Web-based Supplementary Materials for: Expected Estimating Equations for Missing Data, Measurement Error, and Misclassification, with Application to Longitudinal Nonignorable Missing Data by C. Y. Wang, Yijian Huang, Edward C. Chao, and Marjorie K. Jeffcoat 1 Web Appendix A Let I β (Y |X)= {-(∂ 2 /∂ β 2 )logP(Y |X)}. Then I f (β) ≡ E{I β (Y |X)} is the full data informa- tion function when both Y and X are available. It can be shown that var{logP(T i , W i ,δ i )} = I f (β) - E[var{S (Y i , X i , β)|T i , W i ,δ i }]. The following result presents the efficiency loss due to incomplete data or mismeasured data, and estimation of nuisance parameters. Proposition 1: If the full data estimating functions S(Y i , X i , β), Q(T i , Y i , κ), V (W i , X i , η) and Δ(δ i , Y i , X i , W i , α) are likelihood scores, then the EEE estimator  β satisfies var{n 1/2 (  β - β)} = I −1 f (β)+ R(Θ)+ R ∗ (Θ)+ o p (1), (1) for some positive definite matrix R(Θ) and R ∗ (Θ) given in the Appendix. Here R(Θ) is the efficiency loss due to missing data, measurement error or misclassification while R ∗ (Θ) is the efficiency loss due to estimating κ and η. Proof: By direct calculations, (∂ 2 /∂ β 2 ){logP (T , W , δ)} = (∂ 2 /∂ β 2 )P (T , W , δ) P (T , W , δ) -  (∂/∂ β)P (T , W , δ) P (T , W , δ)  2 = -E{I β (Y |X)|T , W , δ} +E  [(∂/∂ β)log{P(Y |X)}] 2 |T , W , δ  - E 2 {S (Y, X, β)|T , W , δ} = -E{I β (Y |X)|T , W , δ} + var{S (Y, X, β)|T , W , δ}. Let B(Θ) = E[var{S (Y,X, β)|T , W , δ}], I (Θ) be the information for Θ, with elements I (β, β), I (β, ζ ), I (ζ , β) and I (ζ , ζ ), where ζ denotes the vector containing κ, η, and α. Let I 1