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A Latent Cluster-Mean Approach to the Contextual Effects Model With Missing Data

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  • Yongyun Shin
  • Stephen W. Raudenbush

Abstract

In organizational studies involving multiple levels, the association between a covariate and an outcome often differs at different levels of aggregation, giving rise to widespread interest in “contextual effects models.†Such models partition the regression into within- and between-cluster components. The conventional approach uses each cluster’s sample average of the covariate as a regressor to identify the between-cluster component of the regression. This procedure, however, yields biased estimates of contextual effects unless the cluster sizes are large. Moreover, bias in estimation of such contextual coefficients in turn introduces bias in estimated coefficients of other correlated cluster-level covariates. Missing data further complicate valid inferences. This article proposes an alternative approach that conditions on the latent “true†cluster means of covariates having contextual effects while taking into account ignorable missing data with a general missing pattern at each level. The proposed model may include random coefficients. We compare inferences under different approaches in estimation of a contextual effects model using data from two national surveys of high school achievement.

Suggested Citation

  • Yongyun Shin & Stephen W. Raudenbush, 2010. "A Latent Cluster-Mean Approach to the Contextual Effects Model With Missing Data," Journal of Educational and Behavioral Statistics, , vol. 35(1), pages 26-53, February.
  • Handle: RePEc:sae:jedbes:v:35:y:2010:i:1:p:26-53
    DOI: 10.3102/1076998609345252
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    Cited by:

    1. Andrew Bell & Malcolm Fairbrother & Kelvyn Jones, 2019. "Fixed and random effects models: making an informed choice," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(2), pages 1051-1074, March.
    2. Jeong, Tay, 2022. "Contextual fallacy in MLMs with cross-level interaction: A critical review of neighborhood effects on psychiatric resilience," Social Science & Medicine, Elsevier, vol. 310(C).
    3. Yongyun Shin & Stephen Raudenbush, 2012. "Confidence Bounds and Power for the Reliability of Observational Measures on the Quality of a Social Setting," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 543-560, July.
    4. Stephen A. Mistler & Craig K. Enders, 2017. "A Comparison of Joint Model and Fully Conditional Specification Imputation for Multilevel Missing Data," Journal of Educational and Behavioral Statistics, , vol. 42(4), pages 432-466, August.
    5. Simon Grund & Oliver Lüdtke & Alexander Robitzsch, 2018. "Multiple Imputation of Missing Data at Level 2: A Comparison of Fully Conditional and Joint Modeling in Multilevel Designs," Journal of Educational and Behavioral Statistics, , vol. 43(3), pages 316-353, June.
    6. Satoshi Usami, 2017. "Generalized SAMPLE SIZE Determination Formulas for Investigating Contextual Effects by a Three-Level Random Intercept Model," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 133-157, March.
    7. Nicholas J. Rockwood, 2020. "Maximum Likelihood Estimation of Multilevel Structural Equation Models with Random Slopes for Latent Covariates," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 275-300, June.
    8. Regnerus, Mark, 2017. "Is structural stigma's effect on the mortality of sexual minorities robust? A failure to replicate the results of a published study," Social Science & Medicine, Elsevier, vol. 188(C), pages 157-165.
    9. Bell, Andrew & Jones, Kelvyn, 2015. "Explaining Fixed Effects: Random Effects Modeling of Time-Series Cross-Sectional and Panel Data," Political Science Research and Methods, Cambridge University Press, vol. 3(1), pages 133-153, January.
    10. Keenan A. Pituch & Laura M. Stapleton, 2012. "Distinguishing Between Cross- and Cluster-Level Mediation Processes in the Cluster Randomized Trial," Sociological Methods & Research, , vol. 41(4), pages 630-670, November.
    11. 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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