Original title: Local average treatment effects on latent outcomes
Sanford R Student, Joshua Gilbert, William Young · September 2026
Psychologists often study traits you cannot directly see, called latent outcomes. They also use encouragement designs, where participants get assigned to a treatment but might not actually take it. To find true cause and effect, researchers use instrumental variablesA technique that uses a random event (like a lottery) to isolate the true effect of a treatment when the treatment is not randomly assigned.. This paper studies using an instrument to find the local average treatment effectThe average effect of a treatment specifically for people who change their behavior because of the random assignment (the 'compliers'). on a latent outcome, or LLATE. This measures the average effect only for compliersPeople who follow the treatment assignment given by the random event (e.g., those who take the therapy when offered and don't when not)., the people who actually follow their assignment. Because effects can vary across people, standard models assume wrong error patterns and fail. The authors created a multiple-group approach that handles these varying effects and describes compliers. Their method recovers the LLATE with trivial bias. In contrast, simpler single-group and two-step methods produce small, persistent bias. Detecting varying effects works, but requires larger samples.
Imagine you want to know if a new study method improves test scores, but you cannot measure the actual learning directly—only the test scores, which are noisy. You randomly assign some students to use the method, but some ignore the assignment. The usual way to estimate the effect assumes the noise is the same for everyone, but if the method works differently for different students, that assumption fails. In this paper, the researchers split students into groups based on whether they followed the assignment, allowing the noise to vary, and get a much more accurate estimate of the true learning effect.
Psychologists often study unobservable traits like depression or intelligence. This work shows how to estimate the causal effect of a treatment on such a latent trait using instrumental variables, with a method that avoids the bias of standard approaches. That means more reliable conclusions from studies where the outcome cannot be directly measured.
Testing for heterogeneous treatment effects requires larger sample sizes. The method is developed for binary instruments and treatments; its performance with other types is not discussed.
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Local average treatment effects on latent outcomes — Sanford R Student, Joshua Gilbert, William Young — PsyArXiv — doi:10.31234/osf.io/grzu3_v2
Abstract licence: CC BY
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.