  Many studies involving large Markov chains require determining a smaller
representative (aggregated) chains. Each {\em superstate} in the representative
chain represents a {\em group of related} states in the original Markov chain.
Typically, the choice of number of superstates in the aggregated chain is
ambiguous, and based on the limited prior know-how. In this paper we present a
structured methodology of determining the best candidate for the number of
superstates. We achieve this by comparing aggregated chains of different sizes.
To facilitate this comparison we develop and quantify a notion of {\em marginal
return}. Our notion captures the decrease in the {\em heterogeneity} within the
group of the {\em related} states (i.e., states represented by the same
superstate) upon a unit increase in the number of superstates in the aggregated
chain. We use Maximum Entropy Principle to justify the notion of marginal
return, as well as our quantification of heterogeneity. Through simulations on
synthetic Markov chains, where the number of superstates are known apriori, we
show that the aggregated chain with the largest marginal return identifies this
number. In case of Markov chains that model real-life scenarios we show that
the aggregated model with the largest marginal return identifies an inherent
structure unique to the scenario being modelled; thus, substantiating on the
efficacy of our proposed methodology.
