The filled skutterudite LaFe4Sb12 shows greatly reduced thermal conductivity compared to that of the related unfilled compound CoSb3, although the microscopic reasons for this are unclear. We calculate harmonic and anharmonic force constants for the interaction of the La filler atom with the framework atoms. We find that force constants show a general trend of decaying rapidly with distance and are very small for the interaction of the La with its next-nearest-neighbor Sb and nearest-neighbor La. However, a few rather long-range interactions, such as with the next-nearest-neighbor La and with the third neighbor Sb, are surprisingly strong, although still small. We test the central-force approximation and find significant deviations from it. Using our force constants we calculate a bare La mode Gruneisen parameter and find a value of 3-4, substantially higher than values associated with cage atom anharmonicity, i.e., a value of about 1 for CoSb3 but much smaller than a previous estimate [Bernstein et al., Phys. Rev. B 81, 134301 (2010), 10.1103/PhysRevB.81.134301]. This latter difference is primarily due to the previously used overestimate of the La-Fe cubic force constants. We also find a substantial negative contribution to this bare La Gruneisen parameter from the aforementioned third-neighbor La-Sb interaction. Our results underscore the need for rather long-range interactions in describing the role of anharmonicity on the dynamics in this material.