TY - JOUR

T1 - Multilevel Analysis with Few Clusters

T2 - Improving Likelihood-Based Methods to Provide Unbiased Estimates and Accurate Inference

AU - Elff, Martin

AU - Heisig, Jan Paul

AU - Schaeffer, Merlin

AU - Shikano, Susumu

PY - 2021

Y1 - 2021

N2 - Quantitative comparative social scientists have long worried about the performance of multilevel models when the number of upper-level units is small. Adding to these concerns, an influential Monte Carlo study by Stegmueller (2013) suggests that standard maximum-likelihood (ML) methods yield biased point estimates and severely anti-conservative inference with few upper-level units. In this article, the authors seek to rectify this negative assessment. First, they show that ML estimators of coefficients are unbiased in linear multilevel models. The apparent bias in coefficient estimates found by Stegmueller can be attributed to Monte Carlo Error and a flaw in the design of his simulation study. Secondly, they demonstrate how inferential problems can be overcome by using restricted ML estimators for variance parameters and a t-distribution with appropriate degrees of freedom for statistical inference. Thus, accurate multilevel analysis is possible within the framework that most practitioners are familiar with, even if there are only a few upper-level units.

AB - Quantitative comparative social scientists have long worried about the performance of multilevel models when the number of upper-level units is small. Adding to these concerns, an influential Monte Carlo study by Stegmueller (2013) suggests that standard maximum-likelihood (ML) methods yield biased point estimates and severely anti-conservative inference with few upper-level units. In this article, the authors seek to rectify this negative assessment. First, they show that ML estimators of coefficients are unbiased in linear multilevel models. The apparent bias in coefficient estimates found by Stegmueller can be attributed to Monte Carlo Error and a flaw in the design of his simulation study. Secondly, they demonstrate how inferential problems can be overcome by using restricted ML estimators for variance parameters and a t-distribution with appropriate degrees of freedom for statistical inference. Thus, accurate multilevel analysis is possible within the framework that most practitioners are familiar with, even if there are only a few upper-level units.

KW - Faculty of Social Sciences

KW - multi-leveled analysis

KW - cross-national comparison

KW - comparative politics

KW - methodology

KW - statistical inference

KW - maximum likelihood

U2 - 10.1017/S0007123419000097

DO - 10.1017/S0007123419000097

M3 - Journal article

VL - 51

SP - 412

EP - 426

JO - British Journal of Political Science

JF - British Journal of Political Science

SN - 0007-1234

IS - 1

ER -