Native Language Identification (NLI) is a task aimed at determining the native language (L1) of learners of second language (L2) on the basis of their written texts. To date, research on NLI has focused on relatively small corpora. We apply NLI to the recently released EFCamDat corpus which is not only multiple times larger than previous L2 corpora but also provides longitudinal data at several proficiency levels. Our investigation using accurate machine learning with a wide range of linguistic features reveals interesting patterns in the longitudinal data which are useful for both further development of NLI and its application to research on L2 acquisition.