MR Dictionary

Two-stage predictor substitution estimators

An extension of the two-stage least squares (TSLS) estimator for one-sample MR analyses.

Like the TSLS method (and the two-stage residual inclusion method), the first stage of the method involves the predicted values from the regression of the exposure and outcome to be generated. Then, also identical to the TSLS method, in the second stage, regression is conducted for the outcome of interest, replacing the exposure with the predicted values from the first stage. As the two-stage predictor substitution estimator is mathematically identical to the TSLS method, it will obtain identical results as the TSLS method for linear models, However, for non-linear models, it is likely that two-stage predictor substitution estimators are biased in the presence of endogeneity (i.e., unmeasured confounders or measurement error in regression covariates). Therefore, other methods (such as the two-stage residual inclusion) have been proposed as more appropriate alternative estimators for non-linear instrumental variable (IV) models where endogeneity is likely. See Two-stage residual inclusion.


Other terms in 'One-sample MR methods':