Chris J. Cieszewski, Mike Strub


In this study, we compare the properties of self-referencing models, such as various site dependent growth and yield models for predictions of height, diameter, basal area, volume, and density, developed using Nonlinear-Fixed-Effects (NFE) versus Nonlinear-Mixed-Effects (NME) modeling approaches. The properties investigated include the following core traditional well-behaved model characteristics applicable to self-referencing functions: Base-Age-Invariance, Path-Invariance, Indifference Under Model Reparameterization, and Model Conditioning to have the predictions at the base-age equal to the reference point, as well as estimation and prediction statistics such as bias and variance of the fitted versus predicted residuals. The results of this investigation demonstrate that self-referencing models based on the NFE approach possess all the desirable properties associated with logical behavior of the model and estimation statistics, while the NME based self-referencing models lack the well-behaved model properties. We illustrate these properties using an example of fitting self-referencing models to panel data of loblolly pine age-height measurements on a range of sites from the South Africa Correlated Curve Trend Study.


Mixed-Effects; Fixed-Effects; Self-Referencing; Base Age Invariance; Path Invariance; Invariance under Reparameterization; Well-Behaved Models; Model Conditioning; Site Models.

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