A Mixed-Effects Model with Different Strategies for Modeling Volume in Cunninghamia lanceolata Plantations

Evaluation of Different Calibration Approaches for Merchantable Volume Predictions of Norway Spruce Using Nonlinear Mixed Effects Model

Research Highlights: Determination of merchantable wood volume is one of the key preconditions for sustainable forest management. This study explores accuracy of calibrated predictions of merchantable wood volume of Norway spruce (Picea abies (L.) H. Karst.) using stem taper curves (STC) in a form of a mixed model. Background and Objectives: The study is devoted to the determination of merchantable wood volume (over bark) of individual standing stems based on the integration of an STC model calibrated using upper diameter measurements. Various options of upper diameter measurement were tested and their impact on the accuracy of merchantable wood volume prediction was evaluated. Materials and Methods: To model stem taper curves, a Kozak 02 function was applied in a form of a nonlinear, mixed effects model. Accuracies of calibrated merchantable wood volume predictions obtained through remote (optical) upper diameter measurements were compared to accuracies corresponding to contact measurements by a caliper. The performance of two alternative methods used in the Czech National Forest Inventory (NFI) and forestry practice, involving diameter at breast height and total tree height as the only predictors, were also tested. The contact measurements were performed at identical stem positions after felling the respective sample tree. The calibration was done in order to account for factors inherent in particular location, and, optionally, also in a particular sample stem (within the respective location). Input data was sourced as part of a dedicated survey involving the entire territory of the Czech Republic. In total, 716 individual spruce trees were measured, felled and analysed at 169 locations. Results: In general, the best merchantable volume predictions were obtained by integrating the STC fitted (and calibrated) by minimising errors of stem cross-sectional areas instead of diameters. In terms of calibrated predictions, using single-directional, caliper measurement of upper diameter at 7 m (after felling) led to the best accuracy. In this case, the observed mean bias of merchantable volume prediction was only 0.63%, indicating underestimation. The best optical calibration strategy involved upper diameter measurements at two heights (5 and 7 m) simultaneously. Bias of this volume prediction approach was estimated at 2.1%, indicating underestimation. Conclusions: Concerning the prediction of merchantable stem volume of standing Norway spruce trees, STC calibration using two optical upper diameter measurements (at 5 and 7 m) was found to be practically applicable, provided a bias up to 3.7% can be accepted. This method was found to be more accurate than the existing national alternatives using diameter at breast height and the total tree height as the only predictors.

Predicting the multi-domain progression of Parkinson's disease: a Bayesian multivariate generalized linear mixed-effect model

BACKGROUND

It is challenging for current statistical models to predict clinical progression of Parkinson's disease (PD) because of the involvement of multi-domains and longitudinal data.

METHODS

Past univariate longitudinal or multivariate analyses from cross-sectional trials have limited power to predict individual outcomes or a single moment. The multivariate generalized linear mixed-effect model (GLMM) under the Bayesian framework was proposed to study multi-domain longitudinal outcomes obtained at baseline, 18-, and 36-month. The outcomes included motor, non-motor, and postural instability scores from the MDS-UPDRS, and demographic and standardized clinical data were utilized as covariates. The dynamic prediction was performed for both internal and external subjects using the samples from the posterior distributions of the parameter estimates and random effects, and also the predictive accuracy was evaluated based on the root of mean square error (RMSE), absolute bias (AB) and the area under the receiver operating characteristic (ROC) curve.

RESULTS

First, our prediction model identified clinical data that were differentially associated with motor, non-motor, and postural stability scores. Second, the predictive accuracy of our model for the training data was assessed, and improved prediction was gained in particularly for non-motor (RMSE and AB: 2.89 and 2.20) compared to univariate analysis (RMSE and AB: 3.04 and 2.35). Third, the individual-level predictions of longitudinal trajectories for the testing data were performed, with ~80% observed values falling within the 95% credible intervals.

CONCLUSIONS

Multivariate general mixed models hold promise to predict clinical progression of individual outcomes in PD.

TRIAL REGISTRATION

The data was obtained from Dr. Xuemei Huang's NIH grant R01 NS060722 , part of NINDS PD Biomarker Program (PDBP). All data was entered within 24 h of collection to the Data Management Repository (DMR), which is publically available ( https://pdbp.ninds.nih.gov/data-management ).

Development and evaluation of height diameter at breast models for native Chinese Metasequoia

Accurate tree height and diameter at breast height (dbh) are important input variables for growth and yield models. A total of 5503 Chinese Metasequoia trees were used in this study. We studied 53 fitted models, of which 7 were linear models and 46 were non-linear models. These models were divided into two groups of single models and multivariate models according to the number of independent variables. The results show that the allometry equation of tree height which has diameter at breast height as independent variable can better reflect the change of tree height; in addition the prediction accuracy of the multivariate composite models is higher than that of the single variable models. Although tree age is not the most important variable in the study of the relationship between tree height and dbh, the consideration of tree age when choosing models and parameters in model selection can make the prediction of tree height more accurate. The amount of data is also an important parameter what can improve the reliability of models. Other variables such as tree height, main dbh and altitude, etc can also affect models. In this study, the method of developing the recommended models for predicting the tree height of native Metasequoias aged 50–485 years is statistically reliable and can be used for reference in predicting the growth and production of mature native Metasequoia.

Models for Predicting the Biomass of Cunninghamialanceolata Trees and Stands in Southeastern China

Using existing equations to estimate the biomass of a single tree or a forest stand still involves large uncertainties. In this study, we developed individual-tree biomass models for Chinese Fir (Cunninghamia lanceolata.) stands in Fujian Province, southeast China, by using 74 previously established models that have been most commonly used to estimate tree biomass. We selected the best fit models and modified them. The results showed that the published model ln(B(Biomass)) = a + b * ln(D) + c * (ln(H))2 + d * (ln(H))3 + e * ln(WD) had the best fit for estimating the tree biomass of Chinese Fir stands. Furthermore, we observed that variables D(diameter at breast height), H (height), and WD(wood density)were significantly correlated with the total tree biomass estimation model. As a result, a natural logarithm structure gave the best estimates for the tree biomass structure. Finally, when a multi-step improvement on tree biomass model was performed, the tree biomass model with Tree volume(TV), WD and biomass wood density conversion factor (BECF),achieved the highest simulation accuracy, expressed as ln(TB) = -0.0703 + 0.9780 * ln(TV) + 0.0213 * ln(WD) + 1.0166 * ln(BECF). Therefore, when TV, WD and BECF were combined with tree biomass volume coefficient bi for Chinese Fir, the stand biomass (SB)model included both volume(SV) and coefficient bi variables of the stand as follows: bi = Exp(-0.0703+0.9780*ln(TV)+0.0213 * ln(WD)+1.0166*ln(BECF)). The stand biomass model is SB = SV/TV * bi.