Simultaneous curve fitting for repeated height–diameter measurements

Omule, Stephen A. Y.; Macdonald, Rhoda

doi:10.1139/x91-199

Cited by 11 publications

(5 citation statements)

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“…Autocorrelation structures were used for I ij matrix to address the within-tree autocorrelations of the errors observed in the data [37], [38]. A method was selected from among three commonly used approaches: first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)], and the compound symmetry structure (CS) [18]. where ρ is the autoregressive parameter, γ is a moving average component, σ 2 is the residual variance, and σ 1 is the residual covariance [37]–[40].…”

Section: Methodsmentioning

confidence: 99%

Nonlinear Mixed-Effects (NLME) Diameter Growth Models for Individual China-Fir (Cunninghamia lanceolata) Trees in Southeast China

Sun

Wang

et al. 2014

PLoS ONE

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An individual-tree diameter growth model was developed for Cunninghamia lanceolata in Fujian province, southeast China. Data were obtained from 72 plantation-grown China-fir trees in 24 single-species plots. Ordinary non-linear least squares regression was used to choose the best base model from among 5 theoretical growth equations; selection criteria were the smallest absolute mean residual and root mean square error and the largest adjusted coefficient of determination. To account for autocorrelation in the repeated-measures data, we developed one-level and nested two-level nonlinear mixed-effects (NLME) models, constructed on the selected base model; the NLME models incorporated random effects of the tree and plot. The best random-effects combinations for the NLME models were identified by Akaike's information criterion, Bayesian information criterion and −2 logarithm likelihood. Heteroscedasticity was reduced with two residual variance functions, a power function and an exponential function. The autocorrelation was addressed with three residual autocorrelation structures: a first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)] and a compound symmetry structure (CS). The one-level (tree) NLME model performed best. Independent validation data were used to test the performance of the models and to demonstrate the advantage of calibrating the NLME models.

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Section: Methodsmentioning

confidence: 99%

Nonlinear Mixed-Effects (NLME) Diameter Growth Models for Individual China-Fir (Cunninghamia lanceolata) Trees in Southeast China

Sun

Wang

et al. 2014

PLoS ONE

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“…A relação hipsométrica mesmo em povoamentos de mesma idade varia com a qualidade do sítio e com a densidade. Em tais circunstâncias, uma única relação hipsométrica ajustada para todo o povoamento englobaria muitas relações diferentes, resultando em alta variabilidade em torno da linha de regressão da altura sobre o diâmetro (PRODAN et al, 1997). Por isso, um procedimento usado em inventários florestais para solucionar esse problema tem sido ajustar equações independentes para cada unidade amostral ou, então, para cada grupo homogêneo de parcelas em termos de idade, sítio e densidade.…”

Section: Introductionunclassified

Dinâmica da relação hipsométrica em função da idade, do sítio e da densidade inicial de povoamentos de bracatinga da Região Metropolitana de Curitiba, PR

et al. 2004

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Esta pesquisa teve como objetivo analisar o comportamento e a dinâmica da curva hipsométrica em função dos fatores sítio, idade e densidade inicial em povoamentos de bracatinga (Mimosa scabrella Benth.), localizados na Região Metropolitana de Curitiba, PR. Os dados provieram da medição de diâmetros à altura do peito (DAP) e alturas totais em 20 parcelas permanentes remedidas quatro vezes da idade de 4 a 7,5 anos, em sítios de qualidades I, II e III, com densidades iniciais controladas para 2.000, 4.000 e 8.000 árvores/ha, e as testemunhas, que em média apresentaram 25.000 árvores/ha no momento em que o experimento foi instalado. Inicialmente, um intenso trabalho de modelagem foi realizado (BARTOSZECK, 2000), ocasião em que foi selecionado o modelo de Curtis para se proceder às análises propostas no objetivo. A técnica de análise de co-variância foi, então, utilizada nas análises dos efeitos da idade, do sítio e da densidade sobre a curva de altura-diâmetro. Paralelamente foi feita a análise gráfica de todas as combinações possíveis, isto é, as quatro idades, três sítios e quatro densidades, usando-se o modelo de Curtis em cada combinação de fatores. Como resultados conclusivos obtidos através das análises de co-variância, detectaram-se efeitos estatisticamente significativos tanto da idade quanto do sítio sobre a relação hipsométrica. No entanto, o fator densidade não exerceu influência significativa sobre a mesma relação.

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“…Correlation structures were used to address the within-tree spatial correlations observed in the data [ 42 ; 43 ]. A method was selected from among three commonly used approaches: the first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)], and the compound symmetry structure (CS) [ 18 ].…”

Section: Methodsmentioning

confidence: 99%

Linear Mixed-Effects Models to Describe Individual Tree Crown Width for China-Fir in Fujian Province, Southeast China

Sun

Wang

et al. 2015

PLoS ONE

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A multiple linear model was developed for individual tree crown width of Cunninghamia lanceolata (Lamb.) Hook in Fujian province, southeast China. Data were obtained from 55 sample plots of pure China-fir plantation stands. An Ordinary Linear Least Squares (OLS) regression was used to establish the crown width model. To adjust for correlations between observations from the same sample plots, we developed one level linear mixed-effects (LME) models based on the multiple linear model, which take into account the random effects of plots. The best random effects combinations for the LME models were determined by the Akaike’s information criterion, the Bayesian information criterion and the -2logarithm likelihood. Heteroscedasticity was reduced by three residual variance functions: the power function, the exponential function and the constant plus power function. The spatial correlation was modeled by three correlation structures: the first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)], and the compound symmetry structure (CS). Then, the LME model was compared to the multiple linear model using the absolute mean residual (AMR), the root mean square error (RMSE), and the adjusted coefficient of determination (adj-R 2). For individual tree crown width models, the one level LME model showed the best performance. An independent dataset was used to test the performance of the models and to demonstrate the advantage of calibrating LME models.

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Simultaneous curve fitting for repeated height–diameter measurements

Cited by 11 publications

References 0 publications

Nonlinear Mixed-Effects (NLME) Diameter Growth Models for Individual China-Fir (Cunninghamia lanceolata) Trees in Southeast China

Nonlinear Mixed-Effects (NLME) Diameter Growth Models for Individual China-Fir (Cunninghamia lanceolata) Trees in Southeast China

Dinâmica da relação hipsométrica em função da idade, do sítio e da densidade inicial de povoamentos de bracatinga da Região Metropolitana de Curitiba, PR

Linear Mixed-Effects Models to Describe Individual Tree Crown Width for China-Fir in Fujian Province, Southeast China

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