Linear Equations and Nonlinear Estimation

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Abstract
When a linear structural equation model results in nonlinear procedures for solution, multiple (but finite) sets of solutions may be possible, even with population data. An example of a three-variable feedback system is given in which two sets of solutions may be generated, and each may be obtained by algebraic analysis or by numerical analysis. Issues of model specification and equilibrium must be considered to differentiate the sets of solutions and choose between them. In the absence of strong information concerning these issues, data at more than one point in time is a minimal requirement to solve for model parameters and evaluate the system of variable relations. Statistical estimation of model parameters is also considered in this context.