Experiment-based calibration in psychology: Optimal design considerations

Psychological theories are often formulated at the level of latent, not directly observable, variables. Empirical measurement of latent variables ought to be valid. Classical psychometric validity indices can be difficult to apply in experimental contexts. A complementary validity index, termed retrodictive validity, is the correlation of theory-derived predicted scores with actually measured scores, in specifically designed calibration experiments. In the current note, I analyse how calibration experiments can be designed to maximise the information garnered and specifically, how to minimise the sample variance of retrodictive validity estimators. First, I harness asymptotic limits to analytically derive different distribution features that impact on estimator variance. Then, I numerically simulate various distributions with combinations of feature values. This allows deriving recommendations for the distribution of predicted values, and for resource investment, in calibration experiments. Finally, I highlight cases in which a misspecified theory is particularly problematic.