I would like to specify a multilevel model including the following variables:

• DV: count data, i.e. a score value between 0 and 13 (resulting from an additive index) for each individual
• Individual level IVs: 4 socioeconomic variables
• Group level IVs: 2 neighborhood characteristics
  

Data comprise approximately 2000 observations nested in 150 neighborhoods. Of interest are the context effects of the neighborhoods, i.e., their mediating role on the individual level variables. I would thus like to specify a varying slope, varying intercept multilevel model including cross-level interaction terms.

My question however relates to the DV. Due to the property of the DV as being count data, I thought of testing for overdispersion and, in case of overdispersion, I would have to take it into consideration when choosing an appropriate distribution. However, I am quite confused regarding the problem of overdispersion in multilevel models and the implementation in R, even after having read a lot in this forum and relevant literature.

I am currently using the lme4 package and have two rather basic questions:

• How do I test for overdispersion?
• How do I account for it in the model?