iForest - Biogeosciences and Forestry


Nonlinear mixed model approaches to estimating merchantable bole volume for Pinus occidentalis

SW Bueno-López (1)   , E Bevilacqua (2)

iForest - Biogeosciences and Forestry, Volume 5, Issue 5, Pages 247-254 (2012)
doi: https://doi.org/10.3832/ifor0630-005
Published: Oct 24, 2012 - Copyright © 2012 SISEF

Research Articles

The ability to predict cumulative bole volume to any predefined upper stem diameter on a standing tree is essential for estimating current inventory levels and making informed decisions regarding the management of forest resources. Several types of mathematical models have been developed to predict cumulative bole volume, requiring only the collection of low cost data but high accuracy tree measurements. This paper reports on the comparison of a variable-exponent taper model and a volume-ratio model for estimating inside-bark cumulative bole volume to three predefined upper stem diameters using stem analysis data Pinus occidentalis trees in La Sierra, Dominican Republic. Each sampled tree was measured at multiple points on the bole, making observations spatially correlated within the tree. Inference problems due to autocorrelation were addressed by using a nonlinear mixed-effects model fitted by restricted maximum likelihood (REML) and including two random parameter coefficients at tree level in each of the two models tested. Using an independent validation data set, the variable-exponent taper model with two random parameters demonstrated better predictive ability as compared to the volume-ratio model when estimating cumulative bole volume to the three predefined upper stem diameters. The taper model allows flexible volume estimation for the population average as well for specific trees.


Nonlinear Mixed-effects Models, Restricted Maximum Likelihood, Taper Model, Volume-ratio Model, Random Coefficients, Calibration, Pinus occidentalis

Authors’ address

SW Bueno-López
Vicerrectoría de Investigaciones e Innovación, Pontificia Universidad Católica Madre y Maestra, Autopista Duarte km 1.500, Santiago de los Caballeros (República Dominicana)
E Bevilacqua
State University of New York, College of Environmental Science and Forestry, 1 Forestry Drive, 13210 Syracuse (NY - USA)

Corresponding author

SW Bueno-López


Bueno-López SW, Bevilacqua E (2012). Nonlinear mixed model approaches to estimating merchantable bole volume for Pinus occidentalis. iForest 5: 247-254. - doi: 10.3832/ifor0630-005

Academic Editor

Marco Borghetti

Paper history

Received: Sep 07, 2012
Accepted: Oct 01, 2012

First online: Oct 24, 2012
Publication Date: Oct 30, 2012
Publication Time: 0.77 months

Breakdown by View Type

(Waiting for server response...)

Article Usage

Total Article Views: 23396
(from publication date up to now)

Breakdown by View Type
HTML Page Views: 18596
Abstract Page Views: 754
PDF Downloads: 3185
Citation/Reference Downloads: 19
XML Downloads: 842

Web Metrics
Days since publication: 2814
Overall contacts: 23396
Avg. contacts per week: 58.20

Article Citations

Article citations are based on data periodically collected from the Clarivate Web of Science web site
(last update: Jun 2020)

Total number of cites (since 2012): 5
Average cites per year: 0.56


Publication Metrics

by Dimensions ©

Articles citing this article

List of the papers citing this article based on CrossRef Cited-by.

Avery TE, Burkhart HE (2002)
Avery TE, Burkhart HE (2002). Forest measurements (5th edn). McGraw Hill, New York, USA, pp. 453.
Bailey RL, Clutter JL (1970)
Bailey RL, Clutter JL (1970). Volume tables for old-field Loblolly pine plantations in the Georgia Piedmont. Forest Research Council, Georgia, USA, pp. 18.
Banco Central de la República Dominicana (2004)
Banco Central de la República Dominicana (2004). Annual report. Gobierno Dominicano, Santo Domingo de Guzman, República Dominicana, pp. 2056.
Bueno-López SW, Bevilacqua E (2010)
Bueno-López SW, Bevilacqua E (2010). Modeling stem increment in individual Pinus occidentalis Sw. trees in La Sierra, Dominican Republic. Forest Systems 19 (2): 170-183. [online] URL:
Online | Gscholar
Bueno-López SW, Bevilacqua E (2011)
Bueno-López SW, Bevilacqua E (2011). Developing a diameter-distribution prediction system for Pinus occidentali, s Sw. in La Sierra, Dominican Republic. Revista Chapingo, Serie Ciencias Forestales y del Ambiente XVII (1): 115-132. [online] URL:
Online | Gscholar
Burkhart HE, Walton SB (1985)
Burkhart HE, Walton SB (1985). Notes: incorporating crown ratio into taper equations for loblolly pine trees. Forest Science 31(2): 478-484.
Burkhart HE (1977)
Burkhart HE (1977). Cubic foot volume of loblolly pine to any merchantable top limit. Southern Journal of Applied Forestry 1 (2): 7-9.
Calama R, Montero G (2006)
Calama R, Montero G (2006). Stand and tree-level variability on stem form and tree volume in Pinus pinea L.: A multilevel random components approach. Investigación Agraria: Sistemas Recursos Forestales 15 (1): 24-41.
Cochran WG (1977)
Cochran WG (1977). Sampling Techniques (3rd edn). John Wiley and Sons, New York, USA, pp. 428.
Dobler G, Peralta LE, Debord LT, Torres JG (1995)
Dobler G, Peralta LE, Debord LT, Torres JG (1995). Investigación y manejo de especies maderables de uso comun en La Sierra: Guía técnica. Plan Sierra Inc., San José de las Matas, Republica Dominicana, pp. 269.
Garber SM, Maguire DA (2003)
Garber SM, Maguire DA (2003). Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures. Forest Ecology and Management 179 (1-3): 507-522. - doi:
CrossRef | Gscholar
Gaztelurrutia M, Montero G (2001)
Gaztelurrutia M, Montero G (2001). Modelo de simulación de claras en masas de Pinus silvestris L. Monografías. Investigación Agraria N. 3, Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria, Madrid, Spain, pp. 114.
Gregoire TG, Schabenberger O (1996a)
Gregoire TG, Schabenberger O (1996a). Nonlinear mixed-effects modeling of cumulative bole volume with spatially correlated within-tree data. Journal of Agricultural, Biological, and Environmental Statistics 1 (1): 107-119. - doi:
CrossRef | Gscholar
Gregoire TG, Schabenberger O (1996b)
Gregoire TG, Schabenberger O (1996b). A nonlinear mixed-effects model to predict cumulative bole volume of standing trees. Journal of Applied Statistics 23: 257-271. - doi:
CrossRef | Gscholar
Huang S, Price D, Morgan D, Peck K (1994)
Huang S, Price D, Morgan D, Peck K (1994). Kozak’s Variable-exponent taper equation regionalized for White spruce in Alberta. Western Journal of Applied Forestry 15(2): 75-85.
Husch B, Beers TW, Kershaw JA (2002)
Husch B, Beers TW, Kershaw JA (2002). Forest mensuration (4th edn). Wiley, New York, USA, pp. 456.
Jones RH (1990)
Jones RH (1990). Serial correlation or random subject effects? Communications in Statistics - Simulation and Computation 19 (3): 1105-1123. - doi:
CrossRef | Gscholar
Kozak A (1988)
Kozak A (1988). A variable-exponent taper equation. Canadian Journal of Forest Research 18: 1363-1368. - doi:
CrossRef | Gscholar
Kozak A (2004)
Kozak A (2004). My last words on taper equations. Forest Chronicle 80: 507-515. - doi:
CrossRef | Gscholar
Leites LP, Robinson AP (2004)
Leites LP, Robinson AP (2004). Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework. Forest Science 50: 204-212.
Lindstrom MJ, Bates DM (1990)
Lindstrom MJ, Bates DM (1990). Nonlinear mixed-effects models for repeated measures data. Biometrics 46: 673-687. - doi:
CrossRef | Gscholar
Littell RC, Henry PR, Ammerman CB (2006)
Littell RC, Henry PR, Ammerman CB (2006). Statistical analysis of repeated measures data using SAS procedures. Journal of Animal Science 76: 1216-1231. [online] URL:
Online | Gscholar
Montalvo JM, Bueno SW, Torres JG (2001)
Montalvo JM, Bueno SW, Torres JG (2001). Ecuación para el cálculo de volumen del árbol para Pinus occidentalis Sw. en el Plan Sierra, Republica Dominicana. Universidad Autonoma Chapingo, Mexico. Revista Chapingo, Serie ciencias forestales y del ambiente 7 (001): 49-53. [online] URL:
Online | Gscholar
Perez DN, Burkhart HE, Stiff CT (1990)
Perez DN, Burkhart HE, Stiff CT (1990). A variable-form taper function for Pinus oocarpa Schiede in central Honduras. Forest Science 36 (1): 186-191.
SAS Institute Inc (2006)
SAS Institute Inc (2006). SAS System for regression (3th edn). SAS Institute Inc., Cary, NC, USA. pp. 157.
Schabenberger O, Pierce FJ (2002)
Schabenberger O, Pierce FJ (2002). Contemporary statistical models for the plant and soil sciences. CRC Press, Boca Raton, FL, USA, pp. 738.
Tasissa G, Burkhart HE (1998)
Tasissa G, Burkhart HE (1998). Modelling thinning effects on ring specific gravity of loblolly pine (Pinus taeda L.). Forest Science 44 (2): 212-223.
Trincado G, Burkhart HE (2006)
Trincado G, Burkhart HE (2006). A generalized approach for modeling and localizing stem profile curves. Forest Science 52 (6): 670-682.
Van der Schaaf CL, Burkhart HE (2007)
Van der Schaaf CL, Burkhart HE (2007). Comparison of methods to estimate Reineke’s maximum size-density relationship species boundary line slope. Forest Science 53 (3): 435-442.
West PW, Ratkowsky DA, Davis AW (1984)
West PW, Ratkowsky DA, Davis AW (1984). Problems of hypothesis testing of regressions with multiple measurements from individual sampling units. Forest Ecology and Management 7: 207-224. - doi:
CrossRef | Gscholar
Yang Y, Huang S, Trincado G, Meng SX (2009)
Yang Y, Huang S, Trincado G, Meng SX (2009). Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta, Canada. European Journal of Forest Research 128: 415-429. - doi:
CrossRef | Gscholar

This website uses cookies to ensure you get the best experience on our website. More info