The conditions which lead to caldera collapse are still poorly constrained. As there have only been four, possibly five, well-documented caldera forming events in the past century, the geodetic signals produced during chamber roof subsidence, or chamber volume reduction (shrinkage) in general, are not well documented or understood. In particular, when two or more geodetic sources are operating and providing signals at the same time, it is important to be able to estimate the likely contribution of each. Simultaneous activities of different geodetic sources are common and include pressure changes in magma chambers/reservoirs occurring at the same time as dyke emplacement. Here we present results from numerical models designed to simulate the subsidence of a magma-chamber roof, either directly (chamber shrinkage) or through ring-fault displacement, and the induced surface deformation and crustal stresses. We consider chamber depths at 3 km, 5 km, and 7 km below the crustal surface, using both non-layered (isotropic) and layered (anisotropic) crustal models. We also model the effects of a caldera lake and of a thick ice cover (ice sheet) on top of the caldera. The results suggest that magma-chamber roof subsidences between 20 m and 100 m generate large (tens of centimetres) vertical and, in particular, horizontal displacements at the surfaces of the ice and the crust out to distances of up to tens of kilometres from the caldera/chamber centre. Crustal layering tends to reduce, but increasing chamber depth to enlarge, the horizontal and vertical surface displacements. Applying the results to the ice subsidence in the Bardarbunga Caldera during the 2014-2015 Bardarbunga-Holuhraun volcanotectonic episode indicates that the modelled ice displacements are less than those geodetically measured. Also, the geodetically measured crustal displacements are less than expected for a 60 m chamber-roof subsidence. The modelling results thus suggest that only part of the ice subsidence is due to chamber-roof subsidence, the other part being related to flow in the ice. We show that such a flow is likely within the caldera as a result of the stress induced by the 45-km-long regional dyke emplaced (primarily in vertical magma flow) during the episode. This conclusion is further supported by the model results suggesting that the ring-fault (piston-like) displacements must have been much less than the total 60 m ice subsidence, or else faults with tens-of-metres displacements would have cut through the ice (these are not observed). We suggest that the ring-fault subsidence was triggered by small doming of the volcanic field and system hosting the Bardarbunga Caldera and that this doming occurred as a result of magma inflow and pressure increase in a deep-seated reservoir. The doming is confirmed by GPS measurements and supported by the seismicity results. The magmatic pressure increase in the reservoir was, in terms of the present model, responsible for the regional dyke emplacement, the Holuhraun eruption, and part of the stress concentration around, and displacement of, the Bardarbunga Caldera.