  A systematic analysis of the spherical-to-deformed shape phase transition in
even-even rare-earth nuclei from $_{58}$Ce to $_{74}$W is carried out in the
framework of the interacting boson model. These results are then used to
calculate nuclear radii and electric monopole (E0) transitions with the same
effective operator. The influence of the hexadecapole degree of freedom ($g$
boson) on the correlation between radii and E0 transitions thus established, is
discussed.
