On the Estimation of Nonlinearly Aggregated Mixed Models

Abstract

The article proposes an iterative algorithm for the estimation of fixed and random effects of a nonlinearly aggregated mixed model. The latter arises when an additive Gaussian model is formulated at the disaggregate level on a nonlinear transformation of the responses, but information is available in aggregate form. The nonlinear transformation breaks the linearity of the aggregate model, yielding a nonlinear tight observational constraint. The algorithm rests upon the sequential linearization of the nonlinear aggregation constraint around proposals that are iteratively updated until convergence. Two alternative pseudo maximum likelihood methods are discussed and compared. As a byproduct we provide a solution to the problem of distributing the aggregate responses over the units of analysis, enforcing the nonlinear observational constraints. Illustrations referring to the temporal disaggregation problem are provided.

Key Words:

• Best linear unbiased prediction
• Box-cox transformation
• Constrained nonlinear optimization
• Temporal and spatial disaggregation