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#LSMeams-like model
\begin{align*} 
\epsilon_{aijs} &\overset{\text{iid}}{\sim} N(0, \sigma)\\
Y_{aijs} &= \mu_s + R_{i} + C_{j} + A_{a} + R_{i}C_{j} + R^2_{i} + C^2_{j} + A^2_{a} + C_{j}A_{a} + R_{i}A_{a} + \lambda \left \| \vec{\theta}\  \right \|_2+ \epsilon_{aijs}
\end{align}

# Trent's model
\begin{align*}
R_{i} &\overset{\text{iid}}{\sim} N(0, 1), \ C_{j} \overset{\text{iid}}{\sim} N(0, 1)\\
\mu_{p(s)} &\overset{\text{iid}}{\sim} N(\mu, \sigma) \\ 
\mu(A)_{as} &\overset{\text{iid}}{\sim} N(\mu_{p(s)}, \sigma_s)\\
\epsilon_{aijs} &\overset{\text{iid}}{\sim} N(0, \sigma)\\
Y_{aijs} &= \mu(A)_{as} + R_{i} + C_{j} + \epsilon_{aijs}\\
\end{align}

#Kurt's approved model
\begin{align*} 
B_{b}&\overset{\text{iid}}{\sim} N(0,\sigma_{B}), \ P(B)_{p}\overset{\text{iid}}{\sim} N(0, \sigma_{P}), \ A(P)_{a}\overset{\text{iid}}{\sim} N(0, \sigma_{A})\\
R(B)_{i} &\overset{\text{iid}}{\sim} N(0, \sigma_R), \ C(B)_{j} \overset{\text{iid}}{\sim} N(0, \sigma_C)\\
\alpha(S)_r &\overset{\text{iid}}{\sim} N(\mu_s, \sigma_s), \ \epsilon_{bpaijr} \overset{\text{iid}}{\sim} N(0, \sigma)\\
Y_{srkapb} &= \alpha(S)_r + R(B)_{i} + C(B)_{j} + A(P)_{a} + P(B)_{p} + B_{b} + \epsilon_{srkapb}
\end{align}