EDA for HLM: Visualization when probabilistic inference fails

Jake Bowers, Katherine W. Drake

Research output: Contribution to journalArticlepeer-review


Nearly all hierarchical linear models presented to political science audiences are estimated using maximum likelihood under a repeated sampling interpretation of the results of hypothesis tests. Maximum likelihood estimators have excellent asymptotic properties but less than ideal small sample properties. Multilevel models common in political science have relatively large samples of units like individuals nested within relatively small samples of units like countries. Often these level-2 samples will be so small as to make inference about level-2 effects uninterpretable in the likelihood framework from which they were estimated. When analysts do not have enough data to make a compelling argument for repeated sampling based probabilistic inference, we show how visualization can be a useful way of allowing scientific progress to continue despite lack of fit between research design and asymptotic properties of maximum likelihood estimators.

Original languageEnglish (US)
Pages (from-to)301-326
Number of pages26
JournalPolitical Analysis
Issue number4
StatePublished - Sep 2005
Externally publishedYes

ASJC Scopus subject areas

  • Sociology and Political Science
  • Political Science and International Relations


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