# Model selection in PGLS?

I am using Phylogenetic General Least Squares in the R package 'caper'.

I have 4 predictor variables and I would like to know which are correlated with my response variable, while taking the phylogeny into account.

I am uncertain on how to assess the models:

1. one way is to include all my predictors in one model and get the F-stat using anova().
2. The other option is to assess multiple models with different combinations of the predictor variables and use AIC() to select the best model.

Which method should I use?

If your goal is to obtain p-values for the individual predictors, then using anova on your fitted pgls models does that. AIC will give you measures of the overall goodness of fit of each model, but doesn't tell you about the significance of individual parameters. In fact, you can have a model favored by AIC that includes parameters with non-significant p-values (see Why applying model selection using AIC gives me non-significant p-values for the variables.
• If your concern is reporting a ridiculous number of results, then you can choose to only report models above a certain Akaike weight. If your concern is doing everything by hand, then you might find help from an R package such as MuMln. You can also look into model averaging rather than model selection. – Slow loris May 19 '16 at 16:20