We have applied two ab initio based methods to study the dramatic change of magnetic properties across a series of strongly correlated electron systems consisting of cerium monopnictides and monochalcogenides. While, the fully ab initio method gives good results for the magnetic moments in the lighter chalcogenides, it entirely fails to give, even qualitatively, the trend of their unusual magnetic behavior. On the other hand, the second approach, which explicitly takes into account the interplay between the hybridization, the Coulomb exchange, and the crystal-field interactions, gives results in excellent agreement with experiment for all compounds in the series, including the moment collapse from CeSb to CeTe and the trend of moments and ordering temperatures across the series.