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I want to study the determinants of homicide rates. However, I see when exploring the data that my dependent variable (homicide rates) has many zeros and is positive skewed. Which distribution family / approach should I use?

Thanks in advance

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In general, these types of data can be analyzed using either via hurdle modelling or via zero-inflated modelling.

Which type of modelling you would use is a function of whether you can assume that there is only one process by which a zero rate can be produced (in which case you would use hurdle modelling), or that there are are two different processes that can produce a zero (in which case you would use zero-inflated modelling). See this link to this Cross Validated post for further details: What is the difference between zero-inflated and hurdle models?.

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