Collective food transport in ant colonies is a striking, albeit poorly understood, example of coordinated group behavior in nature that can serve as a template for robust, decentralized multi-robot cooperative manipulation strategies. We investigate this behavior in Aphaenogaster cockerelli ants in order to derive a model of the ants' roles and behavioral transitions and the resulting dynamics of a transported load. In experimental trials, A. cockerelli are induced to transport a rigid artificial load to their nest. From video recordings of the trials, we obtain time series data on the load position and the population counts of ants in three roles. From our observations, we develop a stochastic hybrid system model that describes the time evolution of these variables and that can be used to derive the dynamics of their statistical moments. In our model, ants switch stochastically between roles at constant, unknown probability rates, and ants in one role pull on the load with a force that acts as a proportional controller on the load velocity with unknown gain and set point. We compute these unknown parameters by using standard numerical optimization techniques to fit the time evolution of the means of the load position and population counts to the averaged experimental time series. The close fit of our model to the averaged data and to data for individual trials demonstrates the accuracy of our proposed model in predicting the ant behavior.