# What happen when model selection ranks null model as the best one and there's another model that is competitive?

I'm analyzing the proportion of marked chicks vs. the number of chicks that were recaptured at one moth of age (not possible to use conventional capture-recapture analysis because we don't have a second recapture event). The idea is to find if there is a change over time in the season using the hatch date and year as explanatory variables and their quadratic terms (looking for nonlinearity) as well as interactions. I ran models using the different combinations of explanatory variables.

glm(cbind(recapt,mark-recaps)~date+year+year2+date:year+date:year2, family="x.quasibinomial", data=df)


So we decided to use proportion analysis. The data has a little overdispersion (c-hat=1.3), so I'm using a quasibinomial family as x.quasibinomial (see: https://cran.r-project.org/web/packages/bbmle/vignettes/quasi.pdf).

When I use model selection from MuMIn package, the best model is the null model (QAIC=2572.0) as well as one model that includes an interaction (QAIC=2572.7, delta=0.68).

I already tried to change the control of my model as suggested here, but I think I don't have a convergence problem.

How can I interpret the output? How can I explain the presence of the null model at the top? Is it possible to use the second best model? what else can I change in the model setting?

## 2 Answers

This is not the way to go about the modeling process. Think model specification and not model selection. Formulate a model based on what you know about the problem, keeping in mind your effective sample size which can put limits on the number of parameters. Give enough parameters to parts of the model that are important. Then make contrasts and hypothesis tests to answer the true questions of interest. Don't drop any "insignificant" terms.

Besides distorting all aspects of the model by doing variable selection, you are using information in the data just to select variables and not to just estimating parameters. This results in noise and poorer prediction.

See my RMS notes for more details.

I am not discussing here my model specification, that wasn't the question. The answer to my question (from the statistics service at my university) is that I it is possible to use the next best model if it is considered equivalent (i.e. delta AIC <2)

• If you want to specify or clarify your question edit your question instead of this answer. – Ferdi Oct 6 '17 at 18:12