The dynamics of the interstellar medium (ISM) are strongly affected by turbulence, which shows increased anisotropy in the presence of a magnetic field. We expand upon the Esquivel & Lazarian method to estimate the Alfvén Mach number using the structure function anisotropy in velocity centroid data from Position-Position-Velocity maps. We utilize three-dimensional magnetohydrodynamic simulations of fully developed turbulence, with a large range of sonic and Alfvénic Mach numbers, to produce synthetic observations of velocity centroids with observational characteristics such as thermal broadening, cloud boundaries, noise, and radiative transfer effects of carbon monoxide. In addition, we investigate how the resulting anisotropy-Alfvén Mach number dependency found in Esquivel & Lazarian might change when taking the second moment of the Position-Position-Velocity cube or when using different expressions to calculate the velocity centroids. We find that the degree of anisotropy is related primarily to the magnetic field strength (i.e., Alfvén Mach number) and the line-of-sight orientation, with a secondary effect on sonic Mach number. If the line of sight is parallel to up to ≈45 deg off of the mean field direction, the velocity centroid anisotropy is not prominent enough to distinguish different Alfvénic regimes. The observed anisotropy is not strongly affected by including radiative transfer, although future studies should include additional tests for opacity effects. These results open up the possibility of studying the magnetic nature of the ISM using statistical methods in addition to existing observational techniques