The local structure of the spinel LiRh$_2$O$_4$ has been studied using atomic pair distribution function (PDF) analysis of powder x-ray diffraction data. This measurement is sensitive to the presence of short Rh-Rh bonds that form due to dimerization of Rh$^{4+}$ ions on the pyrochlore sublattice, independent of the existence of long range order. We show that structural dimers exist in the low-temperature phase, as previously supposed, with a bond shortening of $Delta r sim 0.15$ AA . The dimers persist up to 350 K, well above the insulator-metal transition, with $Delta r$ decreasing in magnitude on warming. Such behavior is inconsistent with the Fermi surface nesting-driven Peierls transition model. Instead, we argue that LiRh$_2$O$_4$ should properly be described as a strongly correlated system.
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