Without knowing your variables and their properties and your research question(specifically saying which variable(s) are dependent), It is impossible to even guess. More information is needed.

Best, David Booth

N.B. Step is about your worst choice. It is extremely unstable. See the attachment

BTW My dissertation advisor forgot to tell me that lack of time is an important variable in designing an experiment.

Before answer your question of "which model is the best for my data", there are some things that you should consider.

• What I want to model? It is the distribution of birds across areas or only the presence or absence?

If it is the presence or absence your data will probably follow on the Bernoulli/Binomial family. On the other hand if it is the number of birds you can consider Poison or even a normal distribution. Thus, to decide the distribution to use it is important to do some descriptive analysis of the data such as plot the distribution of birds vs the covariables of interest and so on.

• That take us to the next question. Which variables are influencing/relevant to the number of birds in each area? There are nested variables?

The most safe approach is to think about these questions and look at the statistical analysis that people have used in your field in order to decide about the model to use.

Finally, you asked regarding using a step wise algorithm for model search. Even though this is a interesting approach for prediction you should think about if what you want is to have the best predictive model. Prediction does not means causation and we can have great predictive models that are not very useful if we want to get some sort of insight from the data. Also, it is always important to consider overfitting when searching for the "best" predictive model. A good starting point (on my view) for studying multilevel model is a book by Andrew Gelman , "Data Analysis using Regression and Multilevel/Hierarchival Models".

Sorry for the general/broad answer, but remember:

"All models are wrong, but some are useful."

George Box

I should say that I generally agree with Dr. Fernandes with 2 caveats:

1. Stepwise should NEVER be used. For all the reasons, see the earlier paper I sent and attached again here.. BTW the lasso algorithm is resistant to both overfitting and multicollinearity. As Dr Fernandes says these selection methods are only for predictive models.

2. Gelman's book is excellent but as far as I can see hierarchical models do not really apply to predictive situations as they are covered in the book. They could I think in certain cases be extended to predictive situations, But I am not aware that this has been done. Probably because they are of most use to people that are interested in explanation not prediction. Best wishes, David Booth

Thanks both of you for your answers. I'm sorry if my explanation wasn't clear enough.

• My data are organized within a matrix with the quadrat ID in line and response/explanatory variables in row. The response variable is the number of Corn bunting encounter (or presence/absence, I haven't decide which on is the best) within the quadrat sampling. The explanatory variables are areas of the crops groups (cereals, potatoes + carots, beets + endive, pea, mown meadow and others), AES, both of them in hectare. There is also the size of the margin (=boundaries between two differents cultures).
• About the distribution, I have done it and for the abundance of birds, it looks like a Poisson distribution (see attachment). I know there is an issue on the histogram and I didn't found any solution yet (the step should be of 1, but it's not).
• What I want is to see if there's tendencies of the birds in "choosing" quadrat samplings with AES and if the area of AES has an impact on those tendencies. I don't want to create a predictive map of the distribution of that bird but to see if the abundance (or presence/absence) of the bird can be explain by any of those variables. But I want to inclued the types of crops, the margins and others variables to see if the model is better with one of those.
• About the dependant variables, I know I have to do this but I don't know how to do it. Is there a test to do this ? Like a correlation test ? Because I have read that dependance and correlation are completly different and so now I'm kind of lost...

I'm sorry if my explanations are not good... And thank you for your answer, it's helping me a little bit more everytime to understand what I couldn't without you.

Benjamin