Gregory R. Hancock | Searcharxiv

arXiv2026

Do I Even Need a Multilevel Model? Negligible Effect Significance Testing for Intraclass Correlation Coefficients

In applied research, the decision to utilize multilevel modeling (MLM) is commonly guided by comparing a point estimate of the unconditional intraclass correlation coefficient (ICC) against some recommended threshold (e.g., 0.05). This naive approach, however, fails to account for sampling uncertainty and provides no formal inferential justification for a decision. The current work introduces negligible effect significance testing (NEST; or equivalence testing) for the ICC, proposing a framework that performs this test using a pivotal quantity of the ICC based on the F statistic. Furthermore, we offer guidance to help researchers define "negligible" that utilizes the design effect to characterize a tolerable level of variance inflation. R code illustrating the proposed procedure is provided.

stat.ME↗

arXiv2025

Specifying Composites in Structural Equation Modeling: Traditional, Recent and New Approaches

Composites, or linear combinations of variables, play an important role in multivariate behavioral research. They appear in the form of indices, inventories, formative constructs, parcels, and emergent variables. Although structural equation modeling is widely used to study relations between variables, current approaches to incorporating composites have one or more limitations. These limitations include not modeling composite creation, not employing weights as model parameters, not being able to estimate weights, not allowing for composites in endogenous model positions, and not being able to assess whether a composite fully transmits the effects of or on its components. To address these limitations, we propose two novel composite specifications. The first specification combines the refined H-O specification of composites with phantom variables and uses the inverse of the weights as free parameters. The second specification blends the H-O specification with the pseudo-indicator approach of Rose et al. and uses the weights of all but one indicator as free parameters. We demonstrate the applicability of these specifications using an empirical example. The paper concludes with recommendations for choosing among the available composite specifications, as well as suggestions for future research.

stat.ME↗