How Many Countries for Multilevel Modeling? A Comparison of Frequentist and Bayesian Approaches

By Daniel Stegmueller. 2013

789 citations recorded by the source corpus.

Subfields: Political Science and International Relations, Sociology and Political Science, Strategy and Management

View Paper: https://www.semanticscholar.org/paper/5af9a5697ee71d6f869a5a5d5887f47dc4bd205c

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Citations in the corpus

The relationship between parental literacy involvement, socio-economic status and reading literacy (2017, background): “We model the fact that students in schools are in different countries as a fixed effect for two reasons: (a) we only have 10 possible values for this variable (see Stegmueller 2013 on this issue).”
Multilevel Analysis with Few Clusters: Improving Likelihood-Based Methods to Provide Unbiased Estimates and Accurate Inference (2020, background): “It leads to the rejection of null hypotheses that should have been retained and ultimately to ‘different theoretical conclusions’ (Stegmueller 2013, 757) than a Bayesian approach.”
Fixed and random effects models: making an informed choice (2018, background): “…(3), the REWB model will still be robust for fixed-part parameter estimates (although maximum likelihood estimation may be biased—McNeish 2017; Stegmueller 2013), though it’s efficacy relative to FE would be very limited, since higher level parameters would be estimated with a lot of…”
Gender Equality and Women’s Participation in Transport Cycling (2017, methodology): “For example, when parameters are not normally distributed or sample size is small, Bayesian methods provide more accurate results than the frequentist test (e.g., Lee & Song, 2004; Stegmueller, 2013).”
Small Sample Size Solutions (2020, methodology): “…small sample size issues for structural equation models (SEMs), instead of using frequentist methods (see, for example, Depaoli, 2013; B. O. Muthén & Asparouhov, 2012; Stegmueller, 2013; Van de Schoot, Broere, Perryck, Zondervan-Zwijnenburg & Van Loey, 2015; Van Erp, Mulder & Oberski, 2018).”
Why do higher education institutions internationalize? An investigation of the multilevel determinants of internationalization rationales (2016, methodology): “We employ a Markov Chain Monte Carlo (MCMC) method of estimation, since with a low number of level 2 units it provides more stable parameter estimates than the maximum-likelihood method of estimation (Stegmueller 2013).”
Why Income Inequality Is Dissatisfying—Perceptions of Social Status and the Inequality-Satisfaction Link in Europe (2019, background): “Research suggests that biases in maximum likelihood estimates of macro effects and their confidence intervals (in linear multilevel random intercept models) are only marginal if more than 15 to 20 countries are available at the macro level (Stegmueller, 2013).”
The Externalities of Inequality: Fear of Crime and Preferences for Redistribution in Western Europe (2016, methodology): “Both methods can be severely biased with a small number of clusters (see, e.g., Angrist and Pischke 2008 and Stegmueller 2013a).”
Explaining Fixed Effects: Random Effects Modeling of Time-Series Cross-Sectional and Panel Data* (2014, methodology): “Simulations have shown that the improvement of MCMC-estimated models over likelihood methods is greatest when there are there a small number of higher-level units, for example few countries (Browne and Draper 2006; Stegmueller 2013). ht tp s: // do i.o rg /1 0.”
Regression Analysis of Country Effects Using Multilevel Data: A Cautionary Tale (2013, methodology): “The simulation design of Stegmueller (2013) is the closest to ours in that he uses combinations with C = 5(5)30; NC = 500; ICC = 0.05, 0.10, 0.15, and he considers multilevel linear and non-linear binary models (but probit rather than logit ones).”
Modeling Clustered Data with Very Few Clusters (2016, background): “Other studies have advocated for Bayesianmethods when the number of clusters is small (e.g., Baldwin & Fellingham, 2013; Browne & Draper, 2006; Hox et al., 2012; Stegmueller, 2013; van de Schoot, Broere, Perryck, Zondervan-Zwijnenburg, & van Loey, 2015), particularly for estimates of the variance co”
Multilevel Modelling of Country Effects: A Cautionary Tale (2016, methodology): “Stegmueller (2013) urges caution in using classical ML methods with 10 or 15 groups, especially when the model includes cross-level interactions and random coefficients, whereas Moineddin, Matheson and Glazier (2007) recommend using at least 50 groups.”
The Effect of Small Sample Size on Two-Level Model Estimates: A Review and Illustration (2014, methodology): “Simulation Study Findings The point estimates for the level-1 variance are minimally affected by sample size at either level (Browne and Draper 2006; Maas, C and Hox 2004, 2005; Meuleman and Billiet 2009; Stegmueller 2013).”