We develop computational strategies for extended maximum likelihood
estimation, as defined in Rinaldo (2006), for general classes of
log-linear models of widespred use, under Poisson and
product-multinomial sampling schemes. We derive numerically efficient
procedures for generating and manipulating design matrices and we
propose various algorithms for computing the extended maximum
likelihood estimates of the expectations for the cell counts. These
algorithms allow to identify the set of estimable cell means for any
given observable table and can be used for modifying traditional
goodness-of-fit tests to accommodate for a nonexistent MLE. We
describe and take advantage of the connections between extended
maximum likelihood estimation in hierarchical log-linear models and
graphical models.