  This paper considers nonlinear dynamic models where the main parameter of
interest is a nonnegative matrix characterizing the network (contagion)
effects. This network matrix is usually constrained either by assuming a
limited number of nonzero elements (sparsity), or by considering a reduced rank
approach for nonnegative matrix factorization (NMF). We follow the latter
approach and develop a new probabilistic NMF method. We introduce a new
Identifying Maximum Likelihood (IML) method for consistent estimation of the
identified set of admissible NMF's and derive its asymptotic distribution.
Moreover, we propose a maximum likelihood estimator of the parameter matrix for
a given non-negative rank, derive its asymptotic distribution and the
associated efficiency bound.
