Annals of Forest Science

, Volume 70, Issue 7, pp 707–715 | Cite as

Selection of mixed-effects parameters in a variable–exponent taper equation for birch trees in northwestern Spain

  • Esteban Gómez-GarcíaEmail author
  • Felipe Crecente-Campo
  • Ulises Diéguez-Aranda
Original Paper



Taper equations predict the variation in diameter along the stem, therefore characterizing stem form. Several recent studies have tested mixed models for developing taper equations. Mixed-effects modeling allow the interindividual variation to be explained by considering both fixed-effects parameters (common to the population) and random-effects parameters (specific to each individual).


The objective of this study is to develop a mixed-effect variable exponent taper equation for birch trees in northwestern Spain by determining which fixed-effects parameters should be expanded with random-effects parameters.


All possible combinations of linear expansions with random effects in one and in two of the fixed-effects model parameters were tested. Upper stem diameter measurements were used to estimate random-effects parameters by the use of an approximate Bayesian estimator, which calibrated stem profile curves for individual trees.


Parameter estimates for more than half of the mixed models investigated were nonsignificant. A first order autoregressive error structure was used to completely remove the autocorrelation between residuals, as mixed-effects modeling were not sufficient for this purpose.


The mixed model with the best fitting statistics did not provide the best calibration statistics for all upper stem diameter measurements. From a practical point of view, model calibration should be considered an essential criterion in mixed model selection.


Betula pubescens Ehrh Taper equation Mixed-effects modeling Autocorrelation Calibration Galicia 



The present study was financially supported by the Spanish Ministry of Education and Science through the research project Modelos de evolución de bosques de frondosas caducifolias del noroeste peninsular (AGL2007-66739-C02-01/FOR), co-funded by the European Union through the European Regional Development Fund.


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Copyright information

© INRA and Springer-Verlag France 2013

Authors and Affiliations

  • Esteban Gómez-García
    • 1
    Email author
  • Felipe Crecente-Campo
    • 1
  • Ulises Diéguez-Aranda
    • 1
  1. 1.Departamento de Ingeniería AgroforestalUniversidad de Santiago de Compostela. Escuela Politécnica Superior, R/Benigno Ledo, Campus UniversitarioLugoSpain

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