I am doing some analyses on unethical behaviour scales (e.g. abuse of information) in teams of organisations. I want to analyse whether culture (perceptions of and shared culture) have an impact on unethical behaviour. I have a relatively large dataset. For example for this analysis about 3650 respondents were included in the analysis. I have data on 23 organisations and 2170 teams.
Because intra-class correlations (ICC) were low at the organisational level (below 5%), I only looked at team-level. The linear model was not appropriate because of non-normal error distribution. In a first step, I did some single level analyses on the data just for exploration. I found that, because of some overdispersion in the data, a negative binomial regression seemed better than a poisson. However, when fitting a multilevel model I had convergence problems for the negative binomial (even for the null-model) because the hessian matrix was not positive definite, but had no problem fitting the multilevel poisson regression. I was wondering whether the overdispersion in the single-level analysis may have been caused by the hierarchical structure, and that I have good reason to choose for the multilevel poisson regression. Because the null model had convergence problems for the negative binomial, and not for the poisson, maybe in a multilevel context the poisson is more appropriate? Would using a multilevel poisson regression with robust variance estimator be a valid technique for analyzing the data (this deals with the overdispersion to some extent?)? I was also wondering whether it is possible to test for overdispersion in SPSS in the multilevel context.