This paper proposed a linear mixed-effects model and offered a flexible statistical analysis for controlling potential random effects and identifying significant fixed effects in linguistic data involving island structure. We started from the initial thesis that the two variables in the materials designed in our acceptability-rating experiment, namely GAP-POSITION and STRUCTURE, exert significant fixed effects, and then we tried to come up with an analysis where some interactive aspects of the two variables vis-à-vis other variables like TYPE and PARTICIPANT are taken into account. It was suggested in this paper that the proposed linear mixed-effects model provides the most parsimonious and statistically valid analysis. Specifically it was shown that island effects are most likely to be due to grammatical constraints, considering that the two variables GAP-POSITION and STRUCTURE interact to produce statistically significant effects, and thus it is safe to say that Korean L2 learners of English are as sensitive to the island vs. non-island distinction as L1 native speakers have been reported to be.