Comparing the observed brightness of various buried objects is a straightforward way to characterize the performance of a ground penetrating radar (GPR) system. However, a limitation arises. A simple comparison of buried object brightness values does not disentangle the effects of the GPR system itself from the system's operating environment and the objects being observed. Therefore, with brightness values exhibiting an unknown synthesis of systemic, environmental, and object factors, GPR system analysis becomes a convoluted affair. In this work, we use an experimentally collected dataset of over 25,000 object observations from five different multi-static radar arrays to develop models of buried object brightness and control for these various effects. Our modeling efforts provide a means for quantifying the relative brightness of GPR systems, the objects they detect, and the physical properties of those objects which influence observed brightness. To evaluate the models' performance on new object observations, we repeatedly simulate fitting them to half the dataset and predicting the observed brightness values of the unseen half. Additionally, we introduce a method for estimating the probability that individual observations constitute a visible object, which aids in failure analysis, performance characterization, and dataset cleaning.