Abstract: In practice, HMVCM faces two main challenges: the presence of strong influence points and the absence of data. Strong influence points may seriously distort the model parameter estimation and lead to poor prediction performance. Missing data may lead to information loss, affecting the accuracy and reliability of the model. Therefore, effectively addressing these two types of problems is critical to improve model performance. In order to solve these problems, this paper uses an outlier detection scheme based on Bayesian method, introduces indicative variables to deal with the missing data mechanism, and uses MH algorithm and Gibbs sampling to obtain Bayesian estimation of missing data. The results show that HMVCM combined with Bayesian inference can adapt to datasets with complex dynamic characteristics, and shows good performance in the face of strong influence points and missing data. The effectiveness of the proposed method is verified in simulation experiments, which shows that the model can maintain high accuracy and robustness in the dataset with complex structures.

Key words: complex heterogeneous longitudinal data, hidden Markov, variable coefficient regression model, Bayesian inference, strong points of influence, missing data