An Information-Loss-Minimizing Approach to Multinominal Alignment in Microsimulation Models

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Abstract

There exist a number of alignment methods. They typically address the binary case and they typically put special emphasis on one of the alternatives rather than treating all alternatives in a symmetric way (for a review, see Li & O’Donoghue, 2014). In this paper we propose a more general mathematical foundation of multinominal alignment. Meancorrection alignment is defined as a method that minimizes the information loss in the adjustment process. The analytical solution to the alignment problem is characterized and furthermore applied in deriving various properties for the method. It is demonstrated that there exits an algorithm called Bi-Proportional Scaling that converge to the solution of the problem. This is tested against two versions of the Newton-Raphson-algoritm, and it is demonstrated that it is at least twice as fast as these methods. Finally, it is argued, that the method is very easy to implement.