Local average treatment effects on latent outcomes
Abstract
Instrumental variables (IV) regression models for causal inference have received increased attention in psychology with continuous, observed variables. Yet, latent outcomes are ubiquitous in psychology and research designs involving non-binding treatments and encouragement/manipulation designs are widespread. We consider IV with a binary instrument and treatment to estimate the \textit{local average treatment effect} on a latent variable, or the latent local average treatment effect (LLATE). The LLATE is the average of heterogeneous latent treatment effects for the population of individuals who comply with treatment assignment. Heterogeneous treatment effects imply that a single-group SEM with residual normality of the outcome is misspecified. We propose a multiple-group estimator that allows for this heteroskedasticity, enables tests for heterogeneous treatment effects, and characterizes compliers. The multiple-group estimator recovers the LLATE with trivial bias, while two single-group estimators and a two-step procedure using factor score estimates as observed outcomes all yield small but persistent bias. Testing for heterogeneous treatment effects is possible but limited to larger samples. We conclude that IV with a latent outcome is a viable means of estimating causal effects on latent outcomes, and that the multiple-group approach is usually the safest way to do so.
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BibTeX
@misc{student2026local,
title = {{Local average treatment effects on latent outcomes}},
author = {Sanford R Student and Joshua Gilbert and William Young},
howpublished = {PsyArXiv},
year = {2026},
month = sep,
doi = {10.31234/osf.io/grzu3_v2},
url = {https://osf.io/preprints/psyarxiv/grzu3_v2/},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local average treatment effects on latent outcomes
AU - Sanford R Student
AU - Joshua Gilbert
AU - William Young
PY - 2026
DA - 2026/09/21
PB - PsyArXiv
DO - 10.31234/osf.io/grzu3_v2
UR - https://osf.io/preprints/psyarxiv/grzu3_v2/
AB - Instrumental variables (IV) regression models for causal inference have received increased attention in psychology with continuous, observed variables. Yet, latent outcomes are ubiquitous in psychology and research designs involving non-binding treatments and encouragement/manipulation designs are widespread. We consider IV with a binary instrument and treatment to estimate the \textit{local average treatment effect} on a latent variable, or the latent local average treatment effect (LLATE). The LLATE is the average of heterogeneous latent treatment effects for the population of individuals who comply with treatment assignment. Heterogeneous treatment effects imply that a single-group SEM with residual normality of the outcome is misspecified. We propose a multiple-group estimator that allows for this heteroskedasticity, enables tests for heterogeneous treatment effects, and characterizes compliers. The multiple-group estimator recovers the LLATE with trivial bias, while two single-group estimators and a two-step procedure using factor score estimates as observed outcomes all yield small but persistent bias. Testing for heterogeneous treatment effects is possible but limited to larger samples. We conclude that IV with a latent outcome is a viable means of estimating causal effects on latent outcomes, and that the multiple-group approach is usually the safest way to do so.
ER -