The Impact of Over-Simplifying the Between-Subject Covariance Structure on Inferences of Fixed Effects in Modeling Nested Data

• Published in: Structural equation modeling Vol. 26; no. 1; pp. 1 - 11
• Main Authors: Wang, Lijuan, Yang, Miao, Liu, Xiao
• Format: Journal Article
• Language: English
• Published: Hove Routledge 02.01.2019; Psychology Press
• Subjects: Data Analysis; Economic models; fixed effect inference; growth curve modeling; ignoring nested data structure; Inferences; misspecified between-subject covariance structure; multilevel modeling
• ISSN: 1070-5511; 1532-8007
• DOI: 10.1080/10705511.2018.1489725

This study discusses the effects of oversimplifying the between-subject covariance structure on inferences for fixed effects in modeling nested data. Linear and quadratic growth curve models (GCMs) with both full and simplified between-subject covariance structures were fit to real longitudinal data. The results were contradictory to the statement that using oversimplified between-subject covariance structures (e.g., uni-level analysis) leads to underestimated standard errors of fixed effect estimates and thus inflated Type I error rates. We analytically derived simple mathematical forms to systematically examine the oversimplification effects for the linear GCMs. The derivation results were aligned with the real data analysis results and further revealed the conditions under which the standard errors of the fixed-effect intercept and slope estimates could be underestimated or overestimated for over-simplified linear GCMs. Therefore, our results showed that the underestimation statement is a myth and can be misleading. Implications are discussed and recommendations are provided.