If my outcome variable is count data, people often recommend using some type of poisson regression. I'm struggling to understand why this is the preferred method.
Lets say for this scenario that my mean count is low, so the distribution is skewed and does not look normal.
Given that regression makes no assumptions about the normality of the outcome variable, why does it matter that it is skewed? Why could I not run OLS regression anyway?
If my outcome mean was large the poisson distribution of the variable would look more normal, and I've heard people say in that case OLS with no transformation is acceptable. So there seems to be something special about a low mean count and the skew of the resulting distribution
Is it because the likelihood of a non-normal residual distribution increases with highly positively skewed data, and the reason for using poisson regression is to circumvent that normality violation?
Assuming the residuals are distributed normally, what is the actual problem with modelling (untransformed) count data using OLS regression (barring the decimal predictions)?