Results of the mixed-models, for the parallel-based samples.

The response variable was the rate of use of the target L2 English words (i.e., their count offset by the total number of words in each text). Under fixed effects, distance is the phonological LDN between each L2 word and its most lexically similar L1 counterpart (originally 0–1, scaled to 0–10), proficiency is the EFCAMDAT L2 proficiency level at which the text was written (1–12, corresponding to CEFR A1–B2), and frequency is the baseline Zipf frequency of the target word in English (~1–7.5). Under random effects, τ00 and τ11 respectively represent the SD of the associated random intercepts and slopes, and ρ01 represents the correlation between random intercepts and associated random slopes (here, distance for L1).