Internet of Things devices are expanding rapidly and generating huge amount of data. There is an increasing need to explore data collected from these devices. Collaborative learning provides a strategic solution for the Internet of Things settings but also raises public concern over data privacy. In recent years, large amount of privacy preserving techniques have been developed based on secure multi-party computation and differential privacy. A major challenge of collaborative learning is to balance disclosure risk and data utility while maintaining high computation efficiency. In this paper, we proposed privacy preserving logistic regression model using matrix encryption approach. The secure scheme is resilient to chosen plaintext attack, known plaintext attack, and collusion attack that could compromise any agencies in the collaborative learning. Encrypted model estimate is decrypted to provide true model results with no accuracy degradation. Verification phase is implemented to examine dishonest behavior among agencies. Experimental evaluations demonstrate fast convergence rate and high efficiency of proposed scheme.