This is the third of five papers detailing our national study of general education astronomy students' conceptual and reasoning difficulties with cosmology. In this paper, we use item response theory to analyze students' responses to three out of the four conceptual cosmology surveys we developed. The specific item response theory model we use is known as the partial credit model. Since readers may be unfamiliar with the partial credit model, we provide a pedagogical introduction to this model. We use the partial credit model to assess the reliabilities of the four survey forms and to determine the probabilities of students achieving different scores on survey items. (Contains 3 tables and 12 figures.) [For Part II, see EJ956292.]