Unified generalized iterative scaling and its applications

Generalized iterative scaling (GIS) has become a popular method for getting the maximum likelihood estimates for log-linear models. It is basically a sequence of successive II-projections onto sets of probability vectors with some given linear combinations of probability vectors. However, when a sequence of successive II-projections are applied onto some closed and convex sets (e.g., marginal stochastic order), they may not lead to the actual solution. In this manuscript, we present a unified generalized iterative scaling (UGIS) and the convergence of this algorithm to the optimal solution is shown. The relationship between the UGIS and the constrained maximum likelihood estimation for log-linear models is established. Applications to constrained Poisson regression modeling and marginal stochastic order are used to demonstrate the proposed UGIS.