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.
Publisher Copyright:
© 2020 AERA.
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
SN - 1076-9986
VL - 45
SP - 598
EP - 636
JO - Journal of Educational and Behavioral Statistics
JF - Journal of Educational and Behavioral Statistics
IS - 5
ER -