All-dielectric metamaterials comprised of identical resonators draw a lot of attention as low-loss media providing for negative refraction, which is commonly attributed to double negativity of effective material parameters caused by overlapping of Mie resonances. We study dispersion diagrams of such metamaterials composed of dielectric rod arrays and show that bandwidths of positive and negative refraction and its type are irrelevant to negativity of effective parameters; instead, they are unambiguously defined by the shape and the location of the 2 nd transmission branch in dispersion diagrams and thus can be controlled by the lattice constants.