Understanding the Consequences of Collinearity for Multilevel Models: The Importance of Disaggregation Across Levels

References

• Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. https://doi.org/10.18637/jss.v067.i01
   Web of Science ®Google Scholar
• Beckstead, J. W. (2012). Isolating and examining sources of suppression and multicollinearity in multiple linear regression. Multivariate Behavioral Research, 47(2), 224–246. https://doi.org/10.1080/00273171.2012.658331
   PubMed Web of Science ®Google Scholar
• Belsley, D. A. (1991). A guide to using the collinearity diagnostics. Computer Science in Economics and Management, 4(1), 33–50. https://doi.org/10.1007/BF00426854
   Google Scholar
• Bickel, R. (2007). Grand-mean centering, group-mean centering, and raw scores compared. In Multilevel analysis for applied research: It’s just regression! Guilford Press.
   Google Scholar
• Blaze, T. J., & Ye, F. (2012). The effect of within-and cross-level multicollinearity on parameter estimates and standard errors in multilevel modeling with different centering methods. American Educational Research Association Conference, Vancouver, British Columbia, Canada.
   Google Scholar
• Bonate, P. L. (1999). The effect of collinearity on parameter estimates in nonlinear mixed effect models. Pharmaceutical Research, 16(5), 709–717. https://doi.org/10.1023/a:1018828709196
   PubMed Web of Science ®Google Scholar
• Clark, P. C. (2013). The effects of multicollinearity in multilevel models [Doctoral dissertation]. Wright State University.
   Google Scholar
• Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2023). Applied multiple regression/correlation analysis for the behavioral sciences. Routledge.
   Google Scholar
• Cronbach, L. J., & Webb, N. (1975). Between-class and within-class effects in a reported aptitude* treatment interaction: Reanalysis of a study by GL Anderson. Journal of Educational Psychology, 67, 717–724.
   Google Scholar
• Curran, P. J., & Bauer, D. J. (2011). The disaggregation of within-person and between-person effects in longitudinal models of change. Annual Review of Psychology, 62(1), 583–619. https://doi.org/10.1146/annurev.psych.093008.100356
   PubMed Web of Science ®Google Scholar
• Dalal, D. K., & Zickar, M. J. (2012). Some common myths about centering predictor variables in moderated multiple regression and polynomial regression. Organizational Research Methods, 15(3), 339–362. https://doi.org/10.1177/1094428111430540
   Web of Science ®Google Scholar
• Dormann, C. F., Elith, J., Bacher, S., Buchmann, C., Carl, G., Carré, G., Marquéz, J. R. G., Gruber, B., Lafourcade, B., Leitão, P. J., Münkemüller, T., McClean, C., Osborne, P. E., Reineking, B., Schröder, B., Skidmore, A. K., Zurell, D., & Lautenbach, S. (2013). Collinearity: A review of methods to deal with it and a simulation study evaluating their performance. Ecography, 36(1), 27–46. https://doi.org/10.1111/j.1600-0587.2012.07348.x
   Web of Science ®Google Scholar
• Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12(2), 121–138. https://doi.org/10.1037/1082-989X.12.2.121
   PubMed Web of Science ®Google Scholar
• Farrar, D. E., & Glauber, R. R. (1967). Multicollinearity in regression analysis: The problem revisited. The Review of Economics and Statistics, 49(1), 92–107. https://doi.org/10.2307/1937887
   Web of Science ®Google Scholar
• Gale, L. C. (1987). Correlations for multilevel data [Doctoral dissertation]. Stanford University.
   Google Scholar
• Goldberger, A. S. (1991). A course in econometrics. Harvard University Press.
   Google Scholar
• Gunst, R. F., & Mason, R. L. (1977). Advantages of examining multicollinearities in regression analysis. Biometrics, 33(1), 249–260. https://doi.org/10.2307/2529320
   PubMed Web of Science ®Google Scholar
• Hayo, B. (2018). On standard-error-decreasing complementarity: Why collinearity is not the whole story. Journal of Quantitative Economics, 16(1), 289–307. https://doi.org/10.1007/s40953-017-0092-5
   Google Scholar
• Hendrickx, J. (2018). Collinearity in mixed models [Paper presentation]. PHUSE EU Connect Conference, Frankfurt, Germany.
   Google Scholar
• Hofmann, D. A., & Gavin, M. B. (1998). Centering decisions in hierarchical linear models: Implications for research in organizations. Journal of Management, 24(5), 623–641. https://doi.org/10.1177/014920639802400504
   Web of Science ®Google Scholar
• Kenny, D. A., & La Voie, L. (1985). Separating individual and group effects. Journal of Personality and Social Psychology, 48(2), 339–348. https://doi.org/10.1037/0022-3514.48.2.339
   Web of Science ®Google Scholar
• Kreft, I. G., & De Leeuw, J. (1998). Introducing multilevel modeling. Sage.
   Google Scholar
• Kubitschek, W. N., & Hallinan, M. T. (1999). Collinearity, bias, and effect size: Modeling “the” effect of track on achievement. Social Science Research, 28(4), 380–402. https://doi.org/10.1006/ssre.1999.0653
   Web of Science ®Google Scholar
• Lüdtke, O., Marsh, H. W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies. Psychological Methods, 13(3), 203–229. https://doi.org/10.1037/a0012869
   PubMed Web of Science ®Google Scholar
• Mason, C. H., & Perreault, W. D. Jr, (1991). Collinearity, power, and interpretation of multiple regression analysis. Journal of Marketing Research, 28(3), 268–280. https://doi.org/10.1177/002224379102800302
   Web of Science ®Google Scholar
• Mela, C. F., & Kopalle, P. K. (2002). The impact of collinearity on regression analysis: The asymmetric effect of negative and positive correlations. Applied Economics, 34(6), 667–677. https://doi.org/10.1080/00036840110058482
   Web of Science ®Google Scholar
• Muthén, B. O. (1990). Mean and covariance structure analysis of hierarchical data. UCLA (Statistics Series No. 62).
   Google Scholar
• O’Brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality & Quantity, 41(5), 673–690. https://doi.org/10.1007/s11135-006-9018-6
   Web of Science ®Google Scholar
• Raudenbush, S. W. (2009). Adaptive centering with random effects: An alternative to the fixed effects model for studying time-varying treatments in school settings. Education Finance and Policy, 4(4), 468–491. https://doi.org/10.1162/edfp.2009.4.4.468
   Web of Science ®Google Scholar
• Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods. Sage.
   Google Scholar
• Raudenbush, S. W., & Willms, J. (1995). The estimation of school effects. Journal of Educational and Behavioral Statistics, 20(4), 307–335. https://doi.org/10.2307/1165304
   Web of Science ®Google Scholar
• Rights, J. D. (2022). Aberrant distortion of variance components in multilevel models under conflation of level-specific effects. Psychological Methods, 28(5), 1154–1177. https://doi.org/10.1037/met0000514
   PubMed Web of Science ®Google Scholar
• Rights, J. D., & Sterba, S. K. (2019). Quantifying explained variance in multilevel models: An integrative framework for defining R-squared measures. Psychological Methods, 24(3), 309–338. https://doi.org/10.1037/met0000184
   PubMed Web of Science ®Google Scholar
• Rights, J. D., & Sterba, S. K. (2021). Effect size measures for longitudinal growth analyses: Extending a framework of multilevel model R‐squared to accommodate heteroscedasticity, autocorrelation, nonlinearity, and alternative centering strategies. New Directions for Child and Adolescent Development, 2021(175), 65–110. https://doi.org/10.1002/cad.20387
   PubMedGoogle Scholar
• Robinson, W. S. (1950). Ecological correlations and the behavior of individuals. American Sociological Review, 15(3), 351–357. https://doi.org/10.2307/2087176
   Web of Science ®Google Scholar
• Scott, A. J., & Holt, D. (1982). The effect of two-stage sampling on ordinary least squares methods. Journal of the American Statistical Association, 77(380), 848–854. https://doi.org/10.1080/01621459.1982.10477897
   Web of Science ®Google Scholar
• Shieh, Y. Y., & Fouladi, R. T. (2003). The effect of multicollinearity on multilevel modeling parameter estimates and standard errors. Educational and Psychological Measurement, 63(6), 951–985. https://doi.org/10.1177/0013164403258402
   Web of Science ®Google Scholar
• Silvey, S. D. (1969). Multicollinearity and imprecise estimation. Journal of the Royal Statistical Society: Series B, 31(3), 539–552. https://doi.org/10.1111/j.2517-6161.1969.tb00813.x
   Google Scholar
• Snijders, T. A., & Bosker, R. J. (2012). Multilevel analysis: An introduction to basic and advanced multilevel modeling. Sage.
   Google Scholar
• Stinnett, S. S. (1994). Collinearity in mixed models [Doctoral dissertation]. The University of North Carolina at Chapel Hill.
   Google Scholar
• Willan, A. R., & Watts, D. G. (1978). Meaningful multicollinearity measures. Technometrics, 20(4), 407–412. https://doi.org/10.1080/00401706.1978.10489694
   Web of Science ®Google Scholar
• Yaremych, H. E., Preacher, K. J., & Hedeker, D. (2021). Centering categorical predictors in multilevel models: Best practices and interpretation. Psychological Methods, 28(3), 613–630. https://doi.org/10.1037/met0000434
   PubMed Web of Science ®Google Scholar
• Yu, H., Jiang, S., & Land, K. C. (2015). Multicollinearity in hierarchical linear models. Social Science Research, 53, 118–136. https://doi.org/10.1016/j.ssresearch.2015.04.008
   PubMed Web of Science ®Google Scholar
• Zhang, G., & Chen, J. J. (2013). Adaptive fitting of linear mixed-effects models with correlated random effects. Journal of Statistical Computation and Simulation, 83(12), 2291–2314. https://doi.org/10.1080/00949655.2012.690763
   Web of Science ®Google Scholar