In many diverse settings, aggregated opinions of others play an increasingly dominant role in shaping individual decision making. One key prerequisite of harnessing the "crowd wisdom" is the independency of individuals' opinions, yet in real settings collective opinions are rarely simple aggregations of independent minds. Recent experimental studies document that disclosing prior collective opinions distorts individuals' decision making as well as their perceptions of quality and value, highlighting a fundamental disconnect from current modeling efforts: How to model social influence and its impact on systems that are constantly evolving? In this paper, we develop a mechanistic framework to model social influence of prior collective opinions (e.g., online product ratings) on subsequent individual decision making. We find our method successfully captures the dynamics of rating growth, helping us separate social influence bias from inherent values. Using large-scale longitudinal customer rating datasets, we demonstrate that our model not only effectively assesses social influence bias, but also accurately predicts long-term cumulative growth of ratings solely based on early rating trajectories. We believe our framework will play an increasingly important role as our understanding of social processes deepens. It promotes strategies to untangle manipulations and social biases and provides insights towards a more reliable and effective design of social platforms.