Multilevel Poisson Regression

If you simply fitted a linear regression model with your covariates, without taking account of clustering, you my obtain biased results. This is because your data are clustered within buildings. This leads to observations that are more similar to others in the same building than to those in other buildings. That is, there is intra-class correlation. Failure to adequately adjust for this can lead to biased fixed effects.

One popular and principled approach is to use a generalized linear mixed effects model, where you would specify random intercepts for buildings.

This would be a 2-level multilevel model with individuals are level 1 and buildings at level 2.

If you simply fitted a (generalized) linear model, the parameter estimates could be biased. Therefore you should definitely fit a model that adjusts for the clustering. Personally I would use a mixed effects model (also known as a mixed model and also known as multilevel model in this case), although there are alternatives, such as a linear model were the building ID is also fixed effect (no random effects) or generalized estimating equations.

One of the advantages of the mixed model framework is that you can easily incorporate random slopes for the fixed effects, if warranted.