Multilevel Model Multilevel Model , 

Level 1 regression equation: $$Y_{ij}=\beta_{0j}+\beta_{1j}X_{ij}+e_{ij}$$
    Level 2 regression equation: $$\beta_{0j}=\gamma_{00}+\gamma_{01}W_j+u_{0j}$$
  $$\beta_{1j}=\gamma_{10}+u_{1j}$$



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*My question is : Why is level 2 predictor $W_j$ only included in $\beta_{0j}$ equation ?
Why is it not in $\beta_{1j}$ equation ,that is, why not $$\beta_{1j}=\gamma_{10}+\gamma_{1?}W_j+u_{1j}$$?

 A: I can't really answer why, but I can hazard an explanation of the meaning of each term:
$i$ indexes level 1 units
  $j$ indexes level 2 units
  $Y_{ij}$ is the outcome and varies at levels 1 and 2 (unspecified data type)
  $\beta_{0j}$ is the level 2 effect
  $\beta_{1j}$ is the effect of $X_{ij}$ on $Y_{ij}$, and this effect varies at level 2 by $u_{1j}$
  $X_{ij}$ is an explanatory variable that varies across both levels 1 and 2
  $\varepsilon_{ij}$ is the level 1 error (i.e. there is no heterogeneity of level 1 effects)
  $\gamma_{00}$ is the level 2 intercept
  $\gamma_{01}$ is the effect of $W_{j}$ on $Y_{ij}$
  $W_{j}$ is an explanatory variable that varies across level 2
  $u_{0j}$ is the level 2 error (see below)
  $\gamma_{10}$ is the mean level 2 effect of $X_{ij}$
  $u_{1j}$ is the level 2 error in the effect of $X_{ij}$, and together with $u_{0j}$ models the heterogeneity in $Y_{ij}$ at level 2.
Left unspecified is the distribution of $\varepsilon_{ij}$, although I would not be surprised were $\varepsilon \sim \mathcal{N}(0,\sigma_{\varepsilon})$.
Likewise, the distribution of $u_{0j}$ and $u_{1j}$ are left unspecified, but might be modeled some multivariate distribution with a covariance matrix including $\sigma_{u0}$,  $\sigma_{u1}$, and $\sigma_{u01}$ terms (these terms are sometimes estimated with constraints of varying sorts, and sometimes estimated unconstrained).
The meaning of only including $W_{j}$ in the $\beta_{0j}$ term and not the $\beta_{1j}$ term is that $W_{j}$ varies only at level 2, and does not correlate with the effect of $X_{ij}$. Of course, one could model the effect of $X_{ij}$ as varying at level 2 by values of $W_{j}$ as you propose... meaning that the effect of $X_{ij}$ on $Y_{ij}$ would vary at level 2 by values of $W_{j}$ (in addition to the mean effect of $X_{ij}$ and the error in that effect).
