The use of conversational agents (CAs) in mental health therapy is gaining traction due to their accessibility, anonymity, and nonjudgmental nature. However, understanding the psychological factors driving preferences for CA-based therapy remains critical to ensure ethical and effective application. Variables such as epistemic trust, attachment styles, personality traits, and fear of intimacy appear central in shaping attitudes toward these artificial intelligence (AI)-driven interventions. This study aimed to investigate the role of epistemic trust, attachment styles, personality traits, and fear of intimacy in influencing individuals' willingness to engage with CA-based therapy. An online survey was administered to 876 psychology students, yielding 736 responses (84.01% response rate). Variables measured included epistemic trust, attachment styles, personality traits, and fear of intimacy. A 5-point ordinal scale assessed willingness to engage in CA-based therapy. The data were analyzed using ordinal logistic regression models, including proportional odds models (POMs), nonproportional odds models (NPOMs), and partial proportional odds models (PPOMs), with residual deviance used to compare model fit. The PPOM provided the best model fit (residual deviance=3530.47), outperforming both the NPOM (deviance=6244.01) and the POM based on Brant test results indicating violations of the proportional odds assumption (χ²105=187.8; P