Questions about the evolution of material culture are widespread in the humanities and social sciences. Statistical modeling of long-term changes in material culture is less common due to a lack of appropriate frameworks. Our goal is to close this gap and provide robust statistical methods for examining changes in the diversity of material culture. We provide an open-source and quantitative workflow for estimating rates of origination, extinction, and preservation, as well as identifying key shift points in the diversification histories of material culture. We demonstrate our approach using two distinct kinds of data: age ranges for the production of American car models, and radiocarbon dates associated with archaeological cultures of the European Neolithic. Our approach improves on existing frameworks by disentangling the relative contributions of origination and extinction to diversification. Our method also permits rigorous statistical testing of competing hypotheses to explain changes in diversity. Finally, we stress the value of a flexible approach that can be applied to data in various forms; this flexibility allows scholars to explore commonalities between forms of material culture and ask questions about the general properties of cultural change.