Multilevel Analysis with Few Clusters: Improving Likelihood-Based Methods to Provide Unbiased Estimates and Accurate Inference
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Multilevel Analysis with Few Clusters : Improving Likelihood-Based Methods to Provide Unbiased Estimates and Accurate Inference. / Elff, Martin; Heisig, Jan Paul; Schaeffer, Merlin; Shikano, Susumu.
In: British Journal of Political Science, Vol. 51, No. 1, 2021, p. 412 - 426.Research output: Contribution to journal › Journal article › Research › peer-review
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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 -
ID: 241114683