Much of the inner Milky Way ’ s ( MW ) global rotation and velocity dispersion patterns can be reproduced by models of secularly-evolved , bar-dominated bulges . More sophisticated constraints , including the higher moments of the line-of-sight velocity distributions ( LOSVDs ) and limits on the chemodynamical substructure , are critical for interpreting observations of the unresolved inner regions of extragalactic systems and for placing the MW in context with other galaxies . Here , we use SDSS-APOGEE data to develop these constraints , by presenting the first maps of the LOSVD skewness and kurtosis of metal-rich and metal-poor inner MW stars ( divided at { [ Fe / H ] } = -0.4 ) , and comparing the observed patterns to those that are seen both in N -body models and in extragalactic bars . Despite closely matching the mean velocity and dispersion , the models do not reproduce the observed LOSVD skewness patterns in different ways , which demonstrates that our understanding of the detailed orbital structure of the inner MW remains an important regime for improvement . We find evidence in the MW of the skewness-velocity correlation that is used as a diagnostic of extragalactic bar/bulges . This correlation appears in metal-rich stars only , providing further evidence for different evolutionary histories of chemically differentiated populations . We connect these skewness measurements to previous work on high-velocity “ peaks ” in the inner Galaxy , confirming the presence of that phenomenon , and we quantify the cylindrical rotation of the inner Galaxy , finding that the latitude-independent rotation vanishes outside of l \sim 7 ^ { \circ } . Finally , we evaluate the MW data in light of select extragalactic bar diagnostics and discuss progress and challenges of using the MW as a resolved analog of unresolved stellar populations .