Oct 12, 2023
2:00 PM
— 3:00 PM
23rd International Conference on Education Research
In education, data are often clustered (e.g., students within schools) and various methods (e.g., multilevel modeling, generalized estimating equations) have been developed over the years to properly account for these nonindependent data structures. Ignoring the clustered data structure is well known to result in erroneous statistical inference tests (e.g., type I errors) due to misestimated standard errors and overly liberal degrees of freedom used. One alternative method when analyzing clustered datasets is to use cluster-robust standard errors (CRSEs; CR0) (Liang & Zeger, 1986). CRSEs are often used in various disciplines (e.g., econometrics) though are not common in educational research. A limitation of CRSEs is that, although they work well with a large number of clusters, CRSEs are known to still underestimate standard errors when there are a limited number of clusters (e.g., < 50). This is of particular importance when analyzing data from cluster randomized controlled trials (CRTs) where often, a limited number of clusters is common. However, over 20 years ago, Bell and McCaffrey (2002) proposed an adjustment to the traditional CRSEs and referred to this as the bias-reduced linearization (or the CR2) estimator used together with Satterthwaite (1946) degrees of freedom (df) adjustments. However, the CR2 has not seen much use in the applied literature due to its limited accessibility. Using Monte Carlo simulations (using R), we evaluated the CR2 estimator using conditions often found in educational research using both continuous and binary outcomes (as well as cross classified data structures). Conditions based on the number of clusters, the intraclass correlation coefficient, and group size (among others) were manipulated. Coverage probabilities, type I error rates, and power were assessed. The CR2 estimator results (with and without df adjustments) were compared to results analyzed using the traditional CR0 CRSEs and multilevel models (MLMs). Findings show that the traditional CRSEs (i.e., CR0) had issues with a few clusters but the CR2 results were comparable to those estimated using multilevel models and are a viable alternative when only a few clusters are present. To extend its use for applied researchers, we also provide a free SPSS add-on that can compute these CRSEs.
Sep 29, 2023
2:00 PM
— 3:00 PM
Society for Research on Educational Effectiveness
Multilevel data can have observations nested within two dimensions of clustering which do not follow a pure nested structure. Failure to consider both dimensions simultaneously may lead to biased results. To address this, cross-classified random effects models (CCREMs) have been developed (Goldstein, 1987) to capture the random effects from multiple dimensions. Although effective, CCREMs may encounter nonconvergence issues. Alternatively, a linear regression model with cluster robust standard errors (OLS-CRSEs) (Liang & Zeger, 1986) can provide asymptotically consistent standard errors. Cameron et al. (2011) introduced the two-way clustering case which is equivalent to the cross-classified data. However, there is a lack of a comprehensive comparison for multilevel data with two dimensions of clustering with a small number of clusters.
Apr 12, 2023
9:00 AM
— 5:00 PM
American Educational Research Association
Data from international large-scale assessments (ILSAs) reflect the nested structure of education systems and is, therefore, very well suited for multilevel modeling (MLM). However, because these data come from complex cluster samples, there are methodological aspects that a researcher needs to understand when doing MLM, e.g., the need for using sampling weights and multiple achievement values for parameter estimation. This course will teach participants how to do MLM with data from ILSAs, such as PIRLS, TIMSS, and PISA. The content of the course will include an overview of the ILSAs and a presentation on the design of these studies and databases and implications for MLM analysis. Participants will learn how to specify two-level models using the HLM software program and also learn about model comparison, centering decisions and their consequences, and available resources for doing three-level models. Time will be allotted for participants to work on practice exercises, with several instructors available to mentor and answer questions. Participants should have a solid understanding of OLS regression and a basic understanding of MLM. Prior experience using a statistical software program, such as Stata or SPSS, is helpful. Prior knowledge about ILSAs or prior experience using the respective databases or HLM software is not required. Rathbun, A., Huang, F., Meinck, S., Park, B., Ikoma, S., & Zhang, Y. (2023, April). Multilevel modeling with large-scale international datasets. Professional development course presented at the annual meeting of the American Educational Research Association