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Estimating Multilevel Logistic Regression Models When the Number of Clusters is Low: A Comparison of Different Statistical Software Procedures
Open accessAbstract
Multilevel logistic regression models are increasingly being used to analyze clustered data in medical, public health, epidemiological, and educational research. Procedures for estimating the parameters of such models are available in many statistical software packages. There is currently little evidence on the minimum number of clusters necessary to reliably fit multilevel regression models. We conducted a Monte Carlo study to compare the performance of different statistical software procedures for estimating multilevel logistic regression models when the number of clusters was low. We examined procedures available in BUGS, HLM, R, SAS, and Stata. We found that there were qualitative differences in the performance of different software procedures for estimating multilevel logistic models when the number of clusters was low. Among the likelihood-based procedures, estimation methods based on adaptive Gauss-Hermite approximations to the likelihood (glmer in R and xtlogit in Stata) or adaptive Gaussian quadrature (Proc NLMIXED in SAS) tended to have superior performance for estimating variance components when the number of clusters was small, compared to software procedures based on penalized quasi-likelihood. However, only Bayesian estimation with BUGS allowed for accurate estimation of variance components when there were fewer than 10 clusters. For all statistical software procedures, estimation of variance components tended to be poor when there were only five subjects per cluster, regardless of the number of clusters.
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“Finally, because validation studies of a certain prediction model are often sparse, traditional (frequentist) meta-analysis models may suffer from convergence issues and yield unreliable estimates of precision and between-study heterogeneity.64”
From A framework for meta-analysis of prediction model studies with binary and time-to-event outcomes (2019) · cites this paper as [64]
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Metadata
- Authors
- Austin, P. C.
- Affiliations
- Institute for Clinical Evaluative Sciences (CA)
- Corresponding author
- Austin, Peter C
- ORCID
- Austin, Peter C
- Venue
- The International Journal of Biostatistics
- Publisher
- Walter de Gruyter GmbH
- Published
- 2010-04-22
- Volume
- 6
- Issue
- 1
- Pages
- Article 16-Article 16
- ISSN
- 1557-4679 (ISSN-L)
- PMC
- PMC2949382
- OpenAlex
- W2093789600
- Cited by
- 193
- References
- 18
- Citations by year
- 2026: 7 · 2025: 15 · 2024: 7 · 2023: 15 · 2022: 10 · 2021: 11 · 2020: 11 · 2019: 11 · 2018: 13 · 2017: 15 · 2016: 24 · 2015: 20 · 2014: 13 · 2013: 14 · 2012: 3
- FWCI
- 5.72
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The International Journal of Biostatistics (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Heart and Stroke Foundation of Canada
- Institute for Clinical Evaluative Sciences
- Ontario Ministry of Health and Long-Term Care
- Canadian Institutes of Health Research (86508, MOP86508)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Keywords
- multilevel logistic regression, small number of clusters, variance component estimation, statistical software comparison, penalized quasi-likelihood, Bayesian estimation, likelihood estimation, clustered data, Monte Carlo simulation
- MeSH terms
- Bayes Theorem, Data Interpretation, Statistical, Humans, Monte Carlo Method, Software, Models, Statistical, Cluster Analysis, Linear Models, Logistic Models
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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