L2 Selves, Control-Value Appraisals, and Engagement in AI-Supported Informal Digital Learning of English: An SEM and fsQCA Approach

This study examined learner engagement in AI-supported informal digital learning of English (IDLE) by integrating L2 selves and control-value appraisals within a Control-Value Theory framework. Drawing on data from 653 Chinese university students, the study employed structural equation modeling (SEM) to test the associations among ideal L2 self, ought-to L2 self, control appraisal, intrinsic value appraisal, extrinsic value appraisal, and learner engagement. It further used fuzzy-set qualitative comparative analysis (fsQCA) to identify configurational pathways associated with high engagement. The SEM results showed that both ideal L2 self and ought-to L2 self were positively associated with the three types of control-value appraisals, which were in turn positively associated with engagement. Mediation analysis indicated that control appraisal, intrinsic value appraisal, and extrinsic value appraisal mediated the associations between L2 selves and engagement. The fsQCA results revealed six configurations associated with high engagement, suggesting that engagement may be linked to multiple motivational-appraisal patterns. These findings highlight the importance of both average associations and configurational diversity in understanding AI-supported IDLE engagement.