Fitting a (maybe Poisson) regression to my data in R

Question

I'm trying to understand the probability distribution for my data. Each point represents an individual patient, the 0 or 1 label indicates whether they have a particular disease, and the number of detections indicates how many times each activity was detected in a patient. I only have 35 data points.

Basically, I want

$P(\textrm{number of detections} | \textrm{label})$.

There isn't enough data here to use something like fitdistr in R, I think, so I'm looking to build a glm in R with the poisson family, i.e.

mdl <- glm(detections ~ label, data = ata, family = poisson(link='log'))

but this isn't giving a great model (I'm guessing because the data is overdispersed).

Any suggestions for what to try next? A negative binomial distribution? Quasi-poisson? And suggestions for goodness-of-fit?

Answer 1

To get the probabilities that you list, you don't need any model, you can just use your data. So, for instance, the probability that number of detections is less than 100, given that label = 0 looks like 3/4 (unless some data points are hidden; as an aside, it would be good to jitter the points on the x axis to make it clearer).

You would need a model to get parameter estimates, standard errors, p values and so on. Do you need those?

As to "isn't giving me a great model", well, you can try other methods but look at the data: There's not going to be a model that does a great job because a) There isn't a lot of data and b) There is a lot of overlap.