On the consequences of misspecifing assumptions concerning residuals distribution in a repeated measures and nonlinear mixed modelling context

In this paper we describe the results of a simulation study performed to elucidate the robustness of the Lindstrom and Bates (1990) approximation method under non-normality of the residuals, under different situations. Concerning the fixed effects, the observed coverage probabilities and the true bias and mean square error values, show that some aspects of this inferential approach are not completely reliable. When the true distribution of the residuals is asymmetrical, the true coverage is markedly lower than the nominal one. The best results are obtained for the skew normal distribution, and not for the normal distribution. On the other hand, the results are partially reversed concerning the random effects. Soybean genotypes data are used to illustrate the methods and to motivate the simulation scenarios

Impact of incorrect assumptions on the covariance structure of random effects and/or residuals in nonlinear mixed models for repeated measures data

In this paper we analyse, using Monte Carlo simulation, the possible consequences of incorrect assumptions on the true structure of the random effects covariance matrix and the true correlation pattern of residuals, over the performance of an estimation method for nonlinear mixed models. The procedure under study is the well known linearization method due to Lindstrom and Bates (1990), implemented in the nlme library of S-Plus and R. Its performance is studied in terms of bias, mean square error (MSE), and true coverage of the associated asymptotic confidence intervals. Ignoring other criteria like the convenience of avoiding over parameterised models, it seems worst to erroneously assume some structure than do not assume any structure when this would be adequate.

Modeling changes in organic carbon stocks for distinct soils in southeastern brazil after four eucalyptus rotations using the century model

Soil organic matter (SOM) plays an important role in carbon (C) cycle and soil quality. Considering the complexity of factors that control SOM cycling and the long time it usually takes to observe changes in SOM stocks, modeling constitutes a very important tool to understand SOM cycling in forest soils. The following hypotheses were tested: (i) soil organic carbon (SOC) stocks would be higher after several rotations of eucalyptus than in low-productivity pastures; (ii) SOC values simulated by the Century model would describe the data better than the mean of observations. So, the aims of the current study were: (i) to evaluate the SOM dynamics using the Century model to simulate the changes of C stocks for two eucalyptus chronosequences in the Rio Doce Valley, Minas Gerais State, Brazil; and (ii) to compare the C stocks simulated by Century with the C stocks measured in soils of different Orders and regions of the Rio Doce Valley growing eucalyptus. In Belo Oriente (BO), short-rotation eucalyptus plantations had been cultivated for 4.0; 13.0, 22.0, 32.0 and 34.0 years, at a lower elevation and in a warmer climate, while in Virginópolis (VG), these time periods were 8.0, 19.0 and 33.0 years, at a higher elevation and in a milder climate. Soil samples were collected from the 0-20 cm layer to estimate C stocks. Results indicate that the C stocks simulated by the Century model decreased after 37 years of poorly managed pastures in areas previously covered by native forest in the regions of BO and VG. The substitution of poorly managed pastures by eucalyptus in the early 1970´s led to an average increase of C of 0.28 and 0.42 t ha-1 year-1 in BO and VG, respectively. The measured C stocks under eucalyptus in distinct soil Orders and independent regions with variable edapho-climate conditions were not far from the values estimated by the Century model (root mean square error - RMSE = 20.9; model efficiency - EF = 0.29) despite the opposite result obtained with the statistical procedure to test the identity of analytical methods. Only for lower soil C stocks, the model over-estimated the C stock in the 0-20 cm layer. Thus, the Century model is highly promising to detect changes in C stocks in distinct soil orders under eucalyptus, as well as to indicate the impact of harvest residue management on SOM in future rotations.

Pedotransfer functions to estimate water retention parameters of soils in northeastern Brazil

Pedotransfer functions (PTF) were developed to estimate the parameters (α, n, θr and θs) of the van Genuchten model (1980) to describe soil water retention curves. The data came from various sources, mainly from studies conducted by universities in Northeast Brazil, by the Brazilian Agricultural Research Corporation (Embrapa) and by a corporation for the development of the São Francisco and Parnaíba river basins (Codevasf), totaling 786 retention curves, which were divided into two data sets: 85 % for the development of PTFs, and 15 % for testing and validation, considered independent data. Aside from the development of general PTFs for all soils together, specific PTFs were developed for the soil classes Ultisols, Oxisols, Entisols, and Alfisols by multiple regression techniques, using a stepwise procedure (forward and backward) to select the best predictors. Two types of PTFs were developed: the first included all predictors (soil density, proportions of sand, silt, clay, and organic matter), and the second only the proportions of sand, silt and clay. The evaluation of adequacy of the PTFs was based on the correlation coefficient (R) and Willmott index (d). To evaluate the PTF for the moisture content at specific pressure heads, we used the root mean square error (RMSE). The PTF-predicted retention curve is relatively poor, except for the residual water content. The inclusion of organic matter as a PTF predictor improved the prediction of parameter a of van Genuchten. The performance of soil-class-specific PTFs was not better than of the general PTF. Except for the water content of saturated soil estimated by particle size distribution, the tested models for water content prediction at specific pressure heads proved satisfactory. Predictions of water content at pressure heads more negative than -0.6 m, using a PTF considering particle size distribution, are only slightly lower than those obtained by PTFs including bulk density and organic matter content.

Lag-one autocorrelation in short series: Estimation and hypothesis testing

In the first part of the study, nine estimators of the first-order autoregressive parameter are reviewed and a new estimator is proposed. The relationships and discrepancies between the estimators are discussed in order to achieve a clear differentiation. In the second part of the study, the precision in the estimation of autocorrelation is studied. The performance of the ten lag-one autocorrelation estimators is compared in terms of Mean Square Error (combining bias and variance) using data series generated by Monte Carlo simulation. The results show that there is not a single optimal estimator for all conditions, suggesting that the estimator ought to be chosen according to sample size and to the information available of the possible direction of the serial dependence. Additionally, the probability of labelling an actually existing autocorrelation as statistically significant is explored using Monte Carlo sampling. The power estimates obtained are quite similar among the tests associated with the different estimators. These estimates evidence the small probability of detecting autocorrelation in series with less than 20 measurement times.

Development and evaluation of neural network models to estimate daily solar radiation at Córdoba, Argentina

The objective of this work was to develop neural network models of backpropagation type to estimate solar radiation based on extraterrestrial radiation data, daily temperature range, precipitation, cloudiness and relative sunshine duration. Data from Córdoba, Argentina, were used for development and validation. The behaviour and adjustment between values observed and estimates obtained by neural networks for different combinations of input were assessed. These estimations showed root mean square error between 3.15 and 3.88 MJ m-2 d-1 . The latter corresponds to the model that calculates radiation using only precipitation and daily temperature range. In all models, results show good adjustment to seasonal solar radiation. These results allow inferring the adequate performance and pertinence of this methodology to estimate complex phenomena, such as solar radiation.

Techniques for Estimating Flood-Frequency Discharges for Streams in Iowa, HR-395A, 2001

A statewide study was conducted to develop regression equations for estimating flood-frequency discharges for ungaged stream sites in Iowa. Thirty-eight selected basin characteristics were quantified and flood-frequency analyses were computed for 291 streamflow-gaging stations in Iowa and adjacent States. A generalized-skew-coefficient analysis was conducted to determine whether generalized skew coefficients could be improved for Iowa. Station skew coefficients were computed for 239 gaging stations in Iowa and adjacent States, and an isoline map of generalized-skew-coefficient values was developed for Iowa using variogram modeling and kriging methods. The skew map provided the lowest mean square error for the generalized-skew- coefficient analysis and was used to revise generalized skew coefficients for flood-frequency analyses for gaging stations in Iowa. Regional regression analysis, using generalized least-squares regression and data from 241 gaging stations, was used to develop equations for three hydrologic regions defined for the State. The regression equations can be used to estimate flood discharges that have recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years for ungaged stream sites in Iowa. One-variable equations were developed for each of the three regions and multi-variable equations were developed for two of the regions. Two sets of equations are presented for two of the regions because one-variable equations are considered easy for users to apply and the predictive accuracies of multi-variable equations are greater. Standard error of prediction for the one-variable equations ranges from about 34 to 45 percent and for the multi-variable equations range from about 31 to 42 percent. A region-of-influence regression method was also investigated for estimating flood-frequency discharges for ungaged stream sites in Iowa. A comparison of regional and region-of-influence regression methods, based on ease of application and root mean square errors, determined the regional regression method to be the better estimation method for Iowa. Techniques for estimating flood-frequency discharges for streams in Iowa are presented for determining ( 1) regional regression estimates for ungaged sites on ungaged streams; (2) weighted estimates for gaged sites; and (3) weighted estimates for ungaged sites on gaged streams. The technique for determining regional regression estimates for ungaged sites on ungaged streams requires determining which of four possible examples applies to the location of the stream site and its basin. Illustrations for determining which example applies to an ungaged stream site and for applying both the one-variable and multi-variable regression equations are provided for the estimation techniques.

Simulating maize phenology as a function of air temperature with a linear and a nonlinear model

The objective of this study was to adapt a nonlinear model (Wang and Engel - WE) for simulating the phenology of maize (Zea mays L.), and to evaluate this model and a linear one (thermal time), in order to predict developmental stages of a field-grown maize variety. A field experiment, during 2005/2006 and 2006/2007 was conducted in Santa Maria, RS, Brazil, in two growing seasons, with seven sowing dates each. Dates of emergence, silking, and physiological maturity of the maize variety BRS Missões were recorded in six replications in each sowing date. Data collected in 2005/2006 growing season were used to estimate the coefficients of the two models, and data collected in the 2006/2007 growing season were used as independent data set for model evaluations. The nonlinear WE model accurately predicted the date of silking and physiological maturity, and had a lower root mean square error (RMSE) than the linear (thermal time) model. The overall RMSE for silking and physiological maturity was 2.7 and 4.8 days with WE model, and 5.6 and 8.3 days with thermal time model, respectively.

Improving node number simulation in soybean

The objective of this study was to improve the simulation of node number in soybean cultivars with determinate stem habits. A nonlinear model considering two approaches to input daily air temperature data (daily mean temperature and daily minimum/maximum air temperatures) was used. The node number on the main stem data of ten soybean cultivars was collected in a three-year field experiment (from 2004/2005 to 2006/2007) at Santa Maria, RS, Brazil. Node number was simulated using the Soydev model, which has a nonlinear temperature response function [f(T)]. The f(T) was calculated using two methods: using daily mean air temperature calculated as the arithmetic average among daily minimum and maximum air temperatures (Soydev tmean); and calculating an f(T) using minimum air temperature and other using maximum air temperature and then averaging the two f(T)s (Soydev tmm). Root mean square error (RMSE) and deviations (simulated minus observed) were used as statistics to evaluate the performance of the two versions of Soydev. Simulations of node number in soybean were better with the Soydev tmm version, with a 0.5 to 1.4 node RMSE. Node number can be simulated for several soybean cultivars using only one set of model coefficients, with a 0.8 to 2.4 node RMSE.

Simulation of soybean growth and yield under northeastern Amazon climatic conditions

The objective of this work was to parameterize, calibrate, and validate a new version of the soybean growth and yield model developed by Sinclair, under natural field conditions in northeastern Amazon. The meteorological data and the values of soybean growth and leaf area were obtained from an agrometeorological experiment carried out in Paragominas, PA, Brazil, from 2006 to 2009. The climatic conditions during the experiment were very distinct, with a slight reduction in rainfall in 2007, due to the El Niño phenomenon. There was a reduction in the leaf area index (LAI) and in biomass production during this year, which was reproduced by the model. The simulation of the LAI had root mean square error (RMSE) of 0.55 to 0.82 m² m-2, from 2006 to 2009. The simulation of soybean yield for independent data showed a RMSE of 198 kg ha-1, i.e., an overestimation of 3%. The model was calibrated and validated for Amazonian climatic conditions, and can contribute positively to the improvement of the simulations of the impacts of land use change in the Amazon region. The modified version of the Sinclair model is able to adequately simulate leaf area formation, total biomass, and soybean yield, under northeastern Amazon climatic conditions.

CO2-response function of radiation use efficiency in rice for climate change scenarios

The objective of this work was to evaluate a generalized response function to the atmospheric CO2 concentration [f(CO2)] by the radiation use efficiency (RUE) in rice. Experimental data on RUE at different CO2 concentrations were collected from rice trials performed in several locations around the world. RUE data were then normalized, so that all RUE at current CO2 concentration were equal to 1. The response function was obtained by fitting normalized RUE versus CO2 concentration to a Morgan-Mercer-Flodin (MMF) function, and by using Marquardt's method to estimate the model coefficients. Goodness of fit was measured by the standard deviation of the estimated coefficients, the coefficient of determination (R²), and the root mean square error (RMSE). The f(CO2) describes a nonlinear sigmoidal response of RUE in rice, in function of the atmospheric CO2 concentration, which has an ecophysiological background, and, therefore, renders a robust function that can be easily coupled to rice simulation models, besides covering the range of CO2 emissions for the next generation of climate scenarios for the 21st century.

Robust power allocation algorithms for MIMO OFDM systems with imperfect CSI

This paper presents a Bayesian approach to the design of transmit prefiltering matrices in closed-loop schemes robust to channel estimation errors. The algorithms are derived for a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. Two different optimizationcriteria are analyzed: the minimization of the mean square error and the minimization of the bit error rate. In both cases, the transmitter design is based on the singular value decomposition (SVD) of the conditional mean of the channel response, given the channel estimate. The performance of the proposed algorithms is analyzed,and their relationship with existing algorithms is indicated. As withother previously proposed solutions, the minimum bit error rate algorithmconverges to the open-loop transmission scheme for very poor CSI estimates.

Motion estimation using higher-order statistics

The objective of this paper is to introduce a fourth-order cost function of the displaced frame difference (DFD) capable of estimatingmotion even for small regions or blocks. Using higher than second-orderstatistics is appropriate in case the image sequence is severely corruptedby additive Gaussian noise. Some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the DFD.

Maximum likelihood estimation of position in GNSS

In this letter, we obtain the Maximum LikelihoodEstimator of position in the framework of Global NavigationSatellite Systems. This theoretical result is the basis of a completelydifferent approach to the positioning problem, in contrastto the conventional two-steps position estimation, consistingof estimating the synchronization parameters of the in-viewsatellites and then performing a position estimation with thatinformation. To the authors’ knowledge, this is a novel approachwhich copes with signal fading and it mitigates multipath andjamming interferences. Besides, the concept of Position–basedSynchronization is introduced, which states that synchronizationparameters can be recovered from a user position estimation. Weprovide computer simulation results showing the robustness ofthe proposed approach in fading multipath channels. The RootMean Square Error performance of the proposed algorithm iscompared to those achieved with state-of-the-art synchronizationtechniques. A Sequential Monte–Carlo based method is used todeal with the multivariate optimization problem resulting fromthe ML solution in an iterative way.

Testing a new multigroup inference approach to reconstructing past environmental conditions

A new, quantitative, inference model for environmental reconstruction (transfer function), based for the first time on the simultaneous analysis of multigroup species, has been developed. Quantitative reconstructions based on palaeoecological transfer functions provide a powerful tool for addressing questions of environmental change in a wide range of environments, from oceans to mountain lakes, and over a range of timescales, from decades to millions of years. Much progress has been made in the development of inferences based on multiple proxies but usually these have been considered separately, and the different numeric reconstructions compared and reconciled post-hoc. This paper presents a new method to combine information from multiple biological groups at the reconstruction stage. The aim of the multigroup work was to test the potential of the new approach to making improved inferences of past environmental change by improving upon current reconstruction methodologies. The taxonomic groups analysed include diatoms, chironomids and chrysophyte cysts. We test the new methodology using two cold-environment training-sets, namely mountain lakes from the Pyrenees and the Alps. The use of multiple groups, as opposed to single groupings, was only found to increase the reconstruction skill slightly, as measured by the root mean square error of prediction (leave-one-out cross-validation), in the case of alkalinity, dissolved inorganic carbon and altitude (a surrogate for air-temperature), but not for pH or dissolved CO2. Reasons why the improvement was less than might have been anticipated are discussed. These can include the different life-forms, environmental responses and reaction times of the groups under study.