scholarly journals A Generalized Model of Complex Allometry I: Formal Setup, Identification Procedures and Applications to Non-Destructive Estimation of Plant Biomass Units

2019 ◽  
Vol 9 (22) ◽  
pp. 4965 ◽  
Author(s):  
Echavarria-Heras ◽  
Leal-Ramirez ◽  
Villa-Diharce ◽  
Castro-Rodríguez
Keyword(s):  
Linear Models ◽  
Plant Biomass ◽  
Simulated Data ◽  
Identification Problem ◽  
Operating Regime ◽  
Continuous Functions ◽  
Generalized Model ◽  
Mixture Regression ◽  
Scaling Parameters ◽  
Geometrical Space

(1) Background: We previously demonstrated that customary regression protocols for curvature in geometrical space all derive from a generalized model of complex allometry combining scaling parameters expressing as continuous functions of covariate. Results highlighted the relevance of addressing suitable complexity in enhancing the accuracy of allometric surrogates of plant biomass units. Nevertheless, examination was circumscribed to particular characterizations of the generalized model. Here we address the general identification problem. (2) Methods: We first suggest a log-scales protocol composing a mixture of linear models weighted by exponential powers. Alternatively, adopting an operating regime-based modeling slant we offer mixture regression or Takagi–Sugeno–Kang arrangements. This last approach allows polyphasic identification in direct scales. A derived index measures the extent on what complexity in arithmetic space drives curvature in arithmetical space. (3) Results: Fits on real and simulated data produced proxies of outstanding reproducibility strength indistinctly of data scales. (4) Conclusions: Presented analytical constructs are expected to grant efficient allometric projection of plant biomass units and also for the general settings of allometric examination. A traditional perspective deems log-transformation and allometry inseparable. Recent views assert that this leads to biased results. The present examination suggests this controversy can be resolved by addressing adequately the complexity of geometrical space protocols

scholarly journals Examination of the Effects of Curvature in Geometrical Space on Accuracy of Scaling Derived Projections of Plant Biomass Units: Applications to the Assessment of Average Leaf Biomass in Eelgrass Shoots

2019 ◽  
Vol 2019 ◽  
pp. 1-23 ◽  
Author(s):  
Héctor Echavarría-Heras ◽  
Cecilia Leal-Ramírez ◽  
Enrique Villa-Diharce ◽  
Abelardo Montesinos-López
Keyword(s):  
Correction Factor ◽  
Plant Biomass ◽  
Leaf Biomass ◽  
Allometric Model ◽  
Log Transformation ◽  
Scaling Parameters ◽  
Regression Error ◽  
Suitable Form ◽  
Factor Form ◽  
Geometrical Space

Conservation of eelgrass relies on transplants and evaluation of success depends on nondestructive measurements of average leaf biomass in shoots among other variables. Allometric proxies offer a convenient way to assessments. Identifying surrogates via log transformation and linear regression can set biased results. Views conceive this approach to be meaningful, asserting that curvature in geometrical space explains bias. Inappropriateness of correction factor of retransformation bias could also explain inconsistencies. Accounting for nonlinearity of the log transformed response relied on a generalized allometric model. Scaling parameters depend continuously on the descriptor. Joining correction factor is conceived as the partial sum of series expansion of mean retransformed residuals leading to highest reproducibility strength. Fits of particular characterizations of the generalized curvature model conveyed outstanding reproducibility of average eelgrass leaf biomass in shoots. Although nonlinear heteroscedastic regression resulted also to be suitable, only log transformation approaches can unmask a size related differentiation in growth form of the leaf. Generally, whenever structure of regression error is undetermined, choosing a suitable form of retransformation correction factor becomes elusive. Compared to customary nonparametric characterizations of this correction factor, present form proved more efficient. We expect that offered generalized allometric model along with proposed correction factor form provides a suitable analytical arrangement for the general settings of allometric examination.

scholarly journals Risk prediction in multicentre studies when there is confounding by cluster or informative cluster size

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Menelaos Pavlou ◽  
Gareth Ambler ◽  
Rumana Z. Omar
Keyword(s):  
Risk Prediction ◽  
Cluster Size ◽  
Linear Models ◽  
Prediction Models ◽  
Predictive Accuracy ◽  
Clustered Data ◽  
Predictor Variable ◽  
Simulated Data ◽  
Predictive Ability ◽  
Informative Cluster Size

Abstract Background Clustered data arise in research when patients are clustered within larger units. Generalised Estimating Equations (GEE) and Generalised Linear Models (GLMM) can be used to provide marginal and cluster-specific inference and predictions, respectively. Methods Confounding by Cluster (CBC) and Informative cluster size (ICS) are two complications that may arise when modelling clustered data. CBC can arise when the distribution of a predictor variable (termed ‘exposure’), varies between clusters causing confounding of the exposure-outcome relationship. ICS means that the cluster size conditional on covariates is not independent of the outcome. In both situations, standard GEE and GLMM may provide biased or misleading inference, and modifications have been proposed. However, both CBC and ICS are routinely overlooked in the context of risk prediction, and their impact on the predictive ability of the models has been little explored. We study the effect of CBC and ICS on the predictive ability of risk models for binary outcomes when GEE and GLMM are used. We examine whether two simple approaches to handle CBC and ICS, which involve adjusting for the cluster mean of the exposure and the cluster size, respectively, can improve the accuracy of predictions. Results Both CBC and ICS can be viewed as violations of the assumptions in the standard GLMM; the random effects are correlated with exposure for CBC and cluster size for ICS. Based on these principles, we simulated data subject to CBC/ICS. The simulation studies suggested that the predictive ability of models derived from using standard GLMM and GEE ignoring CBC/ICS was affected. Marginal predictions were found to be mis-calibrated. Adjusting for the cluster-mean of the exposure or the cluster size improved calibration, discrimination and the overall predictive accuracy of marginal predictions, by explaining part of the between cluster variability. The presence of CBC/ICS did not affect the accuracy of conditional predictions. We illustrate these concepts using real data from a multicentre study with potential CBC. Conclusion Ignoring CBC and ICS when developing prediction models for clustered data can affect the accuracy of marginal predictions. Adjusting for the cluster mean of the exposure or the cluster size can improve the predictive accuracy of marginal predictions.

Empirical Bayes Microarray ANOVA and Grouping Cell Lines by Equal Expression Levels

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Ingrid Lönnstedt ◽  
Rebecca Rimini ◽  
Peter Nilsson
Keyword(s):  
Cell Lines ◽  
Empirical Bayes ◽  
Dna Microarrays ◽  
Linear Models ◽  
Simulated Data ◽  
Probabilistic Methods ◽  
Expression Levels ◽  
Statistical Framework ◽  
Treatment Conditions ◽  
One Way Anova

In the exploding field of gene expression techniques such as DNA microarrays, there are still few general probabilistic methods for analysis of variance. Linear models and ANOVA are heavily used tools in many other disciplines of scientific research. The usual F-statistic is unsatisfactory for microarray data, which explore many thousand genes in parallel, with few replicates.We present three potential one-way ANOVA statistics in a parametric statistical framework. The aim is to separate genes that are differently regulated across several treatment conditions from those with equal regulation. The statistics have different features and are evaluated using both real and simulated data. Our statistic B1 generally shows the best performance, and is extended for use in an algorithm that groups cell lines by equal expression levels for each gene. An extension is also outlined for more general ANOVA tests including several factors.The methods presented are implemented in the freely available statistical language R. They are available at http://www.math.uu.se/staff/pages/?uname=ingrid.

A Growth Model for Multilevel Ordinal Data

2005 ◽  
Vol 30 (4) ◽  
pp. 369-396 ◽  
Author(s):  
Eisuke Segawa
Keyword(s):  
Latent Variable ◽  
Ordinal Data ◽  
Linear Models ◽  
Growth Models ◽  
Simulated Data ◽  
Real Data ◽  
Analytic Structure ◽  
Data Sets ◽  
Data Set ◽  
Time Points

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can analyze not only data with item- and time-level missing observations, but also data with time points freely specified over subjects. Furthermore, features useful for longitudinal analyses, “autoregressive error degree one” structure for the trait residuals and estimated time-scores, were included. The approach is Bayesian with Markov Chain and Monte Carlo, and the model is implemented in WinBUGS. They are illustrated with two simulated data sets and one real data set with planned missing items within a scale.

scholarly journals Structural Health Monitoring under Nonlinear Environmental or Operational Influences

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jyrki Kullaa
Keyword(s):  
Structural Health Monitoring ◽  
Health Monitoring ◽  
Linear Models ◽  
Nonlinear Models ◽  
Novelty Detection ◽  
Minimum Mean Square Error ◽  
Simulated Data ◽  
Principal Component ◽  
Gaussian Mixture ◽  
Structural Health

Vibration-based structural health monitoring is based on detecting changes in the dynamic characteristics of the structure. It is well known that environmental or operational variations can also have an influence on the vibration properties. If these effects are not taken into account, they can result in false indications of damage. If the environmental or operational variations cause nonlinear effects, they can be compensated using a Gaussian mixture model (GMM) without the measurement of the underlying variables. The number of Gaussian components can also be estimated. For the local linear components, minimum mean square error (MMSE) estimation is applied to eliminate the environmental or operational influences. Damage is detected from the residuals after applying principal component analysis (PCA). Control charts are used for novelty detection. The proposed approach is validated using simulated data and the identified lowest natural frequencies of the Z24 Bridge under temperature variation. Nonlinear models are most effective if the data dimensionality is low. On the other hand, linear models often outperform nonlinear models for high-dimensional data.

scholarly journals An Exploration of Link Functions Used in Ordinal Regression

2020 ◽  
Vol 18 (1) ◽  
pp. 2-15
Author(s):  
Thomas J. Smith ◽  
David A. Walker ◽  
Cornelius M. McKenna
Keyword(s):  
Survey Data ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Simulated Data ◽  
Ordinal Regression ◽  
Research Center ◽  
Link Function ◽  
25Th Anniversary ◽  
Link Functions ◽  
The Web

The purpose of this study is to examine issues involved with choice of a link function in generalized linear models with ordinal outcomes, including distributional appropriateness, link specificity, and palindromic invariance are discussed and an exemplar analysis provided using the Pew Research Center 25th anniversary of the Web Omnibus Survey data. Simulated data are used to compare the relative palindromic invariance of four distinct indices of determination/discrimination, including a newly proposed index by Smith et al. (2017).

scholarly journals Dynamics of animal joint space use: a novel application of a time series approach

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Justin T. French ◽  
Hsiao-Hsuan Wang ◽  
William E. Grant ◽  
John M. Tomeček
Keyword(s):  
Time Series ◽  
Field Data ◽  
Linear Models ◽  
Simulated Data ◽  
Space Use ◽  
Joint Space ◽  
Spatial Interactions ◽  
Utilization Distribution ◽  
Time Series Approach ◽  
Utilization Distributions

Abstract Background Animal use is a dynamic phenomenon, emerging from the movements of animals responding to a changing environment. Interactions between animals are reflected in patterns of joint space use, which are also dynamic. High frequency sampling associated with GPS telemetry provides detailed data that capture space use through time. However, common analyses treat joint space use as static over relatively long periods, masking potentially important changes. Furthermore, linking temporal variation in interactions to covariates remains cumbersome. We propose a novel method for analyzing the dynamics of joint space use that permits straightforward incorporation of covariates. This method builds upon tools commonly used by researchers, including kernel density estimators, utilization distribution intersection metrics, and extensions of linear models. Methods We treat the intersection of the utilization distributions of two individuals as a time series. The series is linked to covariates using copula-based marginal beta regression, an alternative to generalized linear models. This approach accommodates temporal autocorrelation and the bounded nature of the response variable. Parameters are easily estimated with maximum likelihood and trend and error structures can be modeled separately. We demonstrate the approach by analyzing simulated data from two hypothetical individuals with known utilization distributions, as well as field data from two coyotes (Canis latrans) responding to appearance of a carrion resource in southern Texas. Results Our analysis of simulated data indicated reasonably precise estimates of joint space use can be achieved with commonly used GPS sampling rates (s.e.=0.029 at 150 locations per interval). Our analysis of field data identified an increase in spatial interactions between the coyotes that persisted for the duration of the study, beyond the expected duration of the carrion resource. Our analysis also identified a period of increased spatial interactions before appearance of the resource, which would not have been identified by previous methods. Conclusions We present a new approach to the analysis of joint space use through time, building upon tools commonly used by ecologists, that permits a new level of detail in the analysis of animal interactions. The results are easily interpretable and account for the nuances of bounded serial data in an elegant way.

Identification of SSR markers associated with saccharification yield using pool-based genome-wide association mapping in sorghum

Genome ◽  
2011 ◽  
Vol 54 (11) ◽  
pp. 883-889 ◽  
Author(s):  
Yi-Hong Wang ◽  
Durga D. Poudel ◽  
Karl H. Hasenstein
Keyword(s):  
Cell Wall ◽  
Association Mapping ◽  
Ssr Markers ◽  
Plant Cell Wall ◽  
Linear Models ◽  
Plant Biomass ◽  
Genome Wide Association ◽  
Whole Genome Sequence ◽  
Genome Wide ◽  
Saccharification Yield

Saccharification describes the conversion of plant biomass by cellulase into glucose. Because plants have never been selected for high saccharification yield, cellulosic ethanol production faces a significant bottleneck. To improve saccharification yield, it is critical to identify the genes that affect this process. In this study, we used pool-based genome-wide association mapping to identify simple sequence repeat (SSR) markers associated with saccharification yield. Screening of 703 SSR markers against the low and high saccharification pools identified two markers on the sorghum chromosomes 2 (23-1062) and 4 (74-508c) associated with saccharification yield. The association was significant at 1% using either general or mixed linear models. Localization of these markers based on the whole genome sequence indicates that 23-1062 is 223 kb from a β–glucanase (Bg) gene and 74-508c is 81 kb from a steroid-binding protein (Sbp) gene. Bg is critical for cell wall assembly and degradation, but Sbp can suppress the expression of Bg as demonstrated in Arabidopsis (Yang et al. 2005). These markers are found physically close to genes encoding plant cell wall synthesis enzymes such as xyloglucan fucosyltransferase (149 kb from 74-508c) and UDP-d-glucose 4-epimerase (46 kb from 23-1062). Genetic transformation of selected candidate genes is in progress to examine their effect on saccharification yield in plants.

A nonlinear viscoelastic model of lung tissue mechanics

1991 ◽  
Vol 71 (3) ◽  
pp. 826-833 ◽  
Author(s):  
B. Suki ◽  
J. H. Bates
Keyword(s):  
Lung Tissue ◽  
Linear Models ◽  
Viscoelastic Model ◽  
Low Frequency ◽  
Simulated Data ◽  
Tissue Mechanics ◽  
Model Parameters ◽  
Volume Dependence ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Model

There have been a number of attempts recently to use linear models to describe the low-frequency (0–2 Hz) dependence of lung tissue resistance (Rti) and elastance (Eti). Only a few attempts, however, have been made to account for the volume dependence of these quantities, all of which require the tissues to be plastoelastic. In this paper we specifically avoid invoking plastoelasticity and develop a nonlinear viscoelastic model that is also capable of accounting for the nonlinear and frequency-dependent features of lung tissue mechanics. The model parameters were identified by fitting the model to data obtained in a previous study from dogs during sinusoidal ventilation. The model was then used to simulate pressure and flow data by use of various types of ventilation patterns similar to those that have been employed experimentally. Rti and Eti were estimated from the simulated data by use of four different estimation techniques commonly applied in respiratory mechanics studies. We found that the estimated volume dependence of Rti and Eti is sensitive to both the ventilation pattern and the estimation technique, being in error by as much as 217 and 22%, respectively.

Measuring growth patterns in the field: effects of sampling regime and methods on standardized estimates

2011 ◽  
Vol 89 (6) ◽  
pp. 529-537 ◽  
Author(s):  
J.G.A. Martin ◽  
F. Pelletier
Keyword(s):  
Mixed Models ◽  
Repeated Measures ◽  
Mixed Model ◽  
Linear Models ◽  
Simulated Data ◽  
Growth Patterns ◽  
Repeated Measurements ◽  
Least Squares Regression ◽  
Sampling Regime ◽  
Parturition Date

Although mixed effects models are widely used in ecology and evolution, their application to standardized traits that change within season or across ontogeny remains limited. Mixed models offer a robust way to standardize individual quantitative traits to a common condition such as body mass at a certain point in time (within a year or across ontogeny), or parturition date for a given climatic condition. Currently, however, most researchers use simple linear models to accomplish this task. We use both empirical and simulated data to underline the application of mixed models for standardizing trait values to a common environment for each individual. We show that mixed model standardizations provide more accurate estimates of mass parameters than linear models for all sampling regimes and especially for individuals with few repeated measures. Our simulations and analyses on empirical data both confirm that mixed models provide a better way to standardize trait values for individuals with repeated measurements compared with classical least squares regression. Linear regression should therefore be avoided to adjust or standardize individual measurements

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