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Multilevel Analysis with Few Clusters: Improving Likelihood-Based Methods to Provide Unbiased Estimates and Accurate Inference

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  • Elff, Martin
  • Heisig, Jan Paul
  • Schaeffer, Merlin
  • Shikano, Susumu

Abstract

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.

Suggested Citation

  • Elff, Martin & Heisig, Jan Paul & Schaeffer, Merlin & Shikano, Susumu, 2021. "Multilevel Analysis with Few Clusters: Improving Likelihood-Based Methods to Provide Unbiased Estimates and Accurate Inference," British Journal of Political Science, Cambridge University Press, vol. 51(1), pages 412-426, January.
  • Handle: RePEc:cup:bjposi:v:51:y:2021:i:1:p:412-426_22
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    Cited by:

    1. Nicholas Charron & Victor Lapuente & Andres Rodriguez-Pose, 2022. "Uncooperative Society, Uncooperative Politics or Both? Trust, Polarisation, Populism and COVID-19 Deaths across European regions," Papers in Evolutionary Economic Geography (PEEG) 2204, Utrecht University, Department of Human Geography and Spatial Planning, Group Economic Geography, revised Jan 2022.
    2. Heisig, Jan Paul & Matthewes, Sönke Hendrik, 2022. "No Evidence that Strict Educational Tracking Improves Student Performance through Classroom Homogeneity: A Critical Reanalysis of Esser and Seuring (2020) [Keine Belege für leistungsfördernde Effek," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 51(1), pages 99-111.
    3. Neimanns, Erik & Blossey, Nils, 2022. "From media-party linkages to ownership concentration causes of cross-national variation in media outlets' economic positioning," MPIfG Discussion Paper 22/8, Max Planck Institute for the Study of Societies.
    4. Fernando Bruna & Juan Fernández‐Sastre, 2021. "Regional characteristics and the decision to innovate in a developing country: A multilevel analysis of Ecuadorian firms," Papers in Regional Science, Wiley Blackwell, vol. 100(6), pages 1337-1354, December.
    5. Fernando Bruna, 2022. "Happy Cultures? A Multilevel Model of Well-Being with Individual and Contextual Human Values," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 164(1), pages 55-77, November.
    6. Anna Gottard & Giulia Vannucci & Leonardo Grilli & Carla Rampichini, 2023. "Mixed-effect models with trees," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 431-461, June.

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