I want to identify the level of a predictive variable X (with Gaussian distribution) able to induce a reduction in a variable y (with Poisson distribution), that has been measured over the same population, several times per day and across several days.
Here is a dataframe I am using to think about it, I have been unable to grasp a sound strategy for analysis. One worrying issue that seems to appear is that the combination of these two variables leads to a scatter that might be confounded with a threshold imposed by x on y.
Would anybody have a suggestion to detect such a threshold reliably, should it exist?
hour=rep(1:24,30) DOY=rep(1:30, each=24) x=rnorm(length(hour), mean=15, sd=3) y=rpois(length(hour), lambda=10) df=data.frame(y, x, hour, DOY) plot(y ~ x)