Modeling Measurement Error When Using Cognitive Test Scores in Social Science Research: The Properties and Assumptions of the Mixed Effects Structural Equations Model

• Activity Number: 658
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Lynne Steuerle Schofield*+ and Brian Junker and Lowell Taylor
• Companies: Swarthmore College and Carnegie Mellon University and Carnegie Mellon University
• Keywords: Bayesian statistics ; item response theory ; measurement error ; latent variables ; errors in variables ; MIMIC model

Abstract

Social science researchers often use cognitive test scores as independent variables to serve as measures of a latent trait. Often, these analyses are regression-based and assume that the independent variables are error-free. The heteroskedastic measurement error in the test score is often not modeled. This paper introduces the Mixed Effects Structural Equations (MESE) model which improves upon current models (e.g., linear regression models which ignore the error, errors-in-variables models which model homoskedastic measurement error, and marginal estimation procedures which require "plausible values" that can be misused). The MESE model uses a hierarchicial linear modeling approach to simultaneously exploit item response theory models to take appropriate account of the measurement error and incorporate that variability in the estimation of coefficients in the regression model. To estimate the regression coefficients, the latent variables are integrated out of the joint likelihood using a computational Bayesian approach and applying an MCMC algorithm. This paper uses both simulation studies and a real-world application to explore the properties and assumptions of the MESE model.