); Confirmatory Factor Analysis; Estimation; Factor Analysis; Factor Analysis, Statistical; Humans; Monte Carlo Method; Multilevel Analysis; Reproducibility of Results; Statistical Reliability; Statistics as Topic; Structural Equation Modeling
• ISSN: 1082-989X; 1939-1463
• DOI: 10.1037/a0032138

Scales with varying degrees of measurement reliability are often used in the context of multistage sampling, where variance exists at multiple levels of analysis (e.g., individual and group). Because methodological guidance on assessing and reporting reliability at multiple levels of analysis is currently lacking, we discuss the importance of examining level-specific reliability. We present a simulation study and an applied example showing different methods for estimating multilevel reliability using multilevel confirmatory factor analysis and provide supporting Mplus program code. We conclude that (a) single-level estimates will not reflect a scale's actual reliability unless reliability is identical at each level of analysis, (b) 2-level alpha and composite reliability (omega) perform relatively well in most settings, (c) estimates of maximal reliability (H) were more biased when estimated using multilevel data than either alpha or omega, and (d) small cluster size can lead to overestimates of reliability at the between level of analysis. We also show that Monte Carlo confidence intervals and Bayesian credible intervals closely reflect the sampling distribution of reliability estimates under most conditions. We discuss the estimation of credible intervals using Mplus and provide R code for computing Monte Carlo confidence intervals.