The drifting Fish Aggregating Device (dFAD) purse seine fishery is complex and fishing effort depends on a multitude of factors. Traditional indices of fishing effort such as searching time are meaningless for this fishery. We composed a comprehensive list of 28 candidate variables that describe the dFAD fishery and used them as predictors of fishing effort in bigeye tuna CPUE standardization of the French purse seiners operating in the Eastern Atlantic Ocean during 2007-2013. We performed variable selection using penalized maximum likelihood in GLM and GLMM frameworks, aiming to improve prediction accuracy and interpretability of the selected models. We applied the Lasso (Least Absolute Shrinkage and Selection Operator) regression models to derive the true parsimonious model, because the number of candidate independent variables is large compared to the number of observations. The penalized model selection process retained explanatory variables such as: the skipper, the vessel, the price of targeted tuna species, the density and spatial distribution of FADs and the number/type of deployed buoys. The inclusion of these predictors in CPUE standardization models provided realistic estimates of uncertainty. We propose the systematic collection of selected explanatory variables and their usage in dFAD related tuna CPUEs standardization in a mixed model framework.