The Born cross section for the process $e^+ e^- to p bar p $ is measured using the initial state radiation technique with an undetected photon. This analysis is based on datasets corresponding to an integrated luminosity of 7.5 fb$^{-1}$, collected with the BESIII detector at the BEPCII collider at center of mass energies between 3.773 and 4.600 GeV. The Born cross section for the process $e^+ e^- to p bar p $ and the proton effective form factor are determined in the $pbar p$ invariant mass range between 2.0 and 3.8 GeV/$c^2$ divided into 30 intervals. The proton form factor ratio ($|G_E|/|G_M|$) is measured in 3 intervals of the $pbar p$ invariant mass between 2.0 and 3.0 GeV/$c^2$.