Regression Estimates of Stochastic Compartmental Parameters Using Net Balance and Cumulative Flow Data

A compartmental network is formulated in which each of N compartments represents a possible behavioral state of a discrete population immigrating from outside sources. The network contains absorbing states (sinks) sufficient to maintain an accounting record of every individual that enters the network. Time dependent distributions of counts of individuals in every compartment are given for the case of random (Poisson) immigration, from which formulae for expected net balances in compartments and expected cumulative flows into compartments are derived. These formulae are used in a regression model from which parameter estimates are obtained for the compartmental model. Model parameters that can be estimated, given data, are: (1) immigration intensities, (2) immigration to individual compartments, (3) emigration intensities from individual compartments, (4) residence time distributions in individual compartments, (5) compartmental transfer probabilities.