Despite many studies on trip inference using call detail record (CDR) data, a fundamental understanding of their limitations is lacking. In particular, because of the sparse nature of CDR data, users may travel to a location without being revealed in the data, which we refer to as a hidden visit. The existence of hidden visits hinders our ability to extract reliable information about human mobility and travel behavior from CDR data. In this study, we propose a data fusion approach to obtain labeled data for statistical inference of hidden visits. In the absence of complementary data, this can be accomplished by extracting labeled observations from more granular cellular data access records, and extracting features from voice call and text messaging records. The proposed approach is demonstrated using a real- world CDR dataset of 3 million users from a large Chinese city. Different machine learning models are used to infer whether a hidden visit exists during an observed displacement. The test results show significant improvement over the naive no-hidden-visit rule, which is an implicit assumption adopted by most existing studies. Based on the proposed model, we estimate that over 10% of the displacements extracted from CDR data involve hidden visits.