# AES Consulting meeting on 21 Sep 2016

The data set under discussion today is count data on a number of species at a number of locations. The primary question of interest is how species A affects the other species. Another question was how to use a bivariate Kolmogov-Smirnov test to look at comparing species A and each of the other species.

## Suggestions

Our main suggestions are to perform

- Poisson log-linear regressions with species A as the explanatory variable and each other species as the response and check for overdispersion
- if overdispersion is present (or perhaps just from the start since these data are likely overdispersed) use negative binomial log-linear regression ith species A as the explanatory variable and each other species as the response
- rank correlation between species A and each of the other species

One issues is that none of these approaches deals with the natural multivariate nature of the data. One approach would be to perform one large Poisson (or negative binomial) log-linear regression with a random effect for the lake where the observations were taken. This results in the counts having a positive relationship, but the whole point of this is that the species compete with each other and therefore you may want to allow for a negative relationship.

Another approach would be to look into compositional data analysis, but this would typically reduce the counts to proportions and the size of the counts themselves may be of interest.

## Bivariate Kolmogov-Smirnov test

Perhaps we didn’t understand the value of this test, but we weren’t convinced that this is the approach that we would take.