Bidirectional Mendelian randomization model with transitional steps in the feedback loop.

X₁ denotes the instrumental variables (IVs) for Y₁ and X₂ denotes the IVs for Y₂. The ε_1.1, ε_1.2, …, ε_2.1, ε_2.2,… are errors due to unobserved confounders at each transitional step. Of note, these transitional steps are not observed and only Y₁ and Y₂ are measured. The δ₁ and δ₂ are errors associated with Y₁ and Y₂, respectively, which includes both errors due to unobserved confounders as well as measurement errors.

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