# Polynomial regression with multilevel data

I want to estimate a polynomial regression to test the effect of self and follower-perception of leadership behavior on some outcome (e.g., followers' job satisfaction). Hence, I have a multilevel data structure with followers' assessments of their supervisors' leadership ($$X_1$$) as well as followers' job satisfaction ($$Y$$) on level 1 and supervisors' self-assessment of their leadership behavior ($$X_2$$) on level 2.

Ignoring the multilevel structure of the data, I would fit the following model:

$$Job Satisfaction = b_0 + b_1SelfRating + b_2FollowerRating + b_3SelfRaring^2 + b_4SelfRating \times FollowerRating + b_5FollowerRating + e$$

My question: Can I fit a similar model as a hierarchical linear model? And if yes, are there any things, like mandatory random effects, I have to consider?

In my mind the final model would look (something) like this:

$$Z_{ij} = \gamma_{00_j} + \gamma_{01_j}Y_j + \gamma_{02_j}Y_j^2 + \gamma_{10_j} X_{ij} + \gamma_{11_j}X_{ij}Y_j + \gamma_{20_j}X_{ij}^2 + u_{0_j}+ u_{1_j} + u_{2_j} + e_{ij}$$