Most common methods for inferring transposable element (TE) evolutionary relationships are based on dividing TEs into subfamilies using shared diagnostic nucleotides. Although originally justified based on the "master gene" model of TE evolution, computational and experimental work indicates that many of the subfamilies generated by these methods contain multiple source elements. This implies that subfamily-based methods give an incomplete picture of TE relationships. Studies on selection, functional exaptation, and predictions of horizontal transfer may all be affected. Here, we develop a Bayesian method for inferring TE ancestry that gives the probability that each sequence was replicative, its frequency of replication, and the probability that each extant TE sequence came from each possible ancestral sequence. Applying our method to 986 members of the newly-discovered LAVA family of TEs, we show that there were far more source elements in the history of LAVA expansion than subfamilies identified using the CoSeg subfamily-classification program. We also identify multiple replicative elements in the AluSc subfamily in humans. Our results strongly indicate that a reassessment of subfamily structures is necessary to obtain accurate estimates of mutation processes, phylogenetic relationships and historical times of activity.