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

Crown class, site class, and breast-height age were incorporated into Kozak's variable-exponent taper equation (A. Kozak. 1988. Can. J. For. Res. 18: 1363–1368) for three species: Douglas-fir (Pseudotsugamenziesii (Mirb.) Franco), western red cedar (Thujaplicata Donn), and aspen (Populustremuloides Michx.). For lodgepole pine (Pinuscontorta Dougl.), crown ratio, breast-height age, and quadratic mean diameter were incorporated into Kozak's taper equation. The effects of adding these variables to the exponent part of the taper equation on the prediction abilities of the taper model were assessed for prediction of diameter inside bark along the stem, total tree volume, and tree merchantable height. It was found that apart from the use of crown ratio for lodgepole pine, the additional variables resulted in only marginal improvements to the published version of Kozak's taper function. Therefore, the cost of measuring these additional variables is not justifiable.

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The utility of mixed-effects covariate analysis in rapid selection of doses in pediatric subjects: A case study with fexofenadine hydrochloride

Biopharmaceutics & Drug Disposition ◽

10.1002/bdd.425 ◽

2004 ◽

Vol 25 (9) ◽

pp. 373-387 ◽

Cited By ~ 19

Author(s):

Rajesh Krishna ◽

Sriram Krishnaswami ◽

Barbara Kittner ◽

Abdul J. Sankoh ◽

Bradford K. Jensen

Keyword(s):

Mixed Effects ◽

Covariate Analysis ◽

Selection Of

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Stem volume models with random coefficients for Pinus kesiya in Tanzania, Zambia, and Zimbabwe

Canadian Journal of Forest Research ◽

10.1139/x01-019 ◽

2001 ◽

Vol 31 (5) ◽

pp. 879-888 ◽

Cited By ~ 16

Author(s):

Kalle Eerikäinen

Keyword(s):

Variable Exponent ◽

Generalized Least Squares ◽

General Assumption ◽

Random Coefficients ◽

Stem Volume ◽

Random Parameters ◽

Pinus Kesiya ◽

Taper Equation ◽

Volume Models ◽

Taper Models

The aim of the study was to estimate stem volume and taper models for Pinus kesiya (Royle ex Gordon). The volume function provides a simple prediction model for the stem volume. Taper models were developed for over- and under-bark diameters. The under-bark taper curve was determined with the variable-exponent taper equation, whereas the over-bark taper curve was derived from the predicted under-bark taper model using the variable-exponent form of the bark-thickness model. Because of the spatial correlation structures of the data, the general assumption of uncorrelated residuals did not hold. In addition, the models were assumed to contain random parameters that vary from stand to stand and from tree to tree. Therefore, the fixed and random parameters of the models were estimated with the generalized least squares technique. The results of the study show that the mixed models for stem volume and taper are more reliable volume and diameter predictors for P. kesiya than earlier taper and volume functions.

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Mixed effects of an introduced ecosystem engineer on the foraging behavior and habitat selection of predators

Ecology ◽

10.1002/ecy.2495 ◽

2018 ◽

Vol 99 (12) ◽

pp. 2751-2762 ◽

Cited By ~ 8

Author(s):

Linsey E. Haram ◽

Kaitlin A. Kinney ◽

Erik E. Sotka ◽

James E. Byers

Keyword(s):

Habitat Selection ◽

Foraging Behavior ◽

Ecosystem Engineer ◽

Mixed Effects ◽

Selection Of

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Double Penalized H-Likelihood for Selection of Fixed and Random Effects in Mixed Effects Models

Statistics in Biosciences ◽

10.1007/s12561-013-9105-x ◽

2013 ◽

Vol 7 (1) ◽

pp. 108-128 ◽

Cited By ~ 2

Author(s):

Peirong Xu ◽

Tao Wang ◽

Hongtu Zhu ◽

Lixing Zhu

Keyword(s):

Random Effects ◽

Mixed Effects ◽

Mixed Effects Models ◽

Fixed And Random Effects ◽

Selection Of

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Perils and pitfalls of mixed-effects regression models in biology

PeerJ ◽

10.7717/peerj.9522 ◽

2020 ◽

Vol 8 ◽

pp. e9522 ◽

Cited By ~ 2

Author(s):

Matthew J. Silk ◽

Xavier A. Harrison ◽

David J. Hodgson

Keyword(s):

Biological Sciences ◽

Regression Models ◽

Mixed Model ◽

Mixed Effects ◽

Biological Research ◽

Functional Relationships ◽

Fixed And Random Effects ◽

Statistical Relationships ◽

Biological Literature ◽

Selection Of

Biological systems, at all scales of organisation from nucleic acids to ecosystems, are inherently complex and variable. Biologists therefore use statistical analyses to detect signal among this systemic noise. Statistical models infer trends, find functional relationships and detect differences that exist among groups or are caused by experimental manipulations. They also use statistical relationships to help predict uncertain futures. All branches of the biological sciences now embrace the possibilities of mixed-effects modelling and its flexible toolkit for partitioning noise and signal. The mixed-effects model is not, however, a panacea for poor experimental design, and should be used with caution when inferring or deducing the importance of both fixed and random effects. Here we describe a selection of the perils and pitfalls that are widespread in the biological literature, but can be avoided by careful reflection, modelling and model-checking. We focus on situations where incautious modelling risks exposure to these pitfalls and the drawing of incorrect conclusions. Our stance is that statements of significance, information content or credibility all have their place in biological research, as long as these statements are cautious and well-informed by checks on the validity of assumptions. Our intention is to reveal potential perils and pitfalls in mixed model estimation so that researchers can use these powerful approaches with greater awareness and confidence. Our examples are ecological, but translate easily to all branches of biology.

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On the analysis of cubic smoothing spline-based stem curve prediction for forest harvesters

Canadian Journal of Forest Research ◽

10.1139/x06-165 ◽

2006 ◽

Vol 36 (11) ◽

pp. 2909-2919 ◽

Cited By ~ 14

Author(s):

Laura Koskela ◽

Tapio Nummi ◽

Simone Wenzel ◽

Veli-Pekka Kivinen

Keyword(s):

Variable Exponent ◽

Mixed Model ◽

Linear Mixed Model ◽

Prediction Method ◽

Smoothing Spline ◽

Model Based ◽

Cutting Pattern ◽

Taper Equation

In the cut-to-length (CTL) harvesting system the felling, delimbing, and bucking processes take place at the harvesting site. The optimal cutting points along the stem can be determined if the whole stem curve is known. In practice, however, it is not economically feasible to measure the whole stem first before crosscutting, and hence the first cutting decisions are usually made when only a short part of the stem is known. Predictions are used to determine the cutting pattern to compensate for the unknown part of the stem. In this paper our interest focuses on stem curve prediction in a harvesting situation and we study a modified version of a cubic smoothing spline-based prediction method devised by Nummi and Mottonen (T. Nummi and J. Mottonen. 2004. J. Appl. Stat. 31: 105–114). The method's performance was assessed in five different final felling stands of spruce and pine, collected by harvesters in southern Finland. The results for the spline approach are very promising and show the superiority of the method over the linear mixed-model-based approach of Liski and Nummi (E. Liski and T. Nummi. 1995. Scand. J. Stat. 22: 255–269) and also over the approach based on the variable-exponent taper equation of Kozak (A. Kozak. 1988. Can. J. For. Res. 18: 1363–1368).

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Effects of upper stem measurements on the predictive ability of a variable-exponent taper equation

Canadian Journal of Forest Research ◽

10.1139/x98-120 ◽

1998 ◽

Vol 28 (7) ◽

pp. 1078-1083 ◽

Cited By ~ 12

Author(s):

Antal Kozak

Keyword(s):

Measurement Errors ◽

Variable Exponent ◽

Predictive Ability ◽

Diameter Measurement ◽

Breast Height ◽

Taper Equation ◽

Taper Equations

Like several other taper equations, the predictive ability of Kozak's (1988. Can. J. For. Res. 18: 1363-1368) variable-exponent taper equations can also be improved by an additional upper stem outside bark diameter measurement. This study indicated that improvements were small and were mainly restricted to increasing the precision of the estimates. Also, it was demonstrated that if additional diameter measurements are justified, they should be taken between 40 and 50% of the height above breast height for greatest improvement. Measurement errors in upper stem diameters and in their heights above breast height affected both the precision and bias of predictions.

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Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

Forests ◽

10.3390/f12020126 ◽

2021 ◽

Vol 12 (2) ◽

pp. 126

Author(s):

Sensen Zhang ◽

Jianjun Sun ◽

Aiguo Duan ◽

Jianguo Zhang

Keyword(s):

Variable Exponent ◽

Southern China ◽

Information Criteria ◽

Chinese Fir ◽

Tree Level ◽

Mixed Effect ◽

Basic Model ◽

Taper Equation ◽

Taper Equations ◽

Taper Models

A variable-exponent taper equation was developed for Chinese fir (Cunninghamia lanceolate (Lamb.) Hook.) trees grown in southern China. Thirty taper equations from different groups of models (single, segmented, or variable-exponent taper equation) were compared to find the excellent basic model with S-plus software. The lowest Akaike information criteria (AIC), Bayesian information criteria (BIC), and -2loglikelihood (-2LL) was chosen to determine the best combination of random parameters. Single taper models were found having the lowest precision, and the variable-exponent taper equations had higher precision than the segmented taper equations. Four variable-exponent taper models that developed by Zeng and Liao, Bi, Kozak, Sharma, and Zhang respectively, were selected as basic model and had no difference in fit statistics between them. Compared with the model without seldom parameter, the nonlinear mixed-effects (NLME) model improves the fitting performance. The plot-level NLME model was found not to remove the residual autocorrelation. The tree-level and two-level NLME model had better simulation accuracy than the plot-level NLME model, and there were no significant differences between the tree-level and two-level NLME model. Variable-exponent taper model developed by Kozak showed the best performance while considering two-level or tree-level NLME model, and produced better predictions for medium stems compared to lower and upper stems.

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