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Regressor and random‐effects dependencies in multilevel models

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  • Peter Ebbes
  • Ulf Böckenholt
  • Michel Wedel

Abstract

The objectives of this paper are (1) to review methods that can be used to test for different types of random effects and regressor dependencies, (2) to present results from Monte Carlo studies designed to investigate the performance of these methods, and (3) to discuss estimation methods that can be used when some but not all of the random effects and regressor independence assumptions, are violated. Because current methods are limited in various ways, we will also present a list of open problems and suggest solutions for some of them. As we will show, the issue of regressor random‐effects independence has received some attention in the econometrics literature, but this important work has had little impact on current research practices in the social and behavioral sciences.

Suggested Citation

  • Peter Ebbes & Ulf Böckenholt & Michel Wedel, 2004. "Regressor and random‐effects dependencies in multilevel models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 161-178, May.
    • Handle: RePEc:bla:stanee:v:58:y:2004:i:2:p:161-178
    DOI: 10.1046/j.0039-0402.2003.00254.x
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    6. Luisa Corrado & Bernard Fingleton, 2016. "The W Matrix in Network and Spatial Econometrics: Issues Relating to Specification and Estimation," CEIS Research Paper 369, Tor Vergata University, CEIS, revised 12 Feb 2016.
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    9. Jee-Seon Kim & Edward Frees, 2006. "Omitted Variables in Multilevel Models," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 659-690, December.
    10. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    11. Calcagnini, Giorgio & Farabullini, Fabio & Giombini, Germana, 2012. "The impact of the recent financial crisis on bank loan interest rates and guarantees," MPRA Paper 36682, University Library of Munich, Germany.
    12. Ugur, Mehmet & Churchill, Sefa Awaworyi & Luong, Hoang M., 2020. "What do we know about R&D spillovers and productivity? Meta-analysis evidence on heterogeneity and statistical power," Research Policy, Elsevier, vol. 49(1).
    13. Manzi, Jorge & San Martin, Ernesto & Van Bellegem, Sébastien, 2010. "School System Evaluation By Value-Added Analysis under Endogeneity," IDEI Working Papers 631, Institut d'Économie Industrielle (IDEI), Toulouse.
    14. Anders Skrondal & Sophia Rabe-Hesketh, 2022. "The Role of Conditional Likelihoods in Latent Variable Modeling," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 799-834, September.
    15. Liouaeddine, Mariem & Bijou, Mohammed & Naji, Faïrouz, 2017. "The Main Determinants of Moroccan Students' Outcomes," MPRA Paper 80247, University Library of Munich, Germany.
    16. Jee-Seon Kim & Edward Frees, 2007. "Multilevel Modeling with Correlated Effects," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 505-533, December.
    17. Paul Clarke & Claire Crawford & Fiona Steele & Anna Vignoles, 2015. "Revisiting fixed- and random-effects models: some considerations for policy-relevant education research," Education Economics, Taylor & Francis Journals, vol. 23(3), pages 259-277, June.
    18. Irene Hueter, 2016. "Latent Instrumental Variables: A Critical Review," Working Papers Series 46, Institute for New Economic Thinking.
    19. Elshandidy, Tamer & Fraser, Ian & Hussainey, Khaled, 2013. "Aggregated, voluntary, and mandatory risk disclosure incentives: Evidence from UK FTSE all-share companies," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 320-333.
    20. Mary Ying-Fang Wang & Paul Tuss & Lihong Qi, 2019. "Augmented Weighted Estimators Dealing with Practical Positivity Violation to Causal inferences in a Random Coefficient Model," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 447-467, June.
    21. Marenya, P. & Kassie, M. & Teklewold, H. & Erenstein, O. & Qaim, M. & Rahut, D., 2018. "Does the adoption of maize-legume cropping diversification and modern seeds affect nutritional security in Ethiopia? Evidence from panel data analysis," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277170, International Association of Agricultural Economists.
    22. Hend Gabr & Fiona Carmichael & Hui Li, 2019. "A Multilevel Simultaneous Equations Modelling Approach to Investigate the Relationship between Poverty and Labour-Force Participation among the Elderly in Egypt," International Journal of Environmental Sciences & Natural Resources, Juniper Publishers Inc., vol. 22(1), pages 01-12, October.
    23. Katherine E. Castellano & Sophia Rabe-Hesketh & Anders Skrondal, 2014. "Composition, Context, and Endogeneity in School and Teacher Comparisons," Journal of Educational and Behavioral Statistics, , vol. 39(5), pages 333-367, October.

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