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. Author manuscript; available in PMC: 2012 Mar 1.

Published in final edited form as: Stat Methods Appt. 2011 Mar 1;20(1):83–100. doi: 10.1007/s10260-010-0150-z

•	I : W_1i = I_i + e_ij,	W_2i = 0, and $σ_{V}^{2} = 0$ ;
•	II : W_1i = I_i + S_it_ij + e_ij,	W_2i = 0, and $σ_{V}^{2} = 0$ ;
•	III : W_1i = I_i + S_it_ij + e_ij,	W_2i = 0;
•	IV : W_1i = I_i + S_it_ij + e_ij,	W_2i = γ₁I_i;
•	V : W_1i = I_i + S_it_ij + e_ij,	W_2i = γ₁I_i + γ₂S_i;
•	VI : W_1i = I_i + S_it_ij + e_ij,	W_2i = γ₁I_i + γ₃ log(V_i);
•	VII : W_1i = I_i + S_it_ij + e_ij,	W_2i = γ₁I_i + γ₂S_i + γ₃ log(V_i);