This study utilizes advanced artificial intelligence techniques to analyze the social media behavior of 1358 users on VK, the largest Russian online social networking service. The analysis comprises 753,252 posts and reposts, combined with Big Five personality traits test results, as well as assessments of verbal and fluid intelligence. The objective of this research is to understand the manifestation of psychological attributes in social media users' behavior and determine their implications on user-interaction models. We employ the integrated gradients method to identify the most influential feature groups. The partial dependence plot technique aids in understanding how these features function across varying severity degrees of the predicted trait. To evaluate feature stability within the models, we cluster calculated Shapley values. Our findings suggest that the emotional tone (joy, surprise, anger, fear) of posts significantly influences the prediction of three personality traits: Extraversion, Agreeableness, and Openness to Experience. Additionally, user social engagement metrics (such as friend count, subscribers, likes, views, and comments) correlate directly with the predicted level of Logical thinking. We also observe a trend towards provocative and socially reprehensible content among users with high Neuroticism levels. The theme of religion demonstrates a multidirectional relationship with Consciousness and Agreeableness. Further findings, including an analysis of post frequency and key text characteristics, are also discussed, contributing to our understanding of the complex interplay between social media behavior and psychological traits. The study proposes a transition from the analysis of correlations between psychological (cognitive) traits to the analysis of indicators of behavior in a social network that are significant for diagnostic models of the corresponding traits.