Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-11T02:11:05.043Z Has data issue: false hasContentIssue false

26 - Multilevel Modeling

from Part IV - Statistical Approaches

Published online by Cambridge University Press:  25 May 2023

Austin Lee Nichols
Affiliation:
Central European University, Vienna
John Edlund
Affiliation:
Rochester Institute of Technology, New York
Get access

Summary

This chapter provides a brief introduction to multilevel models, specifically organizational models, and should be accessible to researchers who are familiar with ordinary least-squares (OLS) regression (i.e., multiple regression models). OLS regression assumes independence of observations; however, the responses of people clustered within organizational units (e.g., schools, classrooms, hospitals, companies) are likely to exhibit some degree of relatedness. In such scenarios, violating the assumption of independence produces incorrect standard errors that are smaller than they should be – multilevel modeling can alleviate this concern. However, the advantages of multilevel modeling are not purely statistical. Substantively, researchers may seek to understand the degree to which people from the same cluster are similar to each other and identify variables that predict variability within and across clusters. Multilevel analyses allow us to exploit the information in clustered samples and partition variance in the outcome variable into between-cluster and within-cluster variability. We can also use predictors at both the individual (level 1) and group (level 2) levels to explain this between- and within-cluster outcome variance.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aiken, L. S. & West, S. G. (1991). Multiple Regression: Testing and Interpreting Interactions. SAGE Publications.Google Scholar
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Petrov, B. N. & Csaki, B. F. (eds.), Second International Symposium on Information Theory (pp. 267281). Academiai Kiado.Google Scholar
Berkhof, J. & Snijders, T. A. B. (2001). Variance component testing in multilevel models. Journal of Educational and Behavioral Statistics, 26(2), 133152. https://doi.org/10.3102/10769986026002133Google Scholar
Box, G. E. P. & Draper, N. R. (1987), Empirical Model-Building and Response Surfaces. John Wiley & Sons.Google Scholar
Burnham, K. P. & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods & Research, 33(2), 261304. https://doi.org/10.1177/0049124104268644Google Scholar
Burnham, K. P., Anderson, D. R., & Huyvaert, K. P. (2011). AIC model selection and multimodel inference in behavioral ecology: Some background, observations, and comparisons. Behavioral Ecological Sociobiology, 65, 2335. https://doi.org/10.1007/s00265-010-1029-6CrossRefGoogle Scholar
Dominicus, A., Skrondal, A., Gjessing, H. K., Pedersen, N. L., & Palmgren, J. (2006). Likelihood ratio tests in behavioral genetics: Problems and solutions. Behavior Genetics, 36(2), 331340. https://doi.org/10.1007/s10519-005-9034-7CrossRefGoogle ScholarPubMed
Enders, C. K. & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12, 121138. http://dx.doi.org/10.1037/1082-989X.12.2.121Google Scholar
Forster, M. R. (2000). Key concepts in model selection: Performance and generalizability. Journal of Mathematical Psychology, 44(1), 205231. https://doi.org/10.1006/jmps.1999.1284CrossRefGoogle ScholarPubMed
Goldstein, H. (2011). Multilevel Statistical Models (Kendall’s Library of Statistics 3), 4th ed. Edward Arnold.Google Scholar
Gully, S. M. & Phillips, J. M. (2019). On finding your level. In Humphrey, S. E. & LeBreton, J. M. (eds.), The Handbook of Multilevel Theory, Measurement, and Analysis (pp. 1138). American Psychological Association. https://doi.org/10.1037/0000115-002CrossRefGoogle Scholar
Hox, J. J. (2010). Multilevel Analysis: Techniques and Applications, 2nd ed. Routledge.Google Scholar
Hox, J. J., Moerbeek, M., & van de Schoot, R. (2017). Multilevel Analysis: Techniques and Applications, 3rd ed. Routledge.CrossRefGoogle Scholar
Kelloway, E. K. (1995). Structural equation modeling in perspective. Journal of Organizational Behavior, 16, 215224.CrossRefGoogle Scholar
LaHuis, D. M. & Ferguson, M. W. (2009). The accuracy of significance tests for slope variance components in multilevel random coefficient models. Organizational Research Methods, 12(3), 418435. https://doi.org/10.1177%2F1094428107308984Google Scholar
McCoach, D. B. (2019). Multilevel modeling. In Hancock, G.R., Stapleton, L. M., & Mueller, R. O. (eds.) The Reviewers Guide to Quantitative Methods in the Social Sciences (pp. 292-312), 2nd ed. Routledge.Google Scholar
McCoach, D. B. & Cintron, D. W. (2022). An Introduction to Modern Modeling Methods. SAGE Publications.Google Scholar
McCoach, D. B., Rifenbark, G. G., Newton, S. D., et al. (2018). Does the package matter? A comparison of five common multilevel modeling software packages. Journal of Educational and Behavioral Statistics, 43(5), 594627. https://doi.org/10.3102/1076998618776348Google Scholar
McCoach, D. B., Newton, S., & Gambino, A. J. (2022). Evaluating the fit and adequacy of multilevel models. In O’Connell, A. A., McCoach, D. B., & Bell, B. A. (eds.), Multilevel Modeling Methods with Introductory and Advanced Applications. Information Age Publishing.Google Scholar
O’Connell, A. A., McCoach, D. B., & Bell, B. A. (eds.), Multilevel Modeling Methods with Introductory and Advanced Applications. Information Age Publishing.Google Scholar
Raudenbush, S. W. & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods, 2nd ed. SAGE Publications.Google Scholar
Raudenbush, S., Bryk, A., Cheong, Y. & Congdon, R. (2000). HLM Manual. SSI International.Google Scholar
Rights, J. D. & Sterba, S. K. (2019a). New recommendations on the use of R-squared differences in multilevel model comparisons. Multivariate Behavioral Research, 55(4), 568599. https://doi.org/10.1080/00273171.2019.1660605Google Scholar
Rights, J. D. & Sterba, S. K. (2019b). Quantifying explained variance in multilevel models: An integrative framework for defining R-squared measures. Psychological Methods, 24(3), 309338. https://doi.org/10.1037/met000018Google Scholar
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461464. https://www.jstor.org/stable/2958889Google Scholar
Skrondal, A. & Rabe-Hesketh, S. (2004). Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models. Chapman & Hall/CRC Press.Google Scholar
Snijders, T. A. B. & Bosker, R. J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling, 2nd ed. SAGE Publications.Google Scholar
Spybrook, J., Raudenbush, S. W., Liu, X. F., Congdon, R., & Martínez, A. (2006). Optimal design for longitudinal and multilevel research: Documentation for the “Optimal Design” software. Survey Research Center of the Institute of Social Research at University of Michigan.Google Scholar
Stoel, R. D., Garre, F. G., Dolan, C., & van den Wittenboer, G. (2006). On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints. Psychological Methods, 11(4), 439455. https://doi.org/10.1037/1082-989X.11.4.439Google Scholar
West, B. T., Welch, K. B., & Galecki, A. T. (2015). Linear Mixed Models: A Practical Guide Using Statistical Software, 2nd ed. Routledge.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×