TY - JOUR

T1 - Propensity Score Analysis With Latent Covariates

T2 - Measurement Error Bias Correction Using the Covariate’s Posterior Mean, aka the Inclusive Factor Score

AU - Nguyen, Trang Quynh

AU - Stuart, Elizabeth A.

N1 - Funding Information:
The author(s) disclosed receipt of the following financial support for the research and/or authorship of this article: This work is supported by grant R01MH099010 (PI Stuart) from the National Institute of Mental Health.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - We address measurement error bias in propensity score (PS) analysis due to covariates that are latent variables. In the setting where latent covariate X is measured via multiple error-prone items W, PS analysis using several proxies for X—the W items themselves, a summary score (mean/sum of the items), or the conventional factor score (i.e., predicted value of X based on the measurement model)—often results in biased estimation of the causal effect because balancing the proxy (between exposure conditions) does not balance X. We propose an improved proxy: the conditional mean of X given the combination of W, the observed covariates Z, and exposure A, denoted (Formula presented.). The theoretical support is that balancing (Formula presented.) (e.g., via weighting or matching) implies balancing the mean of X. For a latent X, we estimate (Formula presented.) by the inclusive factor score (iFS)—predicted value of X from a structural equation model that captures the joint distribution of (Formula presented.) given Z. Simulation shows that PS analysis using the iFS substantially improves balance on the first five moments of X and reduces bias in the estimated causal effect. Hence, within the proxy variables approach, we recommend this proxy over existing ones. We connect this proxy method to known results about valid weighting/matching functions. We illustrate the method in handling latent covariates when estimating the effect of out-of-school suspension on risk of later police arrests using National Longitudinal Study of Adolescent to Adult Health data.

AB - We address measurement error bias in propensity score (PS) analysis due to covariates that are latent variables. In the setting where latent covariate X is measured via multiple error-prone items W, PS analysis using several proxies for X—the W items themselves, a summary score (mean/sum of the items), or the conventional factor score (i.e., predicted value of X based on the measurement model)—often results in biased estimation of the causal effect because balancing the proxy (between exposure conditions) does not balance X. We propose an improved proxy: the conditional mean of X given the combination of W, the observed covariates Z, and exposure A, denoted (Formula presented.). The theoretical support is that balancing (Formula presented.) (e.g., via weighting or matching) implies balancing the mean of X. For a latent X, we estimate (Formula presented.) by the inclusive factor score (iFS)—predicted value of X from a structural equation model that captures the joint distribution of (Formula presented.) given Z. Simulation shows that PS analysis using the iFS substantially improves balance on the first five moments of X and reduces bias in the estimated causal effect. Hence, within the proxy variables approach, we recommend this proxy over existing ones. We connect this proxy method to known results about valid weighting/matching functions. We illustrate the method in handling latent covariates when estimating the effect of out-of-school suspension on risk of later police arrests using National Longitudinal Study of Adolescent to Adult Health data.

KW - bias correction

KW - covariate measurement error

KW - factor score

KW - inclusive factor score

KW - latent variable

KW - matching function

KW - measurement error

KW - propensity score

KW - weighting function

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U2 - 10.3102/1076998620911920

DO - 10.3102/1076998620911920

M3 - Article

AN - SCOPUS:85083109583

VL - 45

SP - 598

EP - 636

JO - Journal of Educational and Behavioral Statistics

JF - Journal of Educational and Behavioral Statistics

SN - 1076-9986

IS - 5

ER -