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Predictive Inference Using Latent Variables with Covariates

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  • Lynne Schofield
  • Brian Junker
  • Lowell Taylor
  • Dan Black

Abstract

Plausible values (PVs) are a standard multiple imputation tool for analysis of large education survey data, which measures latent proficiency variables. When latent proficiency is the dependent variable, we reconsider the standard institutionally generated PV methodology and find it applies with greater generality than shown previously. When latent proficiency is an independent variable, we show that the standard institutional PV methodology produces biased inference because the institutional conditioning model places restrictions on the form of the secondary analysts’ model. We offer an alternative approach that avoids these biases based on the mixed effects structural equations model of Schofield (Modeling measurement error when using cognitive test scores in social science research. Doctoral dissertation. Department of Statistics and Heinz College of Public Policy. Pittsburgh, PA: Carnegie Mellon University, 2008 ). Copyright The Psychometric Society 2015

Suggested Citation

  • Lynne Schofield & Brian Junker & Lowell Taylor & Dan Black, 2015. "Predictive Inference Using Latent Variables with Covariates," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 727-747, September.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:3:p:727-747
    DOI: 10.1007/s11336-014-9415-z
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    References listed on IDEAS

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    1. Brian Junker & Lynne Schofield & Lowell Taylor, 2012. "The use of cognitive ability measures as explanatory variables in regression analysis," IZA Journal of Labor Economics, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 1(1), pages 1-19, December.
    2. Kevin Lang & Michael Manove, 2011. "Education and Labor Market Discrimination," American Economic Review, American Economic Association, vol. 101(4), pages 1467-1496, June.
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    4. Robert Mislevy, 1991. "Randomization-based inference about latent variables from complex samples," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 177-196, June.
    5. Hua-Hua Chang & William Stout, 1993. "The asymptotic posterior normality of the latent trait in an IRT model," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 37-52, March.
    6. Deping Li & Andreas Oranje & Yanlin Jiang, 2009. "On the Estimation of Hierarchical Latent Regression Models for Large-Scale Assessments," Journal of Educational and Behavioral Statistics, , vol. 34(4), pages 433-463, December.
    7. Robert Mislevy, 1993. "Should “multiple imputations” be treated as “multiple indicators”?," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 79-85, March.
    8. Jules Ellis & Brian Junker, 1997. "Tail-measurability in monotone latent variable models," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 495-523, December.
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    Cited by:

    1. Maarten Marsman & Gunter Maris & Timo Bechger & Cees Glas, 2016. "What can we learn from Plausible Values?," Psychometrika, Springer;The Psychometric Society, vol. 81(2), pages 274-289, June.
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    4. Simon Grund & Oliver Lüdtke & Alexander Robitzsch, 2021. "On the Treatment of Missing Data in Background Questionnaires in Educational Large-Scale Assessments: An Evaluation of Different Procedures," Journal of Educational and Behavioral Statistics, , vol. 46(4), pages 430-465, August.
    5. Takashi Yamashita & Thomas J. Smith & Phyllis A. Cummins, 2021. "A Practical Guide for Analyzing Large-Scale Assessment Data Using Mplus: A Case Demonstration Using the Program for International Assessment of Adult Competencies Data," Journal of Educational and Behavioral Statistics, , vol. 46(4), pages 501-518, August.

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