We generalise the spectral EM algorithm for dynamic factor models in Fiorentini, Galesi and Sentana (2014) to bifactor models with pervasive global factors complemented by regional ones. We exploit the sparsity of the loading matrices so that researchers can estimate those models by maximum likelihood with many series from multiple regions. We also derive convenient expressions for the spectral scores and information matrix, which allows us to switch to the scoring algorithm near the optimum. We explore the ability of a model with a global factor and three regional ones to capture inflation dynamics across 25 European countries over 1999-2014.