iForest - Biogeosciences and Forestry


Modeling stand mortality using Poisson mixture models with mixed-effects

Xiong-Qing Zhang (1), Yuan-Cai Lei (2)   , Xian-Zhao Liu (2)

iForest - Biogeosciences and Forestry, Volume 8, Issue 3, Pages 333-338 (2015)
doi: https://doi.org/10.3832/ifor1022-008
Published: Sep 05, 2014 - Copyright © 2015 SISEF

Research Articles

Stand mortality models play an important role in simulating stand dynamic processes. Periodic stand mortality data from permanent plots tend to be dispersed, and frequently contain an excess of zero counts. Such data have commonly been analyzed using the Poisson distribution and Poisson mixture models, such as the zero-inflated Poisson model (ZIP), and the Hurdle Poisson model (HP). Based on mortality data obtained from sixty Chinese pine (Pinus tabulaeformis) permanent plots near Beijing, we added the random-effects to the Poisson mixture models. Results showed that the random-effects in the ZIP model was not convergent, and HP mixed-effects model performed better in modeling stand mortality than the Poisson fixed-effects model, the Poisson mixed-effects model, the ZIP fixed-effects model and the HP fixed-effects model. Moreover, the HP model accounts for two sources of dispersion, the first accounting for extra zeros and the second accounting to some extent for the dispersion due by individual heterogeneity in the positive set. We also found that stand mortality was negatively related to stand arithmetic mean diameter and positively related to dominant height.


Hurdle Model, Mixed Model, Poisson Model, Stand Mortality, Zero Inflated Model

Authors’ address

Xiong-Qing Zhang
Key Laboratory of Tree Breeding and Cultivation, State Forestry Administration, Research Institute of Forestry, Chinese Academy of Forestry, Beijing 100091 (China)
Yuan-Cai Lei
Xian-Zhao Liu
Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091 (China)

Corresponding author

Yuan-Cai Lei


Zhang X-Q, Lei Y-C, Liu X-Z (2015). Modeling stand mortality using Poisson mixture models with mixed-effects. iForest 8: 333-338. - doi: 10.3832/ifor1022-008

Academic Editor

Renzo Motta

Paper history

Received: Apr 26, 2013
Accepted: Jul 13, 2014

First online: Sep 05, 2014
Publication Date: Jun 01, 2015
Publication Time: 1.80 months

Breakdown by View Type

(Waiting for server response...)

Article Usage

Total Article Views: 23351
(from publication date up to now)

Breakdown by View Type
HTML Page Views: 17824
Abstract Page Views: 947
PDF Downloads: 3394
Citation/Reference Downloads: 20
XML Downloads: 1166

Web Metrics
Days since publication: 3553
Overall contacts: 23351
Avg. contacts per week: 46.01

Article Citations

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

Total number of cites (since 2015): 5
Average cites per year: 0.83


Publication Metrics

by Dimensions ©

Articles citing this article

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

Affleck DLR (2006)
Poisson mixture models for regression analysis of stand-level mortality. Canadian Journal of Forest Research 36: 2994-3006.
CrossRef | Gscholar
Álvarez-González JG, Dorado FG, Gonzalez ADR, López-Sánchez CA, Gadow, KV (2004)
A two-step mortality model for even-aged stands of Pinus radiata D.Don in Galicia (Northwestern Spain). Annals of Forest Science 61: 439-448.
CrossRef | Gscholar
Barry SC, Welsh AH (2002)
Generalized additive modeling and zero inflated count data. Ecological Modelling 157: 179-188.
CrossRef | Gscholar
Calama R, Montero G (2005)
Multilevel linear mixed model for tree diameter increment in Stone pine (Pinus pinea): a calibrating approach. Silva Fennica 39: 37-54.
Online | Gscholar
Cameron AC, Trivedi PK (1998)
Regression analysis of count data. Cambridge University Press, Cambridge, UK, pp. 123-137.
Crepon B, Duguet E (1997)
Research and development, competition and innovation - pseudo-maximum likelihood and simulated maximum likelihood methods applied to count data models with heterogeneity. Journal of Econometrics 79: 355-378.
CrossRef | Gscholar
Diéguez-Aranda U, Castedo-Dorado F, Álvarez-González JG, Rodríguez-Soalleiro R (2005)
Modelling mortality of Scots pine (Pinus sylvestris L.) plantations in the northwest of Spain. European Journal of Forest Research 124(2): 143-153.
CrossRef | Gscholar
Eid T, Øyen BH (2003)
Models for prediction of mortality in even-aged forest. Scandinavian Journal of Forest Research 18: 64-77.
CrossRef | Gscholar
Fang Z, Bailey RL (2001)
Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments. Forest Science 47: 287-300.
Online | Gscholar
Fortin M, DeBlois J (2007)
Modeling tree recruitment with zero-inflated models: the example of hardwood stands in Southern Quebec, Canada. Forest Science 53: 529 -539.
Online | Gscholar
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: 507-522.
CrossRef | Gscholar
Gurmu S (1997)
Semi-parametric estimation of hurdle regression models with an application to Medicaid utilization. Journal of Applied Econometrics 12: 225-242.
CrossRef | Gscholar
Hall DB (2000)
Zero-inflated Poisson and binomial regression with random effects: a case study. Biometrics 56: 1030-1039.
CrossRef | Gscholar
Juknys R, Vencloviene J, Jurkonist N, Bartkevicius E, Sepetiene J (2006)
Relation between individual tree mortality and tree characteristics in a polluted and non-polluted environment. Environment Monitoring and Assessment 121: 519-542.
CrossRef | Gscholar
Karazsia BT, van Dulmen MH (2008)
Regression models for count data: illustrations using longitudinal predictors of childhood injury. Journal of Pediatric Psychology 33: 1076-1084.
CrossRef | Gscholar
Keane RE, Austin M, Field C, Huth A, Lexer MJ, Peters D, Solomon A, Wyckoff P (2001)
Tree mortality in gap models: application to climate change. Climatic Change 51: 509-540.
CrossRef | Gscholar
Kiernan DH, Bevilacqua E, Nyland RD (2008)
Individual-tree diameter growth model for sugar maple trees in uneven-aged northern hardwood stands under selection system. Forest Ecology and Management 256: 1579-1586.
CrossRef | Gscholar
Lambert D (1992)
Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics 34: 1-14.
CrossRef | Gscholar
Li R, Weiskittel AR, Kershaw JAJ (2011)
Modeling annualized occurrence, frequency, and composition of ingrowth using mixed-effects zero-inflated models and permanent plots in the Acadian forest region of North America. Canadian Journal of Forest Research 41: 2077-2089.
CrossRef | Gscholar
Littell RC, Milliken GA, Stroup WW, Wolfinger RD (1996)
SAS system for Mixed Models. SAS Institute Inc., Cary, NC, USA, pp. 31-63.
Liu W, Cela J (2008)
Count data models in SAS. In: In Proceedings of the “SAS Global Forum 2008 Conference”. San Antonio (TX, USA) 16-19 March 2008. SAS Institute, Cary, NC, USA, pp. 1-12.
Min Y, Agresti A (2005)
Random-effects models for repeated measures of zero-inflated count data. Statistical Modellling 5: 1-19.
CrossRef | Gscholar
Monserud RA, Sterba H (1999)
Modeling individual tree mortality for Austrian forest species. Forest Ecology and Management 113: 109-123.
CrossRef | Gscholar
Mullahy J (1986)
Specification and testing of some modified count data models. Journal of Econometrics 33: 341-365.
CrossRef | Gscholar
Qin JH, Cao QV (2006)
Using disaggregation to link individual-tree and whole-stand growth models. Canadian Journal of Forest Research 36 (4): 953-960.
CrossRef | Gscholar
Rodrigues-Motta M, Gianola D, Heringstad B (2010)
A mixed effects model for overdispersed zero inflated poisson data with an application in animal breeding. Journal of Data Science 8: 379-396.
Online | Gscholar
Shonkwiler J, Shaw W (1996)
Hurdle count-data models in recreation demand analysis. Journal of Agricultural and Resource Economics 21: 210-219.
Online | Gscholar
Subedi N, Sharma M (2011)
individual-tree diameter growth models for black spruce and jack pine plantations in northern Ontario. Forest Ecology and Management 261: 2140-2148.
CrossRef | Gscholar
Uzoh FCC, Oliver WW (2006)
Individual tree height increment model for managed even-aged stands of ponderosa Pine throughout the western United States using linear mixed effects models. Forest Ecology and Management 221: 147-154.
CrossRef | Gscholar
Vuong QH (1989)
Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57: 307-333.
CrossRef | Gscholar
Woollons RC (1998)
Even-aged stand mortality estimation through a two-step regression process. Forest Ecology and Management 105: 189-195.
CrossRef | Gscholar
Yang Y, Titus SJ, Huang S (2003)
Modeling individual tree mortality for white spruce in Alberta. Ecological Modelling 163(5): 209-222.
CrossRef | Gscholar
Yao X, Titus S, MacDonald SE (2001)
A generalized logistic model of individual tree mortality for aspen, white spruce, and lodgepole pine in Alberta mixedwood forests. Canadian Journal of Forest Research 31: 283-291.
CrossRef | Gscholar
Zhang X, Lei Y, Cao QV (2010)
Compatibility of stand basal area predictions based on forecast combination. Forest Science 56 (6): 552-557.
Online | Gscholar
Zhang X, Lei Y, Cai D, Liu F (2012)
Predicting tree recruitment with negative binomial mixture models. Forest Ecology and Management 270: 209-215.
CrossRef | Gscholar

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