Unbiased Estimation of Central Moments in Unbalanced Two- and Three-Level Models

TL;DR

This paper develops exact unbiased estimators for central moments in unbalanced multilevel models, improving statistical inference in complex hierarchical data structures.

Contribution

It introduces closed-form unbiased estimators for central moments in two- and three-level models with unbalanced group sizes, a novel contribution in multilevel analysis.

Findings

Unbiased estimators for second, third, and fourth moments in two-level models.

Unbiased estimators for second and third moments in three-level models.

Applicable to models with unbalanced group sizes.

Abstract

This paper derives closed-form unbiased estimators of central moments in multilevel random-effects models with unbalanced group sizes. In a two-level model, we provide unbiased estimators for the second, third, and fourth central moments under both group-level and observation-level averaging. In a three-level model, we provide unbiased estimators for the second and third central moments.