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Updated: May 3, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
On the Unidentifiability of the Fixed-Effects 3PL Model
Ernesto San Martín1, Jorge González, Francis Tuerlinckx
1Faculty of Mathematics, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Macul, Santiago, Chile, esanmart@mat.puc.cl.
Abstract:
The paper offers a general review of the basic concepts of both statistical model and parameter identification, and revisits the conceptual relationships between parameter identification and both parameter interpretability and properties of parameter estimates. All these issues are then exemplified for the 1PL, 2PL, and 1PL-G fixed-effects models. For the 3PL model, however, we provide a theorem proving that the item parameters are not identified, do not have an empirical interpretation and that it is not possible to obtain consistent and unbiased estimates of them.
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