Abstract
Based upon a two-level structural equation model, this simulation study compares latent variable matching and matching through manifest variables. Selection bias is simulated on latent variable and/or manifest variables along with different magnitudes of reliability. Besides factor score matching and Mahalanobis distance matching, we examined two types of propensity score matching on: “naïve” propensity score derived from manifest covariates, and “true” propensity score derived from latent factor. Results suggest that 1) Mahalanobis distance matching works less effectively than propensity/factor score matching; 2) propensity score and factor score matching performed the best if both treatment and control groups have high reliability; 3) matching through manifest variables is optimal and preferable if latent composite variable is under-representative; 4) when latent variable represents the manifest variables well, latent variable matching is preferable and more efficient than matching on respective manifest variables; and 5) matching options such as caliper matching and replacement matching interact with the magnitude of reliability and matching with replacement on a smaller caliper performs the best for more reliable measures.
Highlights
There is an increasing need for studies on how educational interventions affect student performance (Raudenbush & Sadoff, 2008; Spybrook, 2007)
Propensity Score Matching Based on Manifest Variables (PSMMV): propensity score matching based on manifest variables; Propensity Score Matching Based on Latent Variable (PSMLV): propensity score Matching based on latent variable; Matching on Factor Score (MFS): matching on factor score; Mahalanobis Distance Matching Based on Factor Score (MDMFS): Mahalanobis distance matching based on factor score
Rather than measurement error, mainly accounts for the variation among manifest variables, matching through the latent variable itself will be equivalent to matching through the propensity score that was computed from the latent variable
Summary
There is an increasing need for studies on how educational interventions affect student performance (Raudenbush & Sadoff, 2008; Spybrook, 2007). Measures of the classroom interventions that students receive can be subject to measurement errors (Raudenbush & Sadoff, 2008) in data collection through large-scale surveys and observational studies (Cochran,1963, 1965, 1969, 1972; Rosenbaum, 2002). The propensity score was estimated through observed covariates that may have measurement error This Monte Carlo study uses an SEM framework (Jöreskog & Sörbom, 1996) to examine the effectiveness of matching through the latent variable and through manifest variables with measurement.
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