Table 1B.

Crossed-Random Effects Models Used in Experiments 1 & 2

Base Models
Posttest	Level 1 (Responsesjik): Logit (πjik = λ0ji
	Level 2 (Personj & Wordi): λ0jk = γ00 + r01j + r02i, r01j ~ N(0, σ2r01)& r02i ~ N(0, σ2 r02)
Mastery	Level 1 (Responsesji): Yij = λ0jik + eijk
	Level 2 (Personj & Wordi): λ0jk = γ00 + r01j + r02i, r01j ~ N(0, σ2r01)& r02i ~ N(0, σ2 r02)& eijk ~ N(0, σ2 e)
Main Effects Models
Posttest, Maintenance	Level 1 (Responsesji): $$\mathit{Logit}({\pi }_{\mathit{ji}})={\lambda }_{0\mathit{jk}}+\sum _{c=1}^C{\gamma }_c{P}_{\mathit{cij}}$$
	Level 2 (Personj & Wordi): $$\begin{array}{cc}\hfill {\lambda }_{0\mathit{jk}}=& {\gamma }_{00}+\sum _{a=1}^A{\gamma }_a{M}_{\mathit{ai}}+\sum _{b=1}^B{\gamma }_b{N}_{\mathit{bj}}+r_{01j}+r_{02i},\hfill \\ \hfill & r_{01j}~N(0,{{\sigma }^2}_{r01})\&r_{02i}~N(0,{{\sigma }^2}_{r02})\hfill \end{array}$$
Mastery	Level 1 (Responsesji): $$Y_{\mathit{ij}}={\lambda }_{0\mathit{jk}}+\sum _{c=1}^C{\gamma }_c{P}_{\mathit{cij}}+e_{\mathit{ijk}}$$
	Level 2 (Personj & Wordi): $$\begin{gathered} {\lambda }_{0jk}={\gamma }_{00}+\sum _{a=1}^A{\gamma }_a{M}_{\mathit{ai}}+\sum _{b=1}^B{\gamma }_b{N}_{\mathit{bj}}+r_{01j}+r_{02i}, \\ {r}_{01j}~N(0,{{\sigma }^2}_{r01})\&r_{02i}~N(0,{{\sigma }^2}_{r02})\&e_{\mathit{ijk}}~N(0,{{\sigma }^2}_e) \end{gathered}$$
Interaction Models
Mastery	Level 1 (Responsesji): $$Y_{\mathit{ij}}={\lambda }_{0\mathit{jk}}+\sum _{c=1}^C{\gamma }_c{P}_{\mathit{cij}}+e_{\mathit{ijk}}$$
	Level 2 (Personj & Wordi): $$\begin{gathered} {\lambda }_{0jk}={\gamma }_{00}+\sum _{a=1}^A{\gamma }_a{M}_{\mathit{ai}}+\sum _{b=1}^B{\gamma }_b{N}_{\mathit{bj}} \\ +r_{01j}+r_{02i}+{\gamma }_d{M}_{1i}{M}_{2i}+{\gamma }_d{M}_{1i}{M}_{3i}, \\ {r}_{01j}~N(0,{{\sigma }^2}_{r01})\&r_{02i}~N(0,{{\sigma }^2}_{r02})\&e_{\mathit{ijk}}~N(0,{{\sigma }^2}_e) \end{gathered}$$