Hello stata folks, I am learning about multilevel poisson model and I have some questions on the interpretation of the model output. Below is my model and the outcome is the total count of incidents each student is having, the predictor is binary and students are nested in schools (identified by school id). First of all, can anyone tell me whether multilevel poisson model is appropriate to use in this scenario? Do I have to check any assumptions before proceeding with the model? If yes, what and how do I check?

My second question is what does the output below tell me about school level random intercept? Many thanks!

Code:
mepoisson outcome i.predictor || schoolid:, irr vce(robust)

Fitting fixed-effects model:

Iteration 0:   log likelihood = -375870.18  
Iteration 1:   log likelihood = -338880.27  
Iteration 2:   log likelihood = -338664.68  
Iteration 3:   log likelihood = -338664.62  
Iteration 4:   log likelihood = -338664.62  

Refining starting values:

Grid node 0:   log likelihood = -339189.54

Refining starting values (unscaled likelihoods):

Grid node 0:   log likelihood = -339189.54

Fitting full model:

Iteration 0:   log pseudolikelihood = -339189.54  (not concave)
Iteration 1:   log pseudolikelihood =    -336963  (not concave)
Iteration 2:   log pseudolikelihood =  -334774.5  (not concave)
Iteration 3:   log pseudolikelihood = -333812.37  (not concave)
Iteration 4:   log pseudolikelihood = -333069.64  
Iteration 5:   log pseudolikelihood = -332913.99  
Iteration 6:   log pseudolikelihood = -332905.67  
Iteration 7:   log pseudolikelihood = -332905.65  

Mixed-effects Poisson regression                Number of obs     =    227,321
Group variable:         cdscode                 Number of groups  =      8,259

                                                Obs per group:
                                                              min =          1
                                                              avg =       27.5
                                                              max =        476

Integration method: mvaghermite                 Integration pts.  =          7

                                                Wald chi2(1)      =      55.73
Log pseudolikelihood = -332905.65               Prob > chi2       =     0.0000
                            (Std. Err. adjusted for 8,259 clusters in cdscode)
------------------------------------------------------------------------------
             |               Robust
 outcome |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
             |
  1.predictor |   1.062885   .0086831     7.47   0.000     1.046002     1.08004
       _cons |   1.497787   .0043098   140.40   0.000     1.489364    1.506258
-------------+----------------------------------------------------------------
schoolid      |
   var(_cons)|   .0385252   .0016894                      .0353524    .0419827
------------------------------------------------------------------------------