Elastic half-space models, widely used to interpret displacements and gravity data in active volcanic areas, usually compute the displacement response to dilatational sources that simulate a change in pressure of the magma chamber. Elastic-gravitational models allow the computation of gravity, deformation, and gravitational potential changes due to pressurized magma cavities and intruding masses together. This type of model takes into account the mass interaction with the self-gravitation of the Earth through coupling between model equations. We perform a dimensional analysis of the elastic-gravitational model estimating the magnitude of intrusion mass and coupling effects at the space scale associated with volcano monitoring. We show that the intrusion mass cannot be neglected in the interpretation of gravity changes while displacements are primarily caused by pressurization. Therefore the intrusion of mass, together with the associated pressurization of the magma chamber, produces distinctive changes in gravity that could be used to interpret gravity changes without ground deformation and vice versa, depending on what type of source plays the main role in the intrusion process. Theoretical experiments indicate that mass and self-gravitation could produce changes in the magnitude and pattern of predicted gravity that may be above microgravity accuracy. Application of the elastic-gravitational model to interpret geodetic precursors observed at Mayon volcano (Philippines) prior to the eruption of 2001 shows that inversions increase in precision by using this model. Therefore our elastic-gravitational model is a refinement of purely elastic models and can better interpret gravity and deformation changes in active volcanic zones.