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\date{}

\title{Multilevel Structural Equation Modeling: \\ \LaTeX~Script for Equations}

\author{Bruno Castanho Silva \and Constantin Manuel Bosancianu \and Levente Littvay}

\begin{document}
\maketitle

\begin{abstract}
    This file contains \LaTeX~code for reproducing all equations in `Multilevel Structural Equation Modeling', by Bruno Castanho Silva, Constantin Manuel Bosancianu, and Levente Littvay (in press, Sage).
\end{abstract}

\clearpage

\section{Introduction}

\begin{equation}
\begin{cases}
Y_i = \beta_{01} + \beta_{11}M_{i} + \epsilon_{1i} \\[7pt]
M_i = \beta_{02} + \beta_{12}X_{i} + \epsilon_{2i},
\end{cases}
\label{eq:eq-01-21}
\end{equation}

\begin{equation}
    AIC = -2 LL + 2 k
    \label{eq:eq-01-19}
\end{equation}

\begin{equation}
    BIC = -2LL + k \ln(N)
    \label{eq:eq-01-20}
\end{equation}

\begin{equation}
 \chi_{M}^{2} = (N-1)F_{ML}
 \label{eq:eq-01-16}
\end{equation}



\begin{equation}
 \hat{\epsilon} = \sqrt{\frac{\hat{\delta}_{M}}{(N-1) d\!f_{M}}}, \quad \mathrm{where} \; \hat{\delta}_{M}=max(0,\chi_M^2 - d\!f_M)
 \label{eq:eq-01-17}
\end{equation}


\begin{equation}
 CFI = 1 - \frac{\hat{\delta}_M}{\hat{\delta}_B}
 \label{eq:eq-01-18}
\end{equation}

\begin{equation}
    \centering
    Y_i = \beta_0 + \beta_1 X_i + \epsilon_i,\quad \epsilon_i \sim \mathcal{N}(0,\sigma^2)
    \label{eq:eq-01-01}
\end{equation}

\begin{equation}
    \centering
    Y_{ij} = \beta_{0j} + \beta_{1j} X_{ij} + \epsilon_{ij},\quad \epsilon_{ij} \sim \mathcal{N}(0,\sigma^2)
    \label{eq:eq-01-02}
\end{equation}

\begin{equation}
    \centering
    \begin{cases}
    \beta_{0j} = \gamma_{00} + \gamma_{01} Z_j + \upsilon_{0j}, \quad \upsilon_{0j} \sim \mathcal{N}(0,\sigma^2) \\[7pt]
    \beta_{1j} = \gamma_{10} + \gamma_{11} Z_j + \upsilon_{1j}, \quad \upsilon_{1j} \sim \mathcal{N}(0,\sigma^2)
    \end{cases}
    \label{eq:eq-01-03}
\end{equation}

\begin{equation}
    \centering
    Y_{ij} = \gamma_{00} + \gamma_{01} Z_j + \gamma_{10} X_{ij} + \gamma_{11} Z_j X_{ij} + \upsilon_{0j} + \upsilon_{1j} X_{ij} + \epsilon_{ij}
    \label{eq:eq-01-04}
\end{equation}

\begin{equation}
\centering
\begin{cases}
Y1_{ij} = \overset{Y1}{\beta_{0j}} + \overset{Y1}{\beta_{1j}} X1_{ij} + \overset{Y1}{\beta_{2j}} Y2_{ij} + \overset{Y1}{\epsilon_{ij}} \\[7pt]
Y2_{ij} = \overset{Y2}{\beta_{0j}} + \overset{Y2}{\beta_{1j}} X1_{ij} + \overset{Y2}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-01-05}
\end{equation}

\begin{equation}
\centering
\begin{cases}
\overset{Y1}{\beta_{0j}} = \overset{Y1}{\gamma_{00}} + \overset{Y1}{\upsilon_{0j}} \\[7pt]
\overset{Y1}{\beta_{1j}} = \overset{Y1}{\gamma_{10}} \\[7pt]
\overset{Y1}{\beta_{2j}} = \overset{Y1}{\gamma_{20}} \\[7pt]
\overset{Y2}{\beta_{0j}} = \overset{Y2}{\gamma_{00}} + \overset{Y2}{\upsilon_{0j}} \\[7pt]
\overset{Y2}{\beta_{1j}} = \overset{Y2}{\gamma_{10}}
\end{cases}
\label{eq:eq-01-06}
\end{equation}

\begin{equation}
\centering
\begin{cases}
Y1_{ij} = \overset{Y1}{\gamma_{00}} + \overset{Y1}{\gamma_{10}} X1_{ij} + \overset{Y1}{\gamma_{20}} Y2_{ij} + \overset{Y1}{\upsilon_{0j}} + \overset{Y1}{\epsilon_{ij}} \\[7pt]
Y2_{ij} = \overset{Y2}{\gamma_{00}} + \overset{Y2}{\gamma_{10}} X1_{ij} + \overset{Y2}{\upsilon_{0j}} + \overset{Y2}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-01-07}
\end{equation}

\begin{equation}
\centering
\begin{cases}
Y1_{ij} = \overset{Y1}{\beta_{0j}} + \overset{Y1}{\beta_{1j}} X1_{ij} + \overset{Y1}{\beta_{2j}} Y2_{ij} + \overset{Y1}{\epsilon_{ij}} \\[7pt]
Y2_{ij} = \overset{Y2}{\beta_{0j}} + \overset{Y2}{\beta_{1j}} X1_{ij} + \overset{Y2}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-01-08}
\end{equation}

\begin{equation}
\centering
\begin{cases}
\overset{Y1}{\beta_{0j}} = \overset{Y1}{\gamma_{00}} + \overset{Y1}{\gamma_{01}} Z_j + \overset{Y1}{\upsilon_{0j}} \\[7pt]
\overset{Y1}{\beta_{1j}} = \overset{Y1}{\gamma_{10}} + \overset{Y1}{\gamma_{11}} Z_j + \overset{Y1}{\upsilon_{1j}} \\[7pt]
\overset{Y1}{\beta_{2j}} = \overset{Y1}{\gamma_{20}} + \overset{Y1}{\gamma_{21}} Z_j + \overset{Y1}{\upsilon_{2j}} \\[7pt]
\overset{Y2}{\beta_{0j}} = \overset{Y2}{\gamma_{00}} + \overset{Y2}{\gamma_{01}} Z_j + \overset{Y2}{\upsilon_{0j}} \\[7pt]
\overset{Y2}{\beta_{1j}} = \overset{Y2}{\gamma_{10}} + \overset{Y2}{\gamma_{11}} Z_j + \overset{Y2}{\upsilon_{1j}}
\end{cases}
\label{eq:eq-01-09}
\end{equation}

\begin{equation}
\centering
\begin{cases}
Y1_{ij} = \overset{Y1}{\gamma_{00}} + \overset{Y1}{\gamma_{10}}X1_{ij} + \overset{Y1}{\gamma_{20}}Y2_{ij} + \overset{Y1}{\gamma_{01}}Z_j + \overset{Y1}{\gamma_{11}}Z_{j}Y2_{ij} + \\[3pt]
\qquad \quad + \overset{Y1}{\gamma_{21}}Z_{j}X1_{ij} + \overset{Y1}{\upsilon_{1j}}X1_{ij} + \overset{Y1}{\upsilon_{2j}}Y2_{ij} + \overset{Y1}{\upsilon_{0j}} + \overset{Y1}{\epsilon_{ij}}\\[7pt]
Y2_{ij} = \overset{Y2}{\gamma_{00}} + \overset{Y2}{\gamma_{10}} X1_{ij} + \overset{Y2}{\gamma_{01}} Z_j + \overset{Y2}{\gamma_{11}} Z_{j}X_{ij} + \overset{Y2}{\upsilon_{1j}} X_{ij} + \\[3pt]
\qquad \quad + \overset{Y2}{\upsilon_{0j}} + \overset{Y2}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-01-10}
\end{equation}

\begin{equation}
\centering
\begin{cases}
Y1_{ij} = \overset{Y1}{\lambda_{0j}} + \overset{Y1}{\lambda_{1}} FW1_{ij} + \overset{Y1}{\epsilon_{ij}} \\[7pt]
Y2_{ij} = \overset{Y2}{\lambda_{0j}} + \overset{Y2}{\lambda_{1}} FW1_{ij} + \overset{Y2}{\epsilon_{ij}} \\[7pt]
Y3_{ij} = \overset{Y3}{\lambda_{0j}} + \overset{Y3}{\lambda_{1}} FW1_{ij} + \overset{Y3}{\epsilon_{ij}} \\[7pt]
Y4_{ij} = \overset{Y4}{\lambda_{0j}} + \overset{Y4}{\lambda_{2}} FW2_{ij} + \overset{Y4}{\epsilon_{ij}} \\[7pt]
Y5_{ij} = \overset{Y5}{\lambda_{0j}} + \overset{Y5}{\lambda_{2}} FW2_{ij} + \overset{Y5}{\epsilon_{ij}} \\[7pt]
Y6_{ij} = \overset{Y6}{\lambda_{0j}} + \overset{Y6}{\lambda_{2}} FW2_{ij} + \overset{Y6}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-01-11}
\end{equation}

\begin{equation}
\centering
\begin{cases}
\overset{Y1}{\lambda_{0j}} = \overset{Y1}{\mu_{00}} + \overset{Y1}{\mu_{01}} FB_{j} + \overset{Y1}{\upsilon_{0j}} \\[7pt]
\overset{Y2}{\lambda_{0j}} = \overset{Y2}{\mu_{00}} + \overset{Y2}{\mu_{01}} FB_{j} + \overset{Y2}{\upsilon_{0j}} \\[7pt]
\overset{Y3}{\lambda_{0j}} = \overset{Y3}{\mu_{00}} + \overset{Y3}{\mu_{01}} FB_{j} + \overset{Y3}{\upsilon_{0j}} \\[7pt]
\overset{Y4}{\lambda_{0j}} = \overset{Y4}{\mu_{00}} + \overset{Y4}{\mu_{01}} FB_{j} + \overset{Y4}{\upsilon_{0j}} \\[7pt]
\overset{Y5}{\lambda_{0j}} = \overset{Y5}{\mu_{00}} + \overset{Y5}{\mu_{01}} FB_{j} + \overset{Y5}{\upsilon_{0j}} \\[7pt]
\overset{Y6}{\lambda_{0j}} = \overset{Y6}{\mu_{00}} + \overset{Y6}{\mu_{01}} FB_{j} + \overset{Y6}{\upsilon_{0j}}
\end{cases}
\label{eq:eq-01-12}
\end{equation}

\begin{equation}
\centering
\begin{cases}
YW_{ij} = \overset{YW}{\beta_{0j}} + \overset{YW}{\beta_{1j}} FW1_{ij} + \overset{YW}{\beta_2} {FW2_{ij}} + \overset{YW}{\epsilon_{ij}} \\[7pt]
FW1_{ij} = \overset{FW1}{\beta_{0j}} + \overset{FW1}{\beta_{1j}} XW_{ij} + \overset{FW1}{\epsilon_{ij}} \\[7pt]
FW2_{ij} = \overset{FW2}{\beta_{0j}} + \overset{FW2}{\beta_{1}} XW_{ij} + \overset{FW2}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-01-13}
\end{equation}

\begin{equation}
\centering
\begin{cases}
YB_{j} = \overset{YB}{\gamma_{00}} + \overset{YB}{\gamma_{10}} FB_{j} + \overset{YB}{\upsilon_{0j}} \\[7pt]
FB_{j} = \overset{FB}{\gamma_{00}} + \overset{FB}{\gamma_{10}} ZB_{j} + \overset{FB}{\upsilon_{0j}} \\[7pt]
\overset{YW}{\beta_{0j}} = \overset{YW}{\gamma_{00}} + \overset{YW}{\gamma_{01}} ZB_{j} + \overset{YW}{\upsilon_{0j}} \\[7pt]
\overset{YW}{\beta_{1j}} = \overset{YW}{\gamma_{10}} + \overset{YW}{\gamma_{11}} ZB_{j} + \overset{YW}{\upsilon_{1j}} \\[7pt]
\overset{FW1}{\beta_{1j}} = \overset{FW1}{\gamma_{10}} + \overset{FW1}{\gamma_{11}} ZB_{j} + \overset{FW1}{\upsilon_{1j}}
\end{cases}
\label{eq:eq-01-14}
\end{equation}

\begin{equation}
\centering
\begin{cases}
\overset{YW}{\beta_{2j}} = \overset{YW}{\gamma_{20}} \\[7pt]
\overset{FW1}{\beta_{0j}} = \overset{FW1}{\gamma_{00}} \\[7pt]
\overset{FW2}{\beta_{0j}} = \overset{FW2}{\gamma_{00}} \\[7pt]
\overset{FW2}{\beta_{1j}} = \overset{FW2}{\gamma_{10}}
\end{cases} 
\label{eq:eq-01-15}
\end{equation}

\begin{equation}
	\centering
	\bm{Y_{ij} = \nu + \Lambda_{B} \eta_{Bj} + \epsilon_{Bj} + \Lambda_{W} \eta_{Wij} + \epsilon_{Wij}}
	\label{eq:eq-01-100}
	\end{equation} 
	

\clearpage

\section{Multilevel Path Models}

\begin{equation}
\centering
\begin{cases}
SEV_{ij} = \overset{SEV}{\beta_{0j}} + \overset{SEV}{\beta_{1j}} INC_{ij} + \overset{SEV}{\beta_{2j}} EDU_{ij} + \overset{SEV}{\beta_{3j}} AGE_{ij} + \overset{SEV}{\epsilon_{ij}} \\[7pt]
INC_{ij} = \overset{INC}{\beta_{0j}} + \overset{INC}{\beta_{1j}} EDU_{ij} + \overset{INC}{\beta_{2j}} AGE_{ij} + \overset{INC}{\epsilon_{ij}} \\[7pt]
EDU_{ij} = \overset{EDU}{\beta_{0j}} + \overset{EDU}{\beta_{1j}} AGE_{ij} + \overset{EDU}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-02-01}
\end{equation}

\begin{equation}
\centering
\begin{cases}
\overset{SEV}{\beta_{0j}} = \overset{SEV}{\gamma_{00}} + \overset{SEV}{\gamma_{01}} GDP_{j} + \overset{SEV}{\upsilon_{0j}} \\[7pt]
\overset{SEV}{\beta_{1j}} = \overset{SEV}{\gamma_{10}} \\[7pt]
\overset{SEV}{\beta_{2j}} = \overset{SEV}{\gamma_{20}} \\[7pt]
\overset{SEV}{\beta_{3j}} = \overset{SEV}{\gamma_{30}} \\[7pt]
\overset{INC}{\beta_{0j}} = \overset{INC}{\gamma_{00}} \\[7pt]
\overset{INC}{\beta_{1j}} = \overset{INC}{\gamma_{10}} \\[7pt]
\overset{INC}{\beta_{2j}} = \overset{INC}{\gamma_{20}} \\[7pt]
\overset{EDU}{\beta_{0j}} = \overset{EDU}{\gamma_{00}} + \overset{EDU}{\gamma_{01}} GDP_{j} + \overset{EDU}{\upsilon_{0j}} \\[7pt]
\overset{EDU}{\beta_{1j}} = \overset{EDU}{\gamma_{10}}
\end{cases}
\label{eq:eq-02-02}
\end{equation}

\begin{equation}
\centering
\begin{cases}
SEV_{ij} = \overset{SEV}{\gamma_{00}} + \overset{SEV}{\gamma_{10}} INC_{ij} + \overset{SEV}{\gamma_{20}} EDU_{ij} + \overset{SEV}{\gamma_{30}} AGE_{ij} + \\[3pt]
\qquad \quad + \overset{SEV}{\gamma_{01}} GDP_{j} + \overset{SEV}{\upsilon_{0j}} + \overset{SEV}{\epsilon_{ij}} \\[7pt]
INC_{ij} = \overset{INC}{\gamma_{00}} + \overset{INC}{\gamma_{10}} EDU_{ij} + \overset{INC}{\gamma_{20}} AGE_{ij} + \overset{INC}{\epsilon_{ij}} \\[7pt]
EDU_{ij} = \overset{EDU}{\gamma_{00}} + \overset{EDU}{\gamma_{10}} AGE_{ij} + \overset{EDU}{\gamma_{01}} GDP_{j} + \overset{EDU}{\upsilon_{0j}} + \overset{EDU}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-02-03}
\end{equation}

\begin{equation}
\centering
\begin{array}{lcl}
SEV_{ij} & = & \overset{SEV}{\gamma_{00}} + \overset{SEV}{\gamma_{10}} INC_{ij} +
\overset{SEV}{\gamma_{20}} EDU_{ij} + \overset{SEV}{\gamma_{30}} AGE_{ij}  + \\[3pt]
         & + & \overset{SEV}{\gamma_{21}} GDP_{j} EDU_{ij} + \overset{SEV}{\gamma_{31}} GDP_{j} AGE_{ij} + \overset{SEV}{\gamma_{01}} GDP_{j} + \\[3pt]
         & + & \overset{SEV}{\upsilon_{2j}} EDU_{ij} + \overset{SEV}{\upsilon_{3j}} AGE_{ij} + \overset{SEV}{\upsilon_{0j}} + \overset{SEV}{\epsilon_{ij}} \\[7pt]
INC_{ij} & = & \overset{INC}{\gamma_{00}} + \overset{INC}{\gamma_{10}} EDU_{ij} + \overset{INC}{\gamma_{20}} AGE_{ij} + \overset{INC}{\epsilon_{ij}} \\[7pt]
EDU_{ij} & = & \overset{EDU}{\gamma_{00}} + \overset{EDU}{\gamma_{10}} AGE_{ij} + \overset{EDU}{\gamma_{01}} GDP_{j} + \overset{EDU}{\gamma_{11}} GDP_{j} AGE_{ij} + \\[3pt]
         & + & \overset{EDU}{\upsilon_{1j}} AGE_{ij} + \overset{EDU}{\upsilon_{0j}} + \overset{EDU}{\epsilon_{ij}}
\end{array}
\label{eq:eq-02-04}
\end{equation}


\clearpage

\section{Multilevel Factor Models}

\begin{equation}
\centering 
\begin{cases}
	VID_{ij} = \overset{VID}{\lambda_{0j}} + \overset{VID}{\lambda_{1}} FUNW_{ij} + \overset{VID}{\epsilon_{ij}} \\[7pt]
	DL1_{ij} = \overset{DL1}{\lambda_{0j}} + \overset{DL1}{\lambda_{1}} FUNW_{ij} + \overset{DL1}{\epsilon_{ij}} \\[7pt]
DL2_{ij} = \overset{DL2}{\lambda_{0j}} + \overset{DL2}{\lambda_{1}} FUNW_{ij} + \overset{DL2}{\epsilon_{ij}} \\[7pt]
	ISC_{ij} = \overset{ISC}{\lambda_{0j}} + \overset{ISC}{\lambda_{2}} SCHW_{ij} + \overset{ISC}{\epsilon_{ij}} \\[7pt]
ILS_{ij} = \overset{ILS}{\lambda_{0j}} + \overset{ILS}{\lambda_{2}} SCHW_{ij} + \overset{ILS}{\epsilon_{ij}} \\[7pt]
	HWC_{ij} = \overset{HWC}{\lambda_{0j}} + \overset{HWC}{\lambda_{2}} SCHW_{ij} + \overset{HWC}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-03-01}
\end{equation}

\begin{equation}
	\centering
	\begin{cases}
	\overset{VID}{\lambda_{0j}} = \overset{VID}{\mu_{00}} + \overset{VID}{\mu_{01}} FUNB_{j} + \overset{VID}{\upsilon_{0j}} \\[7pt]
    \overset{DL1}{\lambda_{0j}} = \overset{DL1}{\mu_{00}} + \overset{DL1}{\mu_{01}} FUNB_{j} + \overset{DL1}{\upsilon_{0j}} \\[7pt]
	\overset{DL2}{\lambda_{0j}} = \overset{DL2}{\mu_{00}} + \overset{DL2}{\mu_{01}} FUNB_{j} + \overset{DL2}{\upsilon_{0j}} \\[7pt]
    \overset{ISC}{\lambda_{0j}} = \overset{ISC}{\mu_{00}} + \overset{ISC}{\mu_{02}} SCHB_{j} + \overset{ISC}{\upsilon_{0j}} \\[7pt]
	\overset{ILS}{\lambda_{0j}} = \overset{ILS}{\mu_{00}} + \overset{ILS}{\mu_{02}} SCHB_{j} + \overset{ILS}{\upsilon_{0j}} \\[7pt]
    \overset{HWC}{\lambda_{0j}} = \overset{HWC}{\mu_{00}} + \overset{HWC}{\mu_{02}} SCHB_{j} + \overset{HWC}{\upsilon_{0j}}
	\end{cases}
	\label{eq:eq-03-02}
\end{equation}

\begin{equation}
\centering
\begin{cases}
VID_{ij} = \overset{VID}{\mu_{00}} + \overset{VID}{\lambda_{1}} FUNW_{ij} + \overset{VID}{\mu_{01}} FUNB_{j} + \overset{VID}{\upsilon_{0j}} + \overset{VID}{\epsilon_{ij}} \\[7pt]
DL1_{ij} = \overset{DL1}{\mu_{00}} + \overset{DL1}{\lambda_{1}} FUNW_{ij} + \overset{DL1}{\mu_{01}} FUNB_{j} + \overset{DL1}{\upsilon_{0j}} + \overset{DL1}{\epsilon_{ij}} \\[7pt]
DL2_{ij} = \overset{DL2}{\mu_{00}} + \overset{DL2}{\lambda_{1}} FUNW_{ij} + \overset{DL2}{\mu_{01}} FUNB_{j} + \overset{DL2}{\upsilon_{0j}} + \overset{DL2}{\epsilon_{ij}} \\[7pt]
ISC_{ij} = \overset{ISC}{\mu_{00}} + \overset{ISC}{\lambda_2} SCHW_{ij} + \overset{ISC}{\mu_{02}} SCHB_{j} + \overset{ISC}{\upsilon_{0j}} + \overset{ISC}{\epsilon_{ij}} \\[7pt]
ILS_{ij} = \overset{ILS}{\mu_{00}} + \overset{ILS}{\lambda_2} SCHW_{ij} + \overset{ILS}{\mu_{02}} SCHB_{j} + \overset{ILS}{\upsilon_{0j}} + \overset{ILS}{\epsilon_{ij}} \\[7pt]
HWC_{ij} = \overset{HWC}{\mu_{00}} + \overset{HWC}{\lambda_2} SCHW_{ij} + \overset{HWC}{\mu_{02}} SCHB_{j} + \overset{HWC}{\upsilon_{0j}} + \overset{HWC}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-03-03}
\end{equation}


\begin{equation}
\centering
\begin{cases}
\overset{VID}{\lambda_{1}} = \overset{VID}{\mu_{01}} \\[7pt]
\overset{DL1}{\lambda_{1}} = \overset{DL1}{\mu_{01}} \\[7pt]
\overset{DL2}{\lambda_{1}} = \overset{DL2}{\mu_{01}} \\[7pt]
\overset{ISC}{\lambda_{2}} = \overset{ISC}{\mu_{02}} \\[7pt]
\overset{ILS}{\lambda_{2}} = \overset{ILS}{\mu_{02}} \\[7pt]
\overset{HWC}{\lambda_{2}} = \overset{HWC}{\mu_{02}}
\label{eq:eq-03-04}
\end{cases}
\end{equation}


\begin{equation}
\centering
\begin{cases}
VID_{ij} = \overset{VID}{\mu_{00}} + \overset{VID}{\mu_{01}} ( FUNW_{ij} + FUNB_{j}) + \overset{VID}{\upsilon_{0j}} + \overset{DL1}{\epsilon_{ij}} \\[7pt]
DL1_{ij} = \overset{DL1}{\mu_{00}} + \overset{DL1}{\mu_{01}} (FUNW_{ij} + FUNB_{j}) + \overset{DL1}{\upsilon_{0j}} + \overset{DL1}{\epsilon_{ij}} \\[7pt]
DL2_{ij} = \overset{DL2}{\mu_{00}} + \overset{DL2}{\mu_{01}} (FUNW_{ij} + FUNB_{j}) + \overset{DL2}{\upsilon_{0j}} + \overset{DL2}{\epsilon_{ij}} \\[7pt]
ISC_{ij} = \overset{ISC}{\mu_{00}} + \overset{ISC}{\mu_{02}} (SCHW_{ij} + SCHB_{j}) + \overset{ISC}{\upsilon_{0j}} + \overset{ISC}{\epsilon_{ij}} \\[7pt]
ILS_{ij} = \overset{ILS}{\mu_{00}} + \overset{ILS}{\mu_{02}} (SCHW_{ij} + SCHB_{j}) + \overset{ILS}{\upsilon_{0j}} + \overset{ILS}{\epsilon_{ij}} \\[7pt]
HWC_{ij} = \overset{HWC}{\mu_{00}} + \overset{HWC}{\mu_{02}} (SCHW_{ij} + SCHB_{j}) + \overset{HWC}{\upsilon_{0j}} + \overset{HWC}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-03-12}
\end{equation}

\begin{equation}
\centering
\begin{cases}
VID_{ij} = \overset{VID}{\mu_{00}} + \overset{VID}{\mu_{01}}  FUN_{ij} + \overset{VID}{\upsilon_{0j}} + \overset{DL1}{\epsilon_{ij}} \\[7pt]
DL1_{ij} = \overset{DL1}{\mu_{00}} + \overset{DL1}{\mu_{01}} FUN_{ij} + \overset{DL1}{\upsilon_{0j}} + \overset{DL1}{\epsilon_{ij}} \\[7pt]
DL2_{ij} = \overset{DL2}{\mu_{00}} + \overset{DL2}{\mu_{01}} FUN_{ij} + \overset{DL2}{\upsilon_{0j}} + \overset{DL2}{\epsilon_{ij}} \\[7pt]
ISC_{ij} = \overset{ISC}{\mu_{00}} + \overset{ISC}{\mu_{02}} SCH_{ij} + \overset{ISC}{\upsilon_{0j}} + \overset{ISC}{\epsilon_{ij}} \\[7pt]
ILS_{ij} = \overset{ILS}{\mu_{00}} + \overset{ILS}{\mu_{02}} SCH_{ij} + \overset{ILS}{\upsilon_{0j}} + \overset{ILS}{\epsilon_{ij}} \\[7pt]
HWC_{ij} = \overset{HWC}{\mu_{00}} + \overset{HWC}{\mu_{02}} SCH_{ij} + \overset{HWC}{\upsilon_{0j}} + \overset{HWC}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-03-13}
\end{equation}


\begin{equation}
\centering
\begin{cases}
\overset{VID}{\lambda_{1j}} = \overset{VID}{\mu_{11}} + \overset{VID}{\upsilon_{1j}} \\[7pt]
\overset{DL1}{\lambda_{1j}} = \overset{DL1}{\mu_{11}} + \overset{DL1}{\upsilon_{1j}} \\[7pt]
\overset{DL2}{\lambda_{1j}} = \overset{DL2}{\mu_{11}} + \overset{DL2}{\upsilon_{1j}} \\[7pt]
\overset{ISC}{\lambda_{2j}} = \overset{ISC}{\mu_{12}} + \overset{ISC}{\upsilon_{1j}} \\[7pt]
\overset{ILS}{\lambda_{2j}} = \overset{ILS}{\mu_{12}} + \overset{ILS}{\upsilon_{1j}} \\[7pt]
\overset{HWC}{\lambda_{2j}} = \overset{HWC}{\mu_{12}} + \overset{HWC}{\upsilon_{1j}}
\end{cases}
\label{eq:eq-03-07}
\end{equation}

\begin{equation}
\centering
\begin{cases}
VID_{ij} = \overset{VID}{\mu_{00}} + \overset{VID}{\mu_{11}} FUNW_{ij} + \overset{VID}{\mu_{01}} FUNB_{j} + \overset{VID}{\upsilon_{1j}} FUNW_{ij} + \\[3pt]
\qquad \quad + \overset{VID}{\upsilon_{0j}} + \overset{VID}{\epsilon_{ij}} \\[7pt]
DL1_{ij} = \overset{DL1}{\mu_{00}} + \overset{DL1}{\mu_{11}} FUNW_{ij} + \overset{DL1}{\mu_{01}} FUNB_{j} + \overset{DL1}{\upsilon_{1j}} FUNW_{ij} + \\[3pt]
\qquad \quad + \overset{DL1}{\upsilon_{0j}} + \overset{DL1}{\epsilon_{ij}} \\[7pt]
DL2_{ij} = \overset{DL2}{\mu_{00}} + \overset{DL2}{\mu_{11}} FUNW_{ij} + \overset{DL2}{\mu_{01}} FUNB_{j} + \overset{DL2}{\upsilon_{1j}} FUNW_{ij} + \\[3pt]
\qquad \quad + \overset{DL2}{\upsilon_{0j}} + \overset{DL2}{\epsilon_{ij}} \\[7pt]
ISC_{ij} = \overset{ISC}{\mu_{00}} + \overset{ISC}{\mu_{12}} SCHW_{ij} + \overset{ISC}{\mu_{02}} SCHB_{j} + \overset{ISC}{\upsilon_{1j}} SCHW_{ij} + \\[3pt]
\qquad \quad + \overset{ISC}{\upsilon_{0j}} + \overset{ISC}{\epsilon_{ij}} \\[7pt]
ILS_{ij} = \overset{ILS}{\mu_{00}} + \overset{ILS}{\mu_{12}} SCHW_{ij} + \overset{ILS}{\mu_{02}} SCHB_{j} + \overset{ILS}{\upsilon_{1j}} SCHW_{ij} + \\[3pt]
\qquad \quad + \overset{ILS}{\upsilon_{0j}} + \overset{ILS}{\epsilon_{ij}} \\[7pt]
HWC_{ij} = \overset{HWC}{\mu_{00}} + \overset{HWC}{\mu_{12}} SCHW_{ij} + \overset{HWC}{\mu_{02}} SCHB_{j} + \overset{HWC}{\upsilon_{1j}} SCHW_{ij} + \\[3pt]
\qquad \quad + \overset{HWC}{\upsilon_{0j}} + \overset{HWC}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-03-08}
\end{equation}

\begin{equation}
\centering
\begin{cases}
VID_{ij} = \overset{VID}{\mu_{00}} + \overset{VID}{\mu_{11}} FUN_{ij} + \overset{VID}{\mu_{01}} DIG_{j} + \overset{VID}{\upsilon_{1j}} FUN_{ij} +  \overset{VID}{\upsilon_{0j}} + \overset{VID}{\epsilon_{ij}} \\[7pt]
DL1_{ij} = \overset{DL1}{\mu_{00}} + \overset{DL1}{\mu_{11}} FUN_{ij} + \overset{DL1}{\mu_{01}} DIG_{j} + \overset{DL1}{\upsilon_{1j}} FUN_{ij} +  \overset{DL1}{\upsilon_{0j}} + \overset{DL1}{\epsilon_{ij}} \\[7pt]
DL2_{ij} = \overset{DL2}{\mu_{00}} + \overset{DL2}{\mu_{11}} FUN_{ij} + \overset{DL2}{\mu_{01}} DIG_{j} + \overset{DL2}{\upsilon_{1j}} FUN_{ij} +  \overset{DL2}{\upsilon_{0j}} + \overset{DL2}{\epsilon_{ij}} \\[7pt]
ISC_{ij} = \overset{ISC}{\mu_{00}} + \overset{ISC}{\mu_{12}} SCH_{ij} + \overset{ISC}{\mu_{01}} DIG_{j} + \overset{ISC}{\upsilon_{1j}} SCH_{ij} +  \overset{ISC}{\upsilon_{0j}} + \overset{ISC}{\epsilon_{ij}} \\[7pt]
ILS_{ij} = \overset{ILS}{\mu_{00}} + \overset{ILS}{\mu_{12}} SCH_{ij} + \overset{ILS}{\mu_{01}} DIG_{j} + \overset{ILS}{\upsilon_{1j}} SCH_{ij} +  \overset{ILS}{\upsilon_{0j}} + \overset{ILS}{\epsilon_{ij}} \\[7pt]
HWC_{ij} = \overset{HWC}{\mu_{00}} + \overset{HWC}{\mu_{12}} SCH_{ij} + \overset{HWC}{\mu_{01}} DIG_{j} + \overset{HWC}{\upsilon_{1j}} SCH_{ij} + \\[3pt]
\qquad \quad + \overset{HWC}{\upsilon_{0j}} + \overset{HWC}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-03-11}
\end{equation}

\clearpage

\section{Multilevel Structural Equation Models}

\begin{equation}
p_{W}(p_{W}+1)/2 + p_{B}(p_{B}+1)/2 + p
\label{eq:eq-04-01}
\end{equation}

\begin{equation}
\centering
\begin{cases}
RE1_{ij} = \overset{RE1}{\lambda_{0}} + \overset{RE1}{\lambda_{1}}RES_{ij} + \overset{RE1}{\epsilon_{ij}} \\[7pt]
RE2_{ij} = \overset{RE2}{\lambda_{0}} + \overset{RE2}{\lambda_{1}}RES_{ij} + \overset{RE2}{\epsilon_{ij}} \\[7pt]
HW1_{ij} = \overset{HW1}{\lambda_{0}} + \overset{HW1}{\lambda_2}HAR_{ij} + \overset{HW1}{\epsilon_{ij}} \\[7pt]
HW2_{ij} = \overset{HW2}{\lambda_{0}} + \overset{HW2}{\lambda_2}HAR_{ij} + \overset{HW2}{\epsilon_{ij}} \\[7pt]
HW3_{ij} = \overset{HW3}{\lambda_{0}} + \overset{HW3}{\lambda_2}HAR_{ij} + \overset{HW3}{\epsilon_{ij}} \\
\end{cases}
\label{eq:eq-04-02}
\end{equation}

\begin{equation}
\centering 
\begin{cases}
HAR_{ij} = \overset{HAR}{\beta_{0}} + \overset{HAR}{\beta_{1}}RES_{ij} + \overset{HAR}{\beta_{2}}PAY_{ij} + \overset{HAR}{\epsilon_{ij}} \\[7pt]
SKL_{ij} = \overset{SKL}{\beta_{0j}} + \overset{SKL}{\beta_{1}}RES_{ij} + \overset{SKL}{\beta_{2}}HAR_{ij} + \overset{SKL}{\beta_{3}}PAY_{ij} + \overset{SKL}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-04-03}
\end{equation}

\begin{equation}
\centering
\overset{SKL}{\beta_{0j}} = \overset{SKL}{\gamma_{00}} + \overset{SKL}{\gamma_{01}}NEM_{j} + \overset{SKL}{\upsilon_{0j}}
\label{eq:eq-04-04}
\end{equation} 

\begin{equation}
\centering
\begin{array}{lll}
SKL_{ij} & = & \overset{SKL}{\gamma_{00}} + \overset{SKL}{\gamma_{01}}NEM_{j} + \overset{SKL}{\beta_{1}}RES_{ij} + \overset{SKL}{\beta_{2}}HAR_{ij} + \\[3pt] 
         & + & \overset{SKL}{\beta_{3}}PAY_{ij} + \overset{SKL}{\upsilon_{0j}} + \overset{SKL}{\epsilon_{ij}}
\label{eq:eq-04-05}
\end{array}
\end{equation}

\begin{equation}
\begin{cases} 
RE1_{ij} = \overset{RE1}{\lambda_{0}} + \overset{RE1}{\lambda_{1}}RES_{ij} + \overset{RE1}{\epsilon_{ij}} \\[7pt]
RE2_{ij} = \overset{RE2}{\lambda_{0}} + \overset{RE2}{\lambda_{1}}RES_{ij} + \overset{RE2}{\epsilon_{ij}} \\[7pt]
HW1_{ij} = \overset{HW1}{\lambda_{0}} + \overset{HW1}{\lambda_{2}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{HW1}{\lambda_{2}}\;\overset{HAR}{\beta_{2}}PAY_{ij} + \overset{HW1}{\lambda_{2}}\;\overset{HAR}{\beta_{0}} + \\[3pt]
\qquad \qquad \overset{HW1}{\lambda_{2}}\;\overset{HAR}{\epsilon_{ij}} + \overset{HW1}{\epsilon_{ij}} \\[7pt]
HW2_{ij} = \overset{HW2}{\lambda_{0}} + \overset{HW2}{\lambda_{2}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{HW2}{\lambda_{2}}\;\overset{HAR}{\beta_{2}}PAY_{ij} + \overset{HW2}{\lambda_{2}}\;\overset{HAR}{\beta_{0}} + \\[3pt] \qquad \qquad \overset{HW2}{\lambda_{2}}\;\overset{HAR}{\epsilon_{ij}} + \overset{HW2}{\epsilon_{ij}} \\[7pt]
HW3_{ij} = \overset{HW3}{\lambda_{0}} + \overset{HW3}{\lambda_{2}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{HW3}{\lambda_{2}}\;\overset{HAR}{\beta_{2}}PAY_{ij} + \overset{HW3}{\lambda_{2}}\;\overset{HAR}{\beta_{0}} + \\[3pt] \qquad \qquad \overset{HW3}{\lambda_{2}}\;\overset{HAR}{\epsilon_{ij}} + \overset{HW3}{\epsilon_{ij}} \\[7pt]
SKL_{ij} =  \overset{SKL}{\gamma_{00}} + \overset{SKL}{\gamma_{01}}NEM_{j} + \overset{SKL}{\beta_{1}}RES_{ij} + \overset{SKL}{\beta_{2}}HAR_{ij} + \overset{SKL}{\beta_{3}}PAY_{ij}  + \\[3pt] 
\qquad \qquad \overset{SKL}{\upsilon_{0j}} + \overset{SKL}{\epsilon_{ij}}
\end{cases} 
\label{eq:eq-04-06}
\end{equation}


\begin{equation}
PAY_{ij} = \overset{PAY}{\gamma_{00}} + \overset{PAY}{\upsilon_{0j}} + \overset{PAY}{\epsilon_{ij}}
\label{eq:eq-04-07}
\end{equation}



\begin{equation}
    \centering
\overset{SKL}{\beta_{0j}} = \overset{SKL}{\gamma_{00}} + \overset{SKL}{\gamma_{01}}NEM_{j} + \overset{SKL}{\gamma_{02}}\;\overset{PAY}{\beta_{0j}} + \overset{SKL}{\upsilon_{0j}}
\label{eq:eq-04-08}
\end{equation}

\begin{equation}
    \centering
    \begin{array}{lcl}
    SKL_{ij} & = & \overset{SKL}{\gamma_{00}} + \overset{SKL}{\gamma_{01}}NEM_{j} +
    \overset{SKL}{\gamma_{02}}\;\overset{PAY}{\beta_{0j}} + \overset{SKL}{\beta_{1}}RES_{ij} + \overset{SKL}{\beta_{2}}HAR_{ij} + \\[3pt]
             & + & \overset{SKL}{\beta_{3}}PAY_{ij}  + \overset{SKL}{\upsilon_{0j}} + \overset{SKL}{\epsilon_{ij}}
    \end{array}
    \label{eq:eq-04-09}
\end{equation}


\begin{equation}
\centering 
\begin{cases}
\overset{RE1}{\lambda_{0j}} = \overset{RE1}{\mu_{00}} + \overset{RE1}{\mu_{01}}REB_{j} + \overset{RE1}{\upsilon_{0j}} \\[7pt]
\overset{RE2}{\lambda_{0j}} = \overset{RE2}{\mu_{00}} + \overset{RE2}{\mu_{01}}REB_{j} + \overset{RE2}{\upsilon_{0j}} \\[7pt]
\overset{HW1}{\lambda_{0j}} = \overset{HW1}{\mu_{00}} + \overset{HW1}{\mu_{02}}HAB_{j} + \overset{HW1}{\upsilon_{0j}} \\[7pt]
\overset{HW2}{\lambda_{0j}} = \overset{HW2}{\mu_{00}} + \overset{HW2}{\mu_{02}}HAB_{j} + \overset{HW2}{\upsilon_{0j}} \\[7pt]
\overset{HW3}{\lambda_{0j}} = \overset{HW3}{\mu_{00}} + \overset{HW3}{\mu_{02}}HAB_{j} + \overset{HW3}{\upsilon_{0j}} \\
\end{cases}
\label{eq:eq-04-10} 
\end{equation}

\begin{equation}
\centering
\begin{cases}
\overset{SKL}{\beta_{0j}} = \overset{SKL}{\gamma_{00}} + \overset{SKL}{\gamma_{01}}NEM_{j} + \overset{SKL}{\gamma_{02}}\;\overset{PAY}{\beta_{0j}} + \overset{SKL}{\gamma_{03}}REB_{j} + \overset{SKL}{\gamma_{04}}HAB_{j} + \overset{SKL}{\upsilon_{0j}} \\[7pt]
HAB_{j} = \overset{HAB}{\gamma_{00}} + \overset{HAB}{\gamma_{01}}NEM_{j} + \overset{HAB}{\gamma_{02}}REB_{j} + \overset{HAB}{\gamma_{03}}\;\overset{PAY}{\beta_{0j}} + \overset{HAB}{\upsilon_{0j}} \\[7pt]
REB_{j} = \overset{REB}{\gamma_{00}} + \overset{REB}{\gamma_{01}}NEM_{j} + \overset{REB}{\upsilon_{0j}} \\
\end{cases} 
\label{eq:eq-04-11}
\end{equation}

\begin{equation}
\begin{cases}
\overset{RE1}{\lambda_{0j}} = \overset{RE1}{\mu_{00}} + \overset{RE1}{\mu_{01}}\;\overset{REB}{\gamma_{00}} + \overset{RE1}{\mu_{01}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{RE1}{\mu_{01}}\;\overset{REB}{\upsilon_{0j}} + \overset{RE1}{\upsilon_{0j}} \\[7pt]
\overset{RE2}{\lambda_{0j}} = \overset{RE2}{\mu_{00}} + \overset{RE2}{\mu_{01}}\;\overset{REB}{\gamma_{00}} + \overset{RE2}{\mu_{01}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{RE2}{\mu_{01}}\;\overset{REB}{\upsilon_{0j}} + \overset{RE2}{\upsilon_{0j}} \\[7pt]
\overset{HW1}{\lambda_{0j}} = \overset{HW1}{\mu_{00}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}REB_{j} + \\[3pt] \qquad \quad \overset{HW1}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW1}{\upsilon_{0j}} \\[7pt]
\overset{HW2}{\lambda_{0j}} = \overset{HW2}{\mu_{00}} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}REB_{j} + \\[3pt] \qquad \quad \overset{HW2}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW2}{\upsilon_{0j}} \\[7pt]
\overset{HW3}{\lambda_{0j}} = \overset{HW3}{\mu_{00}} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}REB_{j} + \\[3pt] \qquad \quad \overset{HW3}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW3}{\upsilon_{0j}} \\
\end{cases}
\label{eq:eq-04-12}
\end{equation}

\begin{equation}
\begin{cases}
\overset{HW1}{\lambda_{0j}} = \overset{HW1}{\mu_{00}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} + 
\overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{03}}\;\overset{PAY}{\beta_{0j}} +\\[3pt] \qquad \quad \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} +   \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW1}{\upsilon_{0j}} \\[7pt]
\overset{HW2}{\lambda_{0j}} = \overset{HW2}{\mu_{00}} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} +
\overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{03}}\;\overset{PAY}{\beta_{0j}} +\\[3pt] \qquad \quad \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW2}{\upsilon_{0j}} \\[7pt]
\overset{HW3}{\lambda_{0j}} = \overset{HW3}{\mu_{00}} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} +
\overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{03}}\;\overset{PAY}{\beta_{0j}} +\\[3pt] \qquad \quad \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} +  \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW3}{\upsilon_{0j}}
\end{cases}
\label{eq:eq-04-13}
\end{equation}

\begin{landscape}
\vspace*{\fill}
\begin{equation}
\begin{cases}
RE1_{ij} = \overset{RE1}{\mu_{00}} + \overset{RE1}{\lambda_{1}}RES_{ij} + \overset{RE1}{\mu_{01}}\;\overset{REB}{\gamma_{00}} + \overset{RE1}{\mu_{01}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{RE1}{\mu_{01}}\;\overset{REB}{\upsilon_{0j}} + \overset{RE1}{\upsilon_{0j}} +  \overset{RE1}{\epsilon_{ij}} \\[7pt]
RE2_{ij} = \overset{RE2}{\mu_{00}} + \overset{RE2}{\lambda_{1}}RES_{ij} + \overset{RE2}{\mu_{01}}\;\overset{REB}{\gamma_{00}} + \overset{RE2}{\mu_{01}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{RE2}{\mu_{01}}\;\overset{REB}{\upsilon_{0j}} + \overset{RE2}{\upsilon_{0j}} +  \overset{RE2}{\epsilon_{ij}} \\[7pt]
HW1_{ij} = \overset{HW1}{\mu_{00}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} +
\overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} +
\overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} +\\[3pt] \qquad \qquad \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{03}}\;\overset{PAY}{\beta_{0j}} +
\overset{HW1}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW1}{\upsilon_{0j}} + 
\overset{HW1}{\lambda_{2}}\;\overset{HAR}{\beta_{0}} +
\overset{HW1}{\lambda_{2}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{HW1}{\lambda_{2}}\;\overset{HAR}{\beta_{2}}PAY_{ij} + \overset{HW1}{\lambda_{2}}\;\overset{HAR}{\epsilon_{ij}} + \overset{HW1}{\epsilon_{ij}}\\[7pt]
HW2_{ij} = \overset{HW2}{\mu_{00}} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} +
\overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} +  \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} +\\[3pt] \qquad \qquad \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{03}}\;\overset{PAY}{\beta_{0j}} +
\overset{HW2}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW2}{\upsilon_{0j}} + 
\overset{HW2}{\lambda_{2}}\;\overset{HAR}{\beta_{0}} +
\overset{HW2}{\lambda_{2}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{HW2}{\lambda_{2}}\;\overset{HAR}{\beta_{2}}PAY_{ij} + \overset{HW2}{\lambda_{2}}\;\overset{HAR}{\epsilon_{ij}} + \overset{HW2}{\epsilon_{ij}}\\[7pt]
HW3_{ij} = \overset{HW3}{\mu_{00}} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} +
\overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} +  \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} +\\[3pt] \qquad \qquad \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{03}}\;\overset{PAY}{\beta_{0j}} +
\overset{HW3}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW3}{\upsilon_{0j}} + \overset{HW3}{\lambda_{2}}\;\overset{HAR}{\beta_{0}} + \overset{HW3}{\lambda_{2}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{HW3}{\lambda_{2}}\;\overset{HAR}{\beta_{2}}PAY_{ij} + \overset{HW3}{\lambda_{2}}\;\overset{HAR}{\epsilon_{ij}} + \overset{HW3}{\epsilon_{ij}}\\[7pt]
SKL_{ij} =  \overset{SKL}{\gamma_{00}} + \overset{SKL}{\gamma_{01}}NEM_{j} + \overset{SKL}{\beta_{1}}RES_{ij} + \overset{SKL}{\beta_{2}}\;\overset{HAR}{\beta_{0}} + \overset{SKL}{\beta_{2}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{SKL}{\beta_{2}}\;\overset{HAR}{\beta_{2}}PAY_{ij} + \overset{SKL}{\beta_{2}}\;\overset{HAR}{\epsilon_{ij}} + \\[3pt] \qquad \qquad
\overset{SKL}{\beta_{3}}PAY_{ij} + \overset{SKL}{\gamma_{02}}\;\overset{PAY}{\beta_{0j}} + \overset{SKL}{\gamma_{03}}\;\overset{REB}{\gamma_{00}} + \overset{SKL}{\gamma_{03}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{SKL}{\gamma_{03}}\;\overset{REB}{\upsilon_{0j}} + \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{00}} +  \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{01}}NEM_{j} +\\[3pt] \qquad \qquad \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} + \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} + \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\upsilon_{0j}} + \overset{SKL}{\upsilon_{0j}} + \overset{SKL}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-04-14}
\end{equation}
\vspace*{\fill}
\end{landscape}

\begin{equation}
\centering
\begin{cases}
\overset{RE1}{\lambda_{1}} = \overset{RE1}{\mu_{01}} \\[7pt]
\overset{RE2}{\lambda_{1}} = \overset{RE2}{\mu_{01}} \\[7pt]
\overset{HW1}{\lambda_{2}} = \overset{HW1}{\mu_{02}} \\[7pt]
\overset{HW2}{\lambda_{2}} = \overset{HW2}{\mu_{02}} \\[7pt]
\overset{HW3}{\lambda_{2}} = \overset{HW3}{\mu_{02}} 
\end{cases} 
\label{eq:eq-04-15}
\end{equation}

\begin{equation}
\overset{HAR}{\beta_{2j}} = \overset{HAR}{\gamma_{20}} + \overset{HAR}{\gamma_{21}}NEM_{j} + \overset{HAR}{\upsilon_{2j}}
\label{eq:eq-04-16}
\end{equation}

\begin{equation}
\begin{array}{lcl}
SKL_{ij} & = & \overset{SKL}{\gamma_{00}} + \overset{SKL}{\gamma_{01}}NEM_{j} + \overset{SKL}{\beta_{1}}RES_{ij} + \overset{SKL}{\beta_{2}}\;\overset{HAR}{\beta_{0}} +\\ [3pt]  
        & + & \overset{SKL}{\beta_{2}}\;\overset{HAR}{\beta_{1}}RES_{ij} +   
        \overset{SKL}{\beta_{2}}\;\overset{HAR}{\gamma_{20}}PAY_{ij} + \\[3pt] & + & \overset{SKL}{\beta_{2}}\;\overset{HAR}{\gamma_{21}}PAY_{ij}NEM_{j} + 
        \overset{SKL}{\beta_{2}}\;\overset{HAR}{\upsilon_{2j}}PAY_{ij} + 
        \overset{SKL}{\beta_{2}}\;\overset{HAR}{\epsilon_{ij}} + \\[3pt] & + & \overset{SKL}{\beta_{3}}PAY_{ij} + \overset{SKL}{\gamma_{03}}\;\overset{REB}{\gamma_{00}} + 
        \overset{SKL}{\gamma_{03}}\;\overset{REB}{\gamma_{01}}NEM_{j} +  \overset{SKL}{\gamma_{03}}\;\overset{REB}{\upsilon_{0j}} + \\[3pt] & + & \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{00}} +  \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{01}}NEM_{j} + 
        \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} + \\[3pt] & + & \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} + \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} + 
        \overset{SKL}{\gamma_{04}}\;\overset{HAB}{\upsilon_{0j}} + \\[3pt] & + & \overset{SKL}{\upsilon_{0j}} + \overset{SKL}{\epsilon_{ij}}
\end{array}
\label{eq:eq-04-17}
\end{equation}

\begin{landscape}
\vspace*{\fill}
\begin{center}
\begin{equation}
\begin{cases}
HW1_{ij} = \overset{HW1}{\mu_{00}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} +
\overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} +  \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} +  \overset{HW1}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} +  \overset{HW1}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} +\\[3pt] \qquad \qquad \overset{HW1}{\upsilon_{0j}} + \overset{HW1}{\mu_{02}}\;\overset{HAR}{\beta_{0j}} + \overset{HW1}{\mu_{02}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{HW1}{\mu_{02}}\;\overset{HAR}{\gamma_{20}}PAY_{ij} + \overset{HW1}{\mu_{02}}\;\overset{HAR}{\gamma_{21}}PAY_{ij}NEM_{j} + \overset{HW1}{\mu_{02}}\;\overset{HAR}{\upsilon_{2j}}PAY_{ij} +  \overset{HW1}{\mu_{02}}\;\overset{HAR}{\epsilon_{ij}} + \overset{HW1}{\epsilon_{ij}} \\[7pt]
HW2_{ij} = \overset{HW2}{\mu_{00}} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} +
\overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} +  \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} +   \overset{HW2}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} +  \overset{HW2}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} +\\[3pt] \qquad \qquad \overset{HW2}{\upsilon_{0j}} + \overset{HW1}{\mu_{02}}\;\overset{HAR}{\beta_{0j}} + \overset{HW2}{\mu_{02}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{HW2}{\mu_{02}}\;\overset{HAR}{\gamma_{20}}PAY_{ij} + \overset{HW2}{\mu_{02}}\;\overset{HAR}{\gamma_{21}}PAY_{ij}NEM_{j} + \overset{HW2}{\mu_{02}}\;\overset{HAR}{\upsilon_{2j}}PAY_{ij} +  \overset{HW2}{\mu_{02}}\;\overset{HAR}{\epsilon_{ij}} + \overset{HW2}{\epsilon_{ij}} \\[7pt]
HW3_{ij} = \overset{HW3}{\mu_{00}} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{00}} + \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{01}}NEM_{j} +
\overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{00}} +  \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\gamma_{01}}NEM_{j} +  \overset{HW3}{\mu_{02}}\;\overset{HAB}{\gamma_{02}}\;\overset{REB}{\upsilon_{0j}} +  \overset{HW3}{\mu_{02}}\;\overset{HAB}{\upsilon_{0j}} + \overset{HW3}{\upsilon_{0j}} + \\[3pt] \qquad \qquad \overset{HW1}{\mu_{02}}\;\overset{HAR}{\beta_{0j}} + \overset{HW3}{\mu_{02}}\;\overset{HAR}{\beta_{1}}RES_{ij} + \overset{HW3}{\mu_{02}}\;\overset{HAR}{\gamma_{20}}PAY_{ij} + \overset{HW3}{\mu_{02}}\;\overset{HAR}{\gamma_{21}}PAY_{ij}NEM_{j} + \overset{HW3}{\mu_{02}}\;\overset{HAR}{\upsilon_{2j}}PAY_{ij} +  \overset{HW3}{\mu_{02}}\;\overset{HAR}{\epsilon_{ij}} + \overset{HW3}{\epsilon_{ij}}
\end{cases}
\label{eq:eq-04-18}
\end{equation}
\end{center}
\vspace*{\fill}
\end{landscape}

\clearpage

\section{Conclusion}

\begin{equation}
    \mu = \sum_{i=1}^kx_i\beta_i
\end{equation}





\end{document}