Dairy cattle feed efficiency (FE) can be defined as the ability to convert DMI into milk energy (MILKE) and maintenance or metabolic body weight (MBW). In other words, FE is DMI conditional on MILKE and MBW (i.e., DMI|MILKE,MBW). These partial regressions or partial efficiencies (PE) of DMI on MILKE and MBW can be separately partitioned into genetic or residual PE; furthermore, either PE category might be heterogeneous across various environmental or management factors. We develop a hierarchical Bayesian multivariate mixed model to infer upon such heterogeneity in PE as well as that of variance components (VC) of FE by modeling genetic and residual components of PE and of VC as mixed model functions of various factors such as station (fixed), parity (fixed), days in milk (fixed), and ration within station (random). After validating our proposed model with a simulation study, we applied it to analysis of a dairy consortium data set involving 5,088 Holstein cows from 13 research stations in 4 countries. Although no significant differences were detected across stations for the genetic PE of DMI|MILKE (0.38 kg/Mcal) and of DMI|MBW (0.10 kg/kg^0.75), as well as the residual PE of DMI|MILKE (0.33 kg/Mcal), the residual PE of DMI|MBW significantly differed across stations (P < 0.05), ranging from 0.05 kg/kg^0.75 to 0.18 kg/ kg^0.75. Substantial heterogeneity in genetic and residual VC in FE across stations, rations, and parities was also inferred. Estimated heritabilities of FE ranged from 0.16 to 0.46 across stations, whereas the overall estimated heritability of FE was 0.23. These results suggest that FE is more complex than what is currently considered in most quantitative genetic analyses.