We present an extensive study of hexadecapole correlations in the rare-earth region near 𝑁=90 and the effects these correlations have on various nuclear properties, such as the low-energy spectra, as well as quadrupole, hexadecapole, and monopole transition strengths. In order to examine hexadecapole correlations, we employ a mapped 𝑠𝑑𝑔 interacting boson model, with parameters derived from a self-consistent mean-field calculations with a relativistic energy density functional. We apply this model to even-even isotopes of Nd, Sm, Gd, Dy, and Er (𝑍=60–68) with neutron numbers 𝑁=84–96. The obtained results show a good agreement with the experiment. By comparing the results with the ones obtained from a simpler mapped 𝑠𝑑 interacting boson model, we show that the inclusion of the hexadecapole degree of freedom via the 𝑔 boson is necessary to improve the results of the 𝐽𝜋≥6+ yrast energies in the nuclei with 𝑁=84 and 86, being near the neutron shell closure. The 𝑠𝑑𝑔 interacting boson model increases the quadrupole transition strengths between yrast states in the 𝑁=90 and 92 well deformed nuclei, which is in good agreement with the experiment for most of those isotopes. The presence of 𝑔 bosons does have an important effect on hexadecapole transition strengths, although experimental data for such transitions are limited. The obtained monopole transition strengths do not differ significantly from the ones obtained from the simpler 𝑠𝑑 model.