Pathways from AI Literacy to Sustained Engagement with AI-Powered Cognitive Behavioural Therapy: A Structural Equation Model with Moderated Mediation in a National UK Sample

ABSTRACT Background AI-powered cognitive behavioural therapy (AI-CBT) tools hold significant promise for addressing the global mental health treatment gap, yet sustained user engagement remains critically low. While patient attitudes and experiential factors have been qualitatively documented, the psychological mechanisms through which AI literacy translates into long-term engagement remain poorly understood. Existing systematic evidence highlights trust, perceived therapeutic alliance, and stigma as salient themes, but no large-scale quantitative study has modelled these as a mediated pathway. Objective This study aimed to (1) examine whether trust in AI systems and perceived therapeutic alliance mediate the relationship between AI literacy and sustained AI-CBT engagement, and (2) determine whether mental health stigma moderates these mediated pathways. Methods A cross-sectional national online survey was conducted in the United Kingdom (N = 1,247). Eligible adults (18+) with a history of anxiety or depression who had used an AI-CBT tool in the preceding 12 months were recruited via stratified random sampling. Structural equation modelling (SEM) with moderated mediation was conducted in R (lavaan 0.6-17). Moderated mediation was evaluated using the PROCESS macro framework adapted for SEM, with 5,000 bootstrap replications for bias-corrected confidence intervals. Model fit was assessed using CFI, TLI, RMSEA, and SRMR indices. Results The final SEM demonstrated excellent fit (CFI = 0.967, TLI = 0.959, RMSEA = 0.043 [90% CI: 0.036–0.051], SRMR = 0.052). AI literacy exerted a significant indirect effect on sustained engagement through trust in AI (β = 0.213, SE = 0.031, p < .001) and perceived therapeutic alliance (β = 0.187, SE = 0.028, p < .001). Mental health stigma significantly moderated the trust→engagement pathway (ΔR 2 = 0.042, p = .003), with the indirect effect being stronger among individuals with lower stigma scores. The total indirect effect accounted for 58.4% of the total effect of AI literacy on engagement. Conclusions AI literacy promotes sustained AI-CBT engagement primarily through its effects on trust and perceived therapeutic alliance, pathways that are attenuated by mental health stigma. These findings underscore the need for stigma-reduction interventions and AI literacy programmes as implementation strategies. Findings have direct implications for the design and deployment of AI-CBT tools across UK NHS digital mental health services.