Plot size related measurement error bias in tree growth models

2005 ◽  
Vol 35 (5) ◽  
pp. 1031-1040 ◽  
Author(s):  
Juha Lappi
Keyword(s):  
Measurement Error ◽  
Tree Growth ◽  
Local Density ◽  
Density Measurement ◽  
Border Zone ◽  
Coefficient Of Determination ◽  
Unbiased Estimation ◽  
Plot Size ◽  
Sample Tree ◽  
True Value

Local tree density around a tree affects tree growth because neighboring trees compete for the same resources. In forestry trees are often sampled by measuring all the trees in sample plots. The total number of the trees in a sample plot or in a larger plot that also encompasses a border zone is often used as the density measurement for all trees in the plot. When the plot density is used as the measurement of local density around a sample tree, the measurement error is correlated both with the measured value and with the true value. Thus none of the standard measurement error assumptions hold. The bias in the estimated density effect is related to the plot size. Assuming random tree locations and a simple linear model including both overall stand density and local density as predictor variables, the bias is analyzed analytically using weighted distributions. The plot size producing the highest coefficient of determination is rather close to the size of the influence zone, but much larger plot sizes are needed for unbiased estimation. It is safe to measure density from a larger plot than that used for sample tree selection. The analysis may give insight for other cases in multilevel modeling where group variables are used to explain individual responses.

Measurement error-filtered machine learning in digital soil mapping

2021 ◽  
Author(s):  
Stephan van der Westhuizen ◽  
Gerard Heuvelink ◽  
David Hofmeyr
Keyword(s):  
Machine Learning ◽  
Measurement Error ◽  
Soil Property ◽  
Soil Mapping ◽  
Digital Soil Mapping ◽  
Simulation Studies ◽  
True Value ◽  
Linear Relationships ◽  
The Difference ◽  
The Relationship

<p>Digital soil mapping (DSM) may be defined as the use of a statistical model to quantify the relationship between a certain observed soil property at various geographic locations, and a collection of environmental covariates, and then using this relationship to predict the soil property at locations where the property was not measured. It is also important to quantify the uncertainty with regards to prediction of these soil maps. An important source of uncertainty in DSM is measurement error which is considered as the difference between a measured and true value of a soil property.</p><p>The use of machine learning (ML) models such as random forests (RF) has become a popular trend in DSM. This is because ML models tend to be capable of accommodating highly non-linear relationships between the soil property and covariates. However, it is not clear how to incorporate measurement error into ML models. In this presentation we will discuss how to incorporate measurement error into some popular ML models, starting with incorporating weights into the objective function of ML models that implicitly assume a Gaussian error. We will discuss the effect that these modifications have on prediction accuracy, with reference to simulation studies.</p>

Local density measurement of additive manufactured copper parts by instrumented indentation

2018 ◽  
Author(s):  
Loredana Santo ◽  
Fabrizio Quadrini ◽  
Denise Bellisario ◽  
Giovanni Matteo Tedde ◽  
Mariano Zarcone ◽  
...  
Keyword(s):  
Local Density ◽  
Density Measurement ◽  
Instrumented Indentation

scholarly journals Measurement errors in the binary instrumental variable model

Biometrika ◽  
2019 ◽  
Vol 107 (1) ◽  
pp. 238-245
Author(s):  
Zhichao Jiang ◽  
Peng Ding
Keyword(s):  
Measurement Error ◽  
Instrumental Variable ◽  
Measurement Errors ◽  
Causal Effects ◽  
Sensitivity Analyses ◽  
Variable Model ◽  
Differential Measurement ◽  
True Value ◽  
Instrumental Variable Model ◽  
Outcome Biases

Summary Instrumental variable methods can identify causal effects even when the treatment and outcome are confounded. We study the problem of imperfect measurements of the binary instrumental variable, treatment and outcome. We first consider nondifferential measurement errors, that is, the mismeasured variable does not depend on other variables given its true value. We show that the measurement error of the instrumental variable does not bias the estimate, that the measurement error of the treatment biases the estimate away from zero, and that the measurement error of the outcome biases the estimate toward zero. Moreover, we derive sharp bounds on the causal effects without additional assumptions. These bounds are informative because they exclude zero. We then consider differential measurement errors, and focus on sensitivity analyses in those settings.

Spatial patterns in the understorey shrub genus Psychotria in central Amazonia: effects of distance and topography

2005 ◽  
Vol 21 (4) ◽  
pp. 363-374 ◽  
Author(s):  
V. F. Kinupp ◽  
William E. Magnusson
Keyword(s):  
Species Composition ◽  
Minimum Distance ◽  
Local Density ◽  
Ecological Factors ◽  
Analysis Of Covariance ◽  
Habitat Specialization ◽  
Forest Reserve ◽  
Plot Size ◽  
Central Amazonia ◽  
Species Abundances

We evaluated the effects of topography on the distribution of understorey herbs, shrubs and small trees of the pantropical genus Psychotria (Rubiaceae) in a 10000-ha rain-forest reserve in central Amazonia. As plots were long and thin, and followed altitudinal isoclines, we were able to avoid the trade off between plot size and precision of measurement of topographical variables. The minimum distance between plots (1 km) was sufficient to avoid spatial autocorrelation in topographical variables. However, indices of plot similarity based on species composition were spatially autocorrelated to distances of at least 4 km. Although Multivariate Analysis of Covariance (MANCOVA) indicated significant effects of altitude, slope, and watershed on species composition within plots, topographical variables were generally poor surrogates for species distributions. Differences between eastern and western watersheds within the reserve were not due to distance effects, and most species occurred in both watersheds, indicating that differences in species assemblages between watersheds are determined by ecological factors. Habitat specialization and local density were not clearly associated with rarity. At scales of 1–10 km, both distance and habitat affect the distribution of understorey shrubs of the genus Psychotria, but much of the variation in species abundances remains unexplained.

Predictive Distributions in the Presence of Measurement Errors

1996 ◽  
Vol 10 (4) ◽  
pp. 601-611 ◽  
Author(s):  
Irwin Guttman ◽  
Ulrich Menzefricke
Keyword(s):  
Measurement Error ◽  
Linear Regression ◽  
Gibbs Sampler ◽  
Linear Regression Model ◽  
Measurement Errors ◽  
Predictive Distribution ◽  
Multivariate Normal ◽  
Prior Distributions ◽  
True Value ◽  
Regression Parameters

We consider a hierarchical linear regression model where the regression parameters for the units have a multivariate normal distribution whose parameters are unknown. Several replications are available for each unit. The design matrices for the units need not be the same. A complicating feature of the model is that each observation is subject to measurement error. The objective of the paper is to derive the predictive distribution of the “true” value of the response at a given design point. A Bayesian treatment is given to the problem. In addition to standard prior distributions, other prior distributions are considered. The calculations are done with the Gibbs sampler. An example is discussed in detail.

scholarly journals Comparison of density cutters for snow profile observations

2009 ◽  
Vol 55 (189) ◽  
pp. 163-169 ◽  
Author(s):  
Steven M. Conger ◽  
David M. McClung
Keyword(s):  
Stainless Steel ◽  
Measurement Errors ◽  
Sampling Error ◽  
Block Design ◽  
Density Measurement ◽  
Stainless Steel Tube ◽  
Snow Density ◽  
True Value ◽  
Under Sampling ◽  
Accepted Practice

AbstractAn investigation was made to estimate the variance, measurement errors and sampling error in currently accepted practices for manual snow density measurement carried out as part of snow profile observations using the available variety of density cutters. A field experiment in dry snow conditions was conducted using a randomized block design to account for layer spatial variability. Cutter types included a 500 cm3 aluminium tube, 200 and 100 cm3 stainless-steel box types, 200 cm3 stainless-steel wedge types and a 100 cm3 stainless-steel tube. Without accounting for variation due to weighing devices, the range of values for ‘accepted practice’ determined in this study included variation within individual cutters of 0.8–6.2%, variation between cutters of 3–12%, variation between cutter means and layer means of 2–7%, and under-sampling errors of 0–2%. The results of a statistical analysis suggest that snow density measurements taken using various density cutters are significantly different from each other. Without adjustment for under-sampling, and given that the mean of all measurements is the accepted true value of the layer density, variation exclusively between cutter types provides ‘accepted practice’ measurements that are within 11% of the true density.

Reliability of Pharmacodynamic Analysis by Logistic Regression

2003 ◽  
Vol 99 (6) ◽  
pp. 1255-1262 ◽  
Author(s):  
Wei Lu ◽  
James G. Ramsay ◽  
James M. Bailey
Keyword(s):  
Logistic Regression ◽  
Coefficient Of Variation ◽  
Binary Data ◽  
Sparse Data ◽  
Unbiased Estimation ◽  
Data Sets ◽  
Data Set ◽  
True Value ◽  
Data Points ◽  
Data Point

Background Many pharmacologic studies record data as binary, yes-or-no, variables with analysis using logistic regression. In a previous study, it was shown that estimates of C50, the drug concentration associated with a 50% probability of drug effect, were unbiased, whereas estimates of gamma, the term describing the steepness of the concentration-effect relationship, were biased when sparse data were naively pooled for analysis. In this study, it was determined whether mixed-effects analysis improved the accuracy of parameter estimation. Methods Pharmacodynamic studies with binary, yes-or-no, responses were simulated and analyzed with NONMEM. The bias and coefficient of variation of C50 and gamma estimates were determined as a function of numbers of patients in the simulated study, the number of simulated data points per patient, and the "true" value of gamma. In addition, 100 sparse binary human data sets were generated from an evaluation of midazolam for postoperative sedation of adult patients undergoing cardiac surgery by random selection of a single data point (sedation score vs. midazolam plasma concentration) from each of the 30 patients in the study. C50 and gamma were estimated for each of these data sets by using NONMEM and were compared with the estimates from the complete data set of 656 observations. Results Estimates of C50 were unbiased, even for sparse data (one data point per patient) with coefficients of variation of 30-50%. Estimates of gamma were highly biased for sparse data for all values of gamma greater than 1, and the value of gamma was overestimated. Unbiased estimation of gamma required 10 data points per patient. The coefficient of variation of gamma estimates was greater than that of the C50 estimates. Clinical data for sedation with midazolam confirmed the simulation results, showing an overestimate of gamma with sparse data. Conclusion Although accurate estimations of C50 from sparse binary data are possible, estimates of gamma are biased. Data with 10 or more observations per patient is necessary for accurate estimations of gamma.

scholarly journals Estimation of Blast Severity on Rye and Triticale Spikes by Digital Image Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
João Leodato Nunes Maciel ◽  
Alfredo do Nascimento Junior ◽  
Cristina Boaretto
Keyword(s):  
Image Analysis ◽  
Image Segmentation ◽  
Digital Image Analysis ◽  
Linear Regression Analysis ◽  
Reference Method ◽  
Coefficient Of Determination ◽  
Breeding Programs ◽  
True Value ◽  
Mouse Cursor ◽  
Selection Of

In Brazil, more efficient methods are a necessity for evaluating blast severity on spikes in the breeding programs of rye, triticale, wheat, and barley. The objective of this work was to determine the feasibility of assessing blast severity based on the analysis of digital images of symptomatic rye and triticale spikes. Triticale and rye genotypes were grown to anthesis in pots and were then inoculated with a mixture ofMagnaporthe oryzaeisolates. Blast severity on the spikes was evaluated visually and after that the spikes were detached and photographed. Blast severity was determined using the program ImageJ to analyze the obtained images. Two methods of image analysis were used: selection of symptomatic areas using a mouse cursor (SCU) and selection of symptomatic areas using image segmentation (SIS). The SCU method was considered the standard reference method for determining the true value of blast severity on spikes. An analysis of variance did not determine any difference among the evaluation methods. The coefficient of determination (R2) obtained from a linear regression analysis between the variables SIS and SCU was 0.615. The obtained data indicate that the evaluation of blast severity on spikes based on image segmentation is feasible and reliable.

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