Abstract Maintaining passenger loyalty to Public Transportation (PT) services is an effective way to sustain ridership of this eco-friendly transport mode. Although numerous studies have investigated how passengers' perception of service quality influences their loyalty and proposed key determinants to secure their PT loyalty, it remains unclear whether these relationships are independent of the methods used for linear or non-linear analysis in different contexts. Given the impact of this question on relevant policy-making, this study simultaneously investigated the relationships between passengers' perceived service quality of specific attributes and their overall loyalty using both linear (Structural Equation Modeling, SEM) and non-linear (Gradient Boosting Decision Tree, GBDT) methods. To interpret the results of the two models, the Total Accumulated Local Effects (TALE) method, a variant of the Accumulated Local Effects (ALE) method, was proposed as a model-independent approach. The case study was conducted in Xiamen, China. The results showed that TALE had an advantage over the conventional ALE method because it considered the impact of the actual score distribution of the samples on the results, making the interpretation more realistic. Furthermore, it was found that there were no significant differences in the results of the normalized TALE in GBDT and SEM for most explanatory variables, both indicating similar non-linear trends. Therefore, regardless of the employed methods, the natural existence of non-linear relationships between increased perceived service quality and improved overall PT loyalty was observed. After determining the relationship between the perceived service quality and overall loyalty, the Importance-Performance Analysis (IPA) method was combined with the TALE of each explanatory variable to suggest key determinants that would enhance passengers’ overall loyalty.

Highlights • The non-linear relationship between PT service quality and passenger loyalty is analyzed. • A new model-independent interpretable machine learning method, TALE, is proposed. • TALE has advantages over conventional ALE by considering sample distribution • Non-linear effects can be found in both SEM and GBDT. • IPA combined with GBDT can find the vital PT service attributes for loyalty improvement. • Bus operational stability is the most vital PT service attribute