scieee AI-readable full text Open interactive document viewer

Fitting and calibrating a multilevel mixed-effects stem taper model for maritime pine in NW Spain

Arias Rodil, Manuel; Castedo Dorado, Fernando; Cámara Obregón, Asunción; Diéguez Aranda, Ulises

Published
2015
Publisher
PLOS
DOI
10.1371/journal.pone.0143521
Repository
minerva.usc.es
Language
en

Abstract

Stem taper data are usually hierarchical (several measurements per tree, and several trees per plot), making application of a multilevel mixed-effects modelling approach essential. However, correlation between trees in the same plot/stand has often been ignored in previous studies. Fitting and calibration of a variable-exponent stem taper function were conducted using data from 420 trees felled in even-aged maritime pine (Pinus pinaster Ait.) stands in NW Spain. In the fitting step, the tree level explained much more variability than the plot level, and therefore calibration at plot level was omitted. Several stem heights were evaluated for measurement of the additional diameter needed for calibration at tree level. Calibration with an additional diameter measured at between 40 and 60% of total tree height showed the greatest improvement in volume and diameter predictions. If additional diameter measurement is not available, the fixed-effects model fitted by the ordinary least squares technique should be used. Finally, we also evaluated how the expansion of parameters with random effects affects the stem taper prediction, as we consider this a key question when applying the mixed-effects modelling approach to taper equations. The results showed that correlation between random effects should be taken into account when assessing the influence of random effects in stem taper prediction

Full text

CORRECTION Correction: Fitting and Calibrating a Multilevel Mixed-Effects Stem Taper Model for Maritime Pine in NW Spain Manuel Arias-Rodil, Fernando Castedo-Dorado, Asunción Cámara-Obregón, Ulises Diéguez-Aranda In Table 4, the value for δin the “MM3 (a 1 ,b 3 )”column is incorrect. Please see the corrected Table 4 here. The value for “delta”in the S1 Appendix is incorrect. Please view the correct S1 Appendix below. Table 4. Parameter estimates of the fixed-effects model (fitted by OLS, FMOLS) and the recommended mixed-effects model (expanding a 1 and b 3 with random effects, MM3), fitted using the whole data set. Parameter FMOLS MM3 (a 1 ,b 3 ) a 0 0.9891 1.050 a 1 0.9633 0.9427 a 2 0.04585 0.04734 b 1 0.3672 0.3619 b 2 -0.3350 -0.6907 b 3 0.5192 0.5847 b 4 0.8471 1.126 b 5 0.01777 0.02271 b 6 -0.02647 -0.05812 s2 i;a1 σ 2i , 1.263 10 −5 s2 i;b38.273 10 −4 s2 i;a1;b3 −1.104 10 −5 s2 ij;a1 1.205 10 −4 s2 ij;b3 3.095 10 −3 s2 ij;a1;b3 3.847 10 −5 σ 2 1.555 6.117 10 −3 δ1.481 s2 i;a1 ,s2 i;b3and s2 i;a1;b3 , variances and covariance of random effects in parameters a 1 and b 3 at plot level; s2 ij;a1 ,s2 ij;b3 and s2 ij;a1;b3 , variances and covariance of random effects in parameters a 1 and b 3 at tree level; σ 2 , residual variance; δparameter of power function. Note that the σ 2 of the mixed-effects model must be multiplied by g=d δ when applied (variance obtained from ordinary residuals is 0.6866). doi:10.1371/journal.pone.0151297.t001 PLOS ONE | DOI:10.1371/journal.pone.0151297 March 3, 2016 1/2 OPEN ACCESS Citation: Arias-Rodil M, Castedo-Dorado F, CámaraObregón A, Diéguez-Aranda U (2016) Correction: Fitting and Calibrating a Multilevel Mixed-Effects Stem Taper Model for Maritime Pine in NW Spain. PLoS ONE 11(3): e0151297. doi:10.1371/journal. pone.0151297 Published: March 3, 2016 Copyright: © 2016 Arias-Rodil et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Supporting Information S1 Appendix. R implementation of the calibration procedure for a multilevel mixed-effects model based on stem taper function of Kozak (2004). (ZIP) Reference 1. Arias-Rodil M, Castedo-Dorado F, Cámara-Obregón A, Diéguez-Aranda U (2015) Fitting and Calibrating a Multilevel Mixed-Effects Stem Taper Model for Maritime Pine in NW Spain. PLoS ONE 10(12): e0143521. doi: 10.1371/journal.pone.0143521 PMID: 26630156 PLOS ONE | DOI:10.1371/journal.pone.0151297 March 3, 2016 2/2