Urban rail services are the principal means of public transportation in many cities. To understand the crowding patterns and develop efficient operation strategies in the system, obtaining path choices is important. This paper proposed an assignment-based path choice estimation framework using automated fare collection (AFC) data. The framework captures the inherent correlation of crowding among stations, as well as the interaction between path choice and left behind. The path choice estimation is formulated as an optimization problem. The original problem is intractable because of a non-analytical constraint and a non-linear equation constraint. A solution procedure is proposed to decompose the original problem into three tractable sub-problems, which can be solved efficiently. The model is validated using both synthetic data and real-world AFC data in Hong Kong Mass Transit Railway (MTR) system. The synthetic data test validates the model's effectiveness in estimating path choice parameters, which can outperform the purely simulation-based optimization methods in both accuracy and efficiency. The test results using actual data show that the estimated path shares are more reasonable than survey-derived path shares and uniform path shares. Model robustness in terms of different initial values and different case study dates are also verified.