In this work we deal with parameter estimation in a latent variable model,
namely the multiple-hidden i.i.d. model, which is derived from multiple
alignment algorithms. We first provide a rigorous formalism for the homology
structure of k sequences related by a star-shaped phylogenetic tree in the
context of multiple alignment based on indel evolution models. We discuss
possible definitions of likelihoods and compare them to the criterion used in
multiple alignment algorithms. Existence of two different Information
divergence rates is established and a divergence property is shown under
additional assumptions. This would yield consistency for the parameter in
parametrization schemes for which the divergence property holds. We finally
extend the definition of the multiple-hidden i.i.d. model and the results
obtained to the case in which the sequences are related by an arbitrary
phylogenetic tree. Simulations illustrate different cases which are not covered
by our results.