Causal Inference in the Absence of Direct Measurement Using Planned Missing Data

Many psychological studies seek to quantify how treatments modify beliefs, attitudes, or behaviors by measuring the same participants on the same constructs both at baseline, before the treatment is administered, and again after it is administered. This procedure raises a problematic counterfactual: how do we know that the treatment is causing observed changes, and not the act of collecting a baseline measurement itself? This threat to validity is often referred to as \textit{measurement reactivity}. Researchers can attempt to quantify and even mitigate measurement reactivity by experimentally truncating baseline measurements, but those baseline measurements improve statistical power and may be critical for key analyses the researchers wish to conduct. We show that it is possible to indirectly recover baseline measurements by using auxiliary variables: variables which don't directly represent baseline measurements but have strong enough correlations with baseline measurements to facilitate informative imputation. We show how the measurement reactivity problem can be reframed using the logic of missing data mechanisms, demonstrate the feasibility of our proposed method in a simulation study, and then implement it in an experimental design on advice taking in which measurement reactivity is a known problem. We show that advice taking behavior clearly depends on the presence or absence of baseline measurement, and that important and ecologically valid insights about how people update their beliefs would remain undetected if measurement reactivity had remained unaddressed.