Linear regression with Type I interval- and left-censored response data

Laboratory analyses in a variety of contexts may result in left- and interval-censored measurements. We develop and evaluate a maximum likelihood approach to linear regression analysis in this setting and compare this approach to commonly used simple substitution methods. We explore via simulation the impact on bias and power of censoring fraction and sample size in a range of settings. The maximum likelihood approach represents only a moderate increase in power, but we show that the bias in substitution estimates may be substantial.     

Dose-response modeling for developmental neurotoxicity data

The fact that maternal exposures to some chemicals during pregnancy can adversely affect the structure and function of the nervous system in the offspring is well established. Government agencies have for a long time been concerned with regulation of developmental neurotoxicants and safe perinatal exposures. However, despite this concern, current guidelines provide only broad and nonspecific recommendations and lack clear directions for a model based approach to risk estimation. In this paper we propose a dose-response model for the nonquantal data obtained from developmental neurotoxicological experiments. To account for the critical issue of the correlation among responses from pups in the same litter, the so called intralitter correlation, a hierarchical distributional structure is used to derive the underlying unconditional distribution of responses. The maximum likelihood method is used to estimate model parameters and the covariance matrix of the estimates is derived. An example is used to illustrate the results.     

On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

Predicting the variation in detection function in line transect sampling through random parameter model

A method for calibrating (localizing) detection function models in line transect sampling is proposed. The method is based on a random parameter model which supplies localized predictions of detection function parameters utilizing a few sample data points from the concerned location(s). The method has the clear advantage of being able to provide density estimates based on very few observations from a location which would be impossible through traditional methods. The method is successfully illustrated using census data on sambar (Cervus unicolor) from a set of wildlife sanctuaries in Kerala, India. The need for further research in this direction is indicated.     

Bayesian testing for trend in a power model for clustered binary data

Developmental toxicity studies are widely used to investigate the potential risk of environmental hazards. In dose–response experiments, subjects are randomly allocated to groups receiving various dose levels. Tests for trend are then often applied to assess possible dose effects. Recent techniques for risk assessment in this area are based on fitting dose–response models. The complexity of such studies implies a number of non-trivial challenges for model development and the construction of dose-related trend tests, including the hierarchical structure of the data, litter effects inducing extra variation, the functional form of the dose–response curve, the adverse event at dam or at fetus level, the inference paradigm, etc. The purpose of this paper is to propose a Bayesian trend test based on a non-linear power model for the dose effect and using an appropriate model for clustered binary data. Our work is motivated by the analysis of developmental toxicity studies, in which the offspring of exposed and control rodents are examined for defects. Simulations show the performance of the method over a number of samples generated under typical experimental conditions.     

Comparison between linear and non-linear forms of pseudo-first-order and pseudo-second-order adsorption kinetic models for the removal of methylene blue by activated carbon

The best-fit equations of linear and non-linear forms of the two widely used kinetic models, namely pseudo-first-order and pseudo-second-order equations, were compared in this study. The experimental kinetics of methylene blue adsorption on activated carbon was used for this research. Both the correlation coefficient (R ²) and the normalized standard deviation Δq(%) were employed as error analysis methods to determine the best-fitting equations. The results show that the non-linear forms of pseudo-first-order and pseudo-second-order models were more suitable than the linear forms for fitting the experimental data. The experimental kinetics may have been distorted by linearization of the linear kinetic equations, and thus, the non-linear forms of kinetic equations should be primarily used to obtain the adsorption parameters. In addition, the Δq(%) method for error analysis may be better to determine the best-fitting model in this case.     

Potentials and limitations of using large-scale forest inventory data for evaluating forest succession models

Forest gap models have been applied widely to examine forest development under natural conditions and to investigate the effect of climate change on forest succession. Due to the complexity and parameter requirements of such models a rigorous evaluation is required to build confidence in the simulation results. However, appropriate data for model assessment are scarce at the large spatial and temporal scales of successional dynamics. In this study, we explore a data source for the evaluation of forest gap models that has been used only little in the past, i.e., large-scale National Forest Inventory data. The key objectives of this study were (a) to examine the potentials and limitations of using large-scale forest inventory data for evaluating the performance of forest gap models and (b) to test two particular models as case studies to derive recommendations for their future improvement.     

Bootstrap methods for simultaneous benchmark analysis with quantal response data

A primary objective in quantitative risk assessment is the characterization of risk which is defined to be the likelihood of an adverse effect caused by an environmental toxin or chemcial agent. In modern risk-benchmark analysis, attention centers on the “benchmark dose” at which a fixed benchmark level of risk is achieved, with a lower confidence limits on this dose being of primary interest. In practice, a range of benchmark risks may be under study, so that the individual lower confidence limits on benchmark dose must be corrected for simultaneity in order to maintain a specified overall level of confidence. For the case of quantal data, simultaneous methods have been constructed that appeal to the large sample normality of parameter estimates. The suitability of these methods for use with small sample sizes will be considered. A new bootstrap technique is proposed as an alternative to the large sample methodology. This technique is evaluated via a simulation study and examples from environmental toxicology.

Using data augmentation via the Gibbs Sampler to incorporate missing covariate structure in linear models for ecological assessments

Missing covariate values in linear regression models can be an important problem facing environmental researchers. Existing missing value treatment methods such as Multiple Imputation (MI), the EM algorithm and Data Augmentation (DA) have the assumption that both observed and unobserved data come from the same distribution, most commonly a multivariate normal or a conditionally multivariate normal family. These methods do try to incorporate the missing data mechanism and rely on the assumption of Missing At Random (MAR). We present a DA method which does not rely on the MAR assumption and can model missing data mechanisms and covariate structure. This method utilizes the Gibbs Sampler as a tool for incorporating these structures and mechanisms. We apply this method to an ecological data set that relates fish condition to environmental variables. Notice that the presented DA method detects relationships that are not detected when other missing data methods are employed.

Multistate models for monitoring individual trees in permanent observation plots

This interdisciplinary research on forest ecosystems begins with some characteristics of ecosystems which are the basis for the derivation of statistical models for the development and vitality of trees. Several ecological problems which could be solved by longitudinal studies are mentioned. Statistical methods for the evaluation of the crowns of spruce trees (Picea abies Karst) in three permanent observation plots in Switzerland are described. In particular, the time-dependent proportional odds model and a transitional model are used. Through application of these multistate models the data give information on the dependence of an ordered categorical response variable on covariates characterizing the ecosystem. The response variable is observed through infrared aerial photographs. This monitoring system gives insight into the dynamic behaviour of the forest ecosystem. The need for more eco-systematically motivated statistical research using longitudinal studies is identified.     

高效液相色谱-荧光检测法同时测定畜禽粪便中4种磺胺类药物残留

建立了高效液相色谱-荧光检测法测定畜禽粪便中4种磺胺药物(磺胺甲基嘧啶(SM1)、磺胺氯哒嗪(SCP)、磺胺邻二甲氧嘧啶(SDM’)、磺胺喹噁啉(SQ))的方法.样品用25 mL甲醇提取3次,合并提取液,浓缩干燥,用0.1 mol.L-1的HCL溶解残渣,经荧光胺衍生化后,用反相C18柱为分离柱,以乙腈∶0.5%乙酸=40∶60(V/V)为流动相进行洗脱,20 min内分离4种药物.在0.05—5.00μg.mL-1范围内,4种磺胺类药物的峰面积与质量浓度的线性关系良好(R2≥0.999),SM1、SCP、SDM’、SQ的定量限(LOQ)分别为2.3、6.3、4.3和9.6μg.kg-1;添加水平为50、100、1000μg.kg-1时,SM1、SCP、SDM’、SQ的回收率分别为74.91%—81.82%、78.45%—91.43%和86.10%—92.88%,RSD小于8.82%.     

A comparison of two models with Landsat data for estimating above ground grassland biomass in Inner Mongolia,China

Two models, artificial neural network (ANN) and multiple linear regression (MLR), were developed to estimate typical grassland aboveground dry biomass in Xilingol River Basin, Inner Mongolia, China. The normalized difference vegetation index (NDVI) and topographic variables (elevation, aspect, and slope) were combined with atmospherically corrected reflectance from the Landsat ETM+ reflective bands as the candidate input variables for building both models. Seven variables (NDVI, aspect, and bands 1, 3, 4, 5 and 7) were selected by the ANN model (implemented in Statistica 6.0 neural network module), while six (elevation, NDVI, and bands 1, 3, 5 and 7) were picked to fit the MLR function after a stepwise analysis was executed between the candidate input variables and the above ground dry biomass. Both models achieved reasonable results with RMSEs ranging from 39.88% to 50.08%. The ANN model provided a more accurate estimation (RMSE_r = 39.88% for the training set, and RMSE_r = 42.36% for the testing set) than MLR (RMSE_r = 49.51% for the training, and RMSE_r = 53.20% for the testing). The final above ground dry biomass maps of the research area were produced based on the ANN and MLR models, generating the estimated mean values of 121 and 147 g/m², respectively.     

A process-based model designed for filling of large data gaps in tower-based measurements of net ecosystem productivity

In this paper we present a simple hybrid gap-filling model (GFM) designed with a minimum number of parameters necessary to capture the ecological processes important for filling medium-to-large gaps in Flux data. As the model is process-based, the model has potential to be used in filling large gaps exhibiting a broad range of micro-meteorological and site conditions. The GFM performance was evaluated using “Punch hole” and extrapolation experiments based on data collected in west-central New Brunswick. These experiments indicated that the GFM is able to provide acceptable results (r² > 0.80) when >500 data points are used in model parameterization. The GFM was shown to address daytime evolution of NEP reasonably well for a wide range of weather and site conditions. An analysis of residuals indicated that for the most part no obvious trends were evident; although a slight bias was detected in NEP with soil temperature. To explore the portability of the GFM across ecosystem types, a transcontinental validation was conducted using NEP and ancillary data from seven ecosystems along a north-south transect (i.e., temperature–moisture gradient) from northern Europe (Finland) to the Middle East (Israel). The GFM was shown to explain over 75% of the variability in NEP measured at most ecosystems, which strongly suggests that the GFM maybe successfully applied to forest ecosystems outside Canada.