Participants are randomized to receive Placebo, Sitagliptin, or 1 of 7 initial LY2189265 doses until a dose decision is made based on quantitative analysis of the benefits and risks of each LY2189265 dose. A clinical utility index (CUI) that applies predicted values for change from baseline in HbA1c at 12 months and change from baseline in weight, diastolic blood pressure, and pulse rate at 6 months for each LY2189265 dose will be used toward this end. After the dose decision, participants in the selected LY2189265 arms and the comparator arms (Sitagliptin and Placebo/Sitagliptin arms) will continue the study, and additional participants will be randomized to the selected and comparator arms. Regardless of the timing of randomization relative to the dose decision point, all participants in the selected and comparator arms are planned to receive treatment for 104 weeks; participants in the Placebo/Sitagliptin arm will receive Placebo treatment for 26 weeks followed by Sitagliptin 100 mg for 78 weeks for blinding purposes only, and participants in the selected and Sitagliptin arms will receive the same treatment for 104 weeks. All participants will remain blinded to their study treatment throughout the study. Participants in the non-selected arms will discontinue from the study after the dose decision