I'm trying to find out what the effect of different characteristics of a product has on sales of this product (count data) by running poisson/negative binominal regression. Is it appropriate to use Pearson's correlation test to check for multicollinearity in poisson/nb regression, or it's only applicable for linear regression? If so, could you recommend a correlation test for count data. Also, when I use the Pearson correlation test, all coefficients show a weak correlation of my dependent variable with independent variables (all around 0.30) However, all coefficients are significant in poisson/nb regression, they also give meaningful results. Can I rely on that coefficients even though there is a weak correlation? Thank you so much in advance!
First, in count data models, it is your outcome that is count, so I would not worry about a Poisson correlation between predictors.
Additionally, multicollinearity is not really a problem for prediction unless you have perfect multicollinearity. Often the software will dump the offending variable or will just not run.
.3 is not the point at which you should start to worry that your predictors contain too much overlapping information. If your predictors were independent of each other, then you wouldn't need a regression to try to control for confounds.
Here's a nice easy-to-read article on multicollinearity explaining why it is often an overblown problem https://statisticalhorizons.com/multicollinearity