Root Of The Mean Square Error Research Articles

A Estimation of Stochastic Volatility Models Using Optimized Filtering Algorithms

In this paper, we describe and implement two recursive filtering algorithms, the optimized particle filter, and the Viterbi algorithm, which allow the joint estimation of states and parameters of continuous-time stochastic volatility models, such as the Cox Ingersoll Ross and Heston model. In practice, good parameter estimates are required so that the models are able to generate accurate forecasts. To achieve the objectives the proposed algorithms were implemented using daily empirical data from the time series of the $S\&P500$ returns of the stock exchange index. The proposed methodology facilitates computational calculations of the marginal likelihood of states and allows the reconstruction of unknown states in a suitable way, and reliable estimation of the parameters. To measure the quality of estimation of the algorithms, we used the square root of the mean square error and relative deviation standard as measures of goodness of fit. The estimated errors are insignificant for the analyzed data and the two models considered. We also calculated the execution times of the algorithms, demonstrating that the Viterbi algorithm has less execution time than the optimized particle filter.

Improving the Quality of Satellite Imagery Based on Ground-Truth Data from Rain Gauge Stations

Multitemporal imagery is by and large geometrically and radiometrically accurate, but the residual noise arising from removal clouds and other atmospheric and electronic effects can produce outliers that must be mitigated to properly exploit the remote sensing information. In this study, we show how ground-truth data from rain gauge stations can improve the quality of satellite imagery. To this end, a simulation study is conducted wherein different sizes of outlier outbreaks are spread and randomly introduced in the normalized difference vegetation index (NDVI) and the day and night land surface temperature (LST) of composite images from Navarre (Spain) between 2011 and 2015. To remove outliers, a new method called thin-plate splines with covariates (TpsWc) is proposed. This method consists of smoothing the median anomalies with a thin-plate spline model, whereby transformed ground-truth data are the external covariates of the model. The performance of the proposed method is measured with the square root of the mean square error (RMSE), calculated as the root of the pixel-by-pixel mean square differences between the original data and the predicted data with the TpsWc model and with a state-space model with and without covariates. The study shows that the use of ground-truth data reduces the RMSE in both the TpsWc model and the state-space model used for comparison purposes. The new method successfully removes the abnormal data while preserving the phenology of the raw data. The RMSE reduction percentage varies according to the derived variables (NDVI or LST), but reductions of up to 20% are achieved with the new proposal.

Estación meteorológica convencional versus automática sus diferencias evaluadas con índices estadísticos Chapingo, México

El objetivo del presente trabajo fue realizar la comparación de los datos meteorológicos medidos por una estación convencional contra los mismos obtenidos por una automática, ambas estaciones están ubicadas en la Universidad Autónoma Chapingo, estos datos fueron: temperatura máxima, mínima, humedad relativa máxima y mínima, colectados de manera diaria y analizados de forma gráfica y estadística, por medio del coeficiente de inconsistencia y consistencia, la raíz cuadrada del cuadrado medio del error y normalizado, el índice de concordancia o Willmott, el coeficiente de determinación, un análisis de regresión, error sistemático y error aleatorio, el periodo comprendido fue de finales de enero de 2004 a junio de 2013. Se encontró que para las variables temperatura máxima y temperatura mínima, se pueden usar indistintamente los datos de la estación meteorológica automática o los de la convencional ya que los datos son semejantes.

Simple nonlinear model for the relationship between maize yield and cumulative water amount

Both the additive and multiplicative models of crop yield and water supply are polynomial equations, and the number of parameters increases linearly when the growing period is specified. However, interactions among multiple parameters occasionally lead to unreasonable estimations of certain parameters, which were water sensitivity coefficients but with negative value. Additionally, evapotranspiration must be measured as a model input. To facilitate the application of these models and overcome the aforementioned shortcomings, a simple model with only three parameters was derived in this paper based on certain general quantitative relations of crop yield (Y) and water supply (W). The new model, Y/Ym–Wk/(Wk+whk), fits an S or a saturated curve of crop yield with the cumulative amount of water. Three parameters are related to biological factors: the yield potential (Ym), the water requirement to achieve half of the yield potential (half-yield water requirement, wh), and the water sensitivity coefficient (k). The model was validated with data from 24 maize lines obtained in the present study and 17 maize hybrids published by other authors. The results showed that the model was well fit to the data, and the normal root of the mean square error (NRMSE) values were 2.8 to 17.8% (average 7.2%) for the 24 maize lines and 2.7 to 12.7% (average 7.4%) for the 17 maize varieties. According to the present model, the maize water-sensitive stages in descending order were pollen shedding and silking, tasselling, jointing, initial grain filling, germination, middle grain filling, late grain filling, and end of grain filling. This sequence was consistent with actual observations in the maize field. The present model may be easily used to analyse the water use efficiency and drought tolerance of maize at specific stages.

An Error Criterion in Digital Image Correlation for Unknown Deformation Fields and Its Application of Parameters Selection

Digital image correlation (DIC) is a widely used optical metrology for surface deformation measurement. In DIC, the square root of the mean square error (RMS error) and standard deviation error (SD error) are used as quantitative criteria in order to evaluate the accuracy and robustness of a DIC method\algorithm. However, RMS and SD error criteria are computed from prescribed and measured displacements, which indicates that the prescribed displacement fields must be precisely generated. Therefore, it is difficult to quantitatively evaluate the accuracy and robustness of an algorithm\method in practical DIC measurements because imposed displacements are unknown (that’s why DIC measurements are needed). Moreover, the accuracy of DIC measurements highly relies on parameters selection, especially the selections of subset size and shape function. In practice, the subset size and shape function are usually selected according to experience because there are numerous factors (e.g. the quality of speckle image, local displacement field) and uncertainties (e.g. noise level, out-of-plane motion, illumination lighting fluctuation during image capturing) that affect the parameters selection, which makes it difficult to select optimal parameters based on previous works which mainly focused on theoretical deduction in ideal condition. In this paper, an error criterion for evaluating the accuracy of practical DIC measurements with unknown displacements is proposed. Numerical experiments are used to validate the effectiveness and feasibility of the proposed criterion for accuracy evaluation. It is concluded that the square root of the sum of squared forward and backward displacements difference (SFBD) error has a significant positive linear correlation with the widely used SD error in most practical DIC measurements where the mismatch between the frequently-used first- and second-order shape functions and the actual field is usually small. Also, an application of the proposed criterion is presented by real experiments for subset size and shape function selections, which verifies that the proposed error criterion can be effectively used for DIC parameters selection.

Regression correlation coefficient for a Poisson regression model

This study examines measures of predictive power for a generalized linear model (GLM). Although many measures of predictive power for GLMs have been proposed, most have limitations. Hence, we focus on the regression correlation coefficient (RCC) (Zheng and Agresti, 2000), which satisfies the four requirements of (i) interpretability, (ii) applicability, (iii) consistency, and (iv) affinity. The RCC is a population value that is defined by the correlation between a response variable and the conditional expectation of the response variable. Its sample value is defined by the sample correlation between the observed response values and estimated values of the response variable. For an arbitrary GLM, we do not always have an explicit form of the RCC. However, for a Poisson regression model, assuming that the predictor variables have a multivariate normal distribution, we can find the explicit form of the RCC (true value). Therefore, it is possible to compare the estimators (sample values) of the RCC in terms of bias and RMSE (root of the mean square error) by using the true value. Furthermore, by using the explicit form, we propose a new estimator of the RCC for the Poisson regression model. We then compare the new estimator with the sample correlation estimator, the jack-knife estimator, and the leave-one-out cross validation estimator in terms of bias and RMSE. The leave-one-out cross validation estimator has large negative bias and large RMSE. Although the remaining three estimators show similar behavior for a large sample size, for a small sample size the new estimator shows the best behavior in terms of bias and RMSE.

Toprakların Agregat Stabilitesi Değerlerinin Yapay Sinir Ağları ile Tahminlenmesi

Tarim alaninda yurutulen calismalarda tahminleme muhendisligi gunumuzde onemli bir noktaya gelmis ve tahminlemede yapay sinir aglarinin (YSA) kullanimi giderek yayginlasmistir. Bu calismada, Kahramanmaras Sutcu Imam Universitesi, Avsar Yerleskesi’nde bulunan pilot alanda yer alan topraklarin, mevsime bagli olarak degisim gosteren islak agregat stabilitesi (WAS) degerlerinin YSA kullanilarak tahminlenebilirligi arastirilmistir. Istatistiksel degerlendirmelerin sonuclarina dayanilarak secilen toprak ozellikleri bagimsiz degiskenler olarak kullanilmis ve WAS’i tahminleyen YSA’lar gelistirilmistir. Ag egitiminde on iki farkli ogrenme algoritmasi kullanilarak gercege en yakin WAS degerlerine ulasilmaya calisilmistir. Egitimde kullanilan bu farkli geri yayilim algoritmalarinin performanslari determinasyon katsayisi (R2), hata kareler ortalamasinin karekoku (RMSE) ve ortalama mutlak hata yuzdesi (MAPE) kriterleri yardimiyla degerlendirilmistir. Farkli algoritmalarin egitimi yoluyla olusturulan YSA’larin R2 degerleri 0.55-0.99, RMSE degerlerinin % 2.12-11.33 ve MAPE’nin ise % 3.55-20 araliklarinda degisim gostermistir. Gelistirilen YSA’lar WAS’i tahminleme gucu bakimindan R2 olcutu esas alinarak birbirleri ile karsilastirildiginda, BFGS (BFGS Quasi-Newton geri yayilim algoritmasi) algoritmasi ile egitilen ag haric butun aglarin R2 degerleri 0.97 ve uzerinde bulunmustur. Diger taraftan, olusturulan YSA’lar RMSE kriterine gore degerlendirildiginde en basarili agin esnek geri yayilim algoritmasi (RP) (% 2.12) ile egitilen ag ve en basarisiz agin BFGS (% 11.33) algortimasi ile gelistirilen ag oldugu sonucuna ulasilmistir. MAPE gostergesi dikkate alindiginda ise, tahminleme gucu en yuksek ag tek adim sekand geri yayilim algoritmasi (OSS) (% 3.55) ile egitilen YSA ve tahminleme gucu en dusuk ag BFGS algoritmasi (% 20) ile egitilen YSA olmustur. Elde edilen bulgular, YSA’larin dogru egitim algoritmasi kullanilarak olusturulduklarinda WAS’i tahminlemede kullanilabilecegine isaret etmektedir.

Weighted-Hausdorff distance using gradient orientation information for visible and infrared image registration

Hausdorff distance measures the distance between two sets in a metric space. The conventional Hausdorff distance is calculated by using only individual point and each point is equally weighted. The gradient orientation of each point is ignored, which limits the performance of Hausdorff distance in the image registration. Moreover, different points are of different importance and thus should be assigned different weights. This paper proposes a method to register visible and infrared images with modified Hausdorff distance measure, which uses both the position and the gradient orientation of each point. Each point is differently weighted by corner response value of each point. The experimental results demonstrate a better performance of the proposed method for registration of multi-sensor images in comparison with existing methods, which are based on conventional Hausdorff distance by the root of the mean square error (RMSE).

Alveolar to Arterial Gas Exchange During Constant-load Exercise in Healthy Active Men and Women

Lung diffusion capacity for carbon monoxide (DLCO) and cardiac output (Q) are commonly measured at rest using rebreathing or open circuit techniques, however, a single breath hold maneuver, or an intrabreath slow exhalation method can be done, too. Intrabreath measurements may be more convenient when measuring DLCO and Q during exercise, but they may be more difficult to perform and the reproducibility of intrabreath slow exhalation remains largely unexplored. PURPOSE: To determine the reproducibility and precision of intrabreath DLCO and Q measurements during stationary cycling at various intensities. METHODS: Seven physically active males were tested on three sessions. On day 1, subjects completed single-breath and intrabreath measurements of DLCO and Q at rest and were familiarized with the technique during exercise. They then completed an incremental cycling protocol to determine aerobic capacity (VO2max). For the second and third sessions (randomized order), subjects performed three 4-minute trials of (rest and 70%; or 45% and 90% of oxygen uptake reserve). Individuals performed the intrabreath maneuver within the last 15s of each cycling trial to obtain exercise DLCO and Q values. Subjects rested 5 minutes between successive trials. Average measures intraclass correlation coefficients (ICC2,k) using absolute measures of agreement were used to quantify reproducibility between trials. Average coefficient of variation (C.V., %) was computed as standard deviation divided by mean x 100. Smallest measurable change (SMC) was computed as 1.385 times the square root of the mean square error from a repeated measures ANOVA, and then normalized to mean scores to be expressed as a percentage. Trials in which the subject did not correctly complete the exhalation maneuver were not analyzed. RESULTS: Average measures ICC for DLCO (0.87) and Q (0.86) were greatest at rest, but varied with exercise intensity (0.50 to 0.87). At rest and during exercise, C.V. for DLCO (12 to 30%) and Q (18 to 38%) were poor. SMC was poor for all DLCO (16 to 36%) and Q (23 to 95%). CONCLUSIONS: The large CV and SMC suggest that intrabreath techniques for measuring DLCO and Q have limited clinical utility for evaluating changes in cardiorespiratory function. Subjects also found the maneuver increasingly difficult as exercise intensity increased.

Use of Artificial Neural Network in Predicting Permeability of Dispersive Clay Treated With Lime and Pozzolan

The treatment of a dispersive core soil can be achieved by mixing with lime and pozzolan, separately or simultaneously. On a dispersive soil treated with lime and pozzolan, experimental measurements of permeability were carried out with varying curing times and percentages of the additives. The results from these measurements were used in establishing an artificial neural network model meant to predict the permeability of more samples while being treated as carrying out laboratory measurements would be time consuming. Six parameters namely percentage passing of the 0.005 mm size (p), plasticity index (PI), maximum dry density (MDD), lime percentage (L), pozzolan percentage (pp), and curing time (t) were the inputs to the model while the output was permeability value. The prediction performances of various neural network models were evaluated using statistical performance indices such as root of the mean squared error (RMSE), the mean squared error (MSE), and the multiple coefficient of determination (R 2 ). The results show that the multilayer perceptron (MLP) neural network model with nine nodes in the hidden layer was desirable for predicting permeability of dispersive soils while being stabilized by lime and pozzolan, separately or simultaneously. For the model, R 2 =0.9895 and RMSE=3.5604×10 -8 cm/sec.

Bayesian Estimation and Prediction of Stochastic Volatility Models via INLA

In this article, we assess Bayesian estimation and prediction using integrated Laplace approximation (INLA) on a stochastic volatility (SV) model. This was performed through a Monte Carlo study with 1,000 simulated time series. To evaluate the estimation method, two criteria were considered: the bias and square root of the mean square error (smse). The criteria used for prediction are the one step ahead forecast of volatility and the one day Value at Risk (VaR). The main findings are that the INLA approximations are fairly accurate and relatively robust to the choice of prior distribution on the persistence parameter. Additionally, VaR estimates are computed and compared for three financial time series returns indexes.

Prediction of survival with alternative modeling techniques using pseudo values.

BackgroundThe use of alternative modeling techniques for predicting patient survival is complicated by the fact that some alternative techniques cannot readily deal with censoring, which is essential for analyzing survival data. In the current study, we aimed to demonstrate that pseudo values enable statistically appropriate analyses of survival outcomes when used in seven alternative modeling techniques.MethodsIn this case study, we analyzed survival of 1282 Dutch patients with newly diagnosed Head and Neck Squamous Cell Carcinoma (HNSCC) with conventional Kaplan-Meier and Cox regression analysis. We subsequently calculated pseudo values to reflect the individual survival patterns. We used these pseudo values to compare recursive partitioning (RPART), neural nets (NNET), logistic regression (LR) general linear models (GLM) and three variants of support vector machines (SVM) with respect to dichotomous 60-month survival, and continuous pseudo values at 60 months or estimated survival time. We used the area under the ROC curve (AUC) and the root of the mean squared error (RMSE) to compare the performance of these models using bootstrap validation.ResultsOf a total of 1282 patients, 986 patients died during a median follow-up of 66 months (60-month survival: 52% [95% CI: 50%−55%]). The LR model had the highest optimism corrected AUC (0.791) to predict 60-month survival, followed by the SVM model with a linear kernel (AUC 0.787). The GLM model had the smallest optimism corrected RMSE when continuous pseudo values were considered for 60-month survival or the estimated survival time followed by SVM models with a linear kernel. The estimated importance of predictors varied substantially by the specific aspect of survival studied and modeling technique used.ConclusionsThe use of pseudo values makes it readily possible to apply alternative modeling techniques to survival problems, to compare their performance and to search further for promising alternative modeling techniques to analyze survival time.

Multilevel bootstrap analysis with assumptions violated.

Likelihood-based methods can work poorly when the residuals are not normally distributed and the variances across clusters are heterogeneous. The performance of two estimation methods, the non-parametric residual bootstrap (RB) and the restricted maximum likelihood (REML) for fitting multilevel models are compared through simulation studies in terms of bias, coverage, and precision. We find that (a) both methods produce unbiased estimates of the fixed parameters, but biased estimates of the random parameters, although the REML was more prone to give biased estimates for the variance components; (b) the RB method yields substantial reductions in the difference between nominal and actual confidence interval coverage, compared with the REML method; and (c) for the square root of the mean squared error (RMSE) of the fixed effects, the RB method performed slightly better than the REML method. For the variance components, however, the RB method did not offer a systematic improvement over the REML method in terms of RMSE. It can be stated that the RB method is, in general, superior to the REML method with violated assumptions.

Body composition prediction equations based on deuterium oxide dilution method in Mexican children: a national study

Obesity and undernutrition co-exist in many regions of Mexico. However, accurate assessments are difficult because epidemiological data on body composition are not available. The aim of this study was to facilitate assessments of body composition in Mexican school children of different geographical regions and ethnicity by developing equations for bioelectrical impedance and anthropometry based on deuterium oxide dilution. We evaluated 336 subjects (143 belonged to six major indigenous groups) from Northern, Central and Southern Mexico. We measured height (Ht), weight (Wt), tricipital skinfold (Tricp-SKF) and resistance (R) based on a bioimpedance analysis (BIA). Fat-free mass (FFM) and fat mass (FM) were estimated from measurements of total body water with the deuterium dilution technique. The final BIA equation was FFM (kg)=0.661 × Ht²/R+0.200 × Wt-0.320. The R² was 0.96; the square root of the mean square error (SRMSE) was 1.39 kg. The final anthropometric equation was FM (kg)=-1.067 × sex+0.458 × Tricp-SKF+0.263 × Wt-5.407. The R² was 0.91; SRMSE was 1.60 kg. The BIA equation had a bias of 0.095 kg and precision of 1.43 kg. The anthropometric equation had a bias of 0.047 kg and precision of 1.58 kg. We validated two equations for evaluating body composition in Mexican indigenous and non-indigenous children and youth from three main regions of the country. These equations provided reliable estimates and will promote a better understanding of both obesity and undernutrition.

Evaluation of mathematical models to describe growth of grazing young bulls

The objective of this study was to evaluate the use of different mathematical models to describe growth of grazing beef cattle. Data of 20 Nellore bulls with initial weight of 129±28.1 kg and final weight of 405±62.0 kg were used. The animals were randomly divided into four plots and placed on B. decumbens Stapf pastures. Three plots received concentrate supplement with different protein profiles and the fourth plot received only mineral supplement. Animals were weighed every 28 days to design growth curve of full body weight. Five mathematical models were evaluated to describe animal growth: Multiphase, Linear, Logarithmic, Gompertz and Logistic models. Assessment of adequacy of the models was performed by using coefficient of determination, simultaneous F-test for identity of parameters, concordance correlation coefficient, root of the mean square error of prediction and partition of the mean square error of prediction. The analysis of the pairwise mean square error of prediction and the delta Akaike's information criterion were used to compare the models for accuracy and precision. Evaluation of all the tested models showed that all of them were able to predict variability among animals. However, Gompertz, Logarithmic and Logistic models created individual predictions that were not satisfactory. Models differed from each other concerning accuracy and precision; the best were in the following order: Multiphase, Linear, Gompertz, Logarithmic and Logistic. The Multiphase model was more efficient than the others for description of grazing beef cattle growth.

Estimativas da evapotranspiração de referência em diferentes condições de nebulosidade

O objetivo deste trabalho foi avaliar o desempenho de métodos de estimativa da evapotranspiração de referência (ETo), em diferentes condições de nebulosidade, no Município de Seropédica, RJ. As estimativas de ETo, entre 1/6/2006 e 31/7/2007, foram comparadas com medidas diárias realizadas em lisímetro de pesagem, com agrupamento total dos dados e com a discretização pela variação do índice de claridade diário K T em quatro classes: K T<0,35, nublado (Nub); 0,35<K T<0,55, céu parcialmente nublado (PNAd); 0,55<K T<0,65, céu parcialmente aberto (PNAb); e K T>0,65, céu aberto (Ab). Para avaliação da qualidade das estimativas realizadas pelos diferentes métodos, foram empregados o erro absoluto médio (MBE), a raiz quadrada do quadrado médio do erro (RMSE), e índices de ajustamento e de desempenho. No agrupamento total dos dados, os métodos Penman-Monteith FAO (PMF) e Hargreaves-Samani (HS) apresentaram coeficientes de desempenho de 84,05 e 79,52%, respectivamente, enquanto os métodos Jensen & Haise, Linacre e Makking apresentaram desempenho inferior a 60%. A variação das condições de nebulosidade influenciaram o desempenho dos métodos de estimativa de ETo. Os melhores resultados foram obtidos pelos métodos da radiação solar (86,1%) e de Camargo (81,8%), nas condições Ab e Nub. Os métodos PMF e HS podem ser empregados de forma complementar, pois apresentaram desempenhos de 78,4% (Nub e PNAd) e de 77,6% (PNAb e Ab), respectivamente.

Comparing plastic syringes and disposable columns to extract n-alkanes in forage and concentrate feeds

Saturated aliphatic hydrocarbons (n-alkanes) were extracted from feed, orts, and bovine fecal samples using disposable, plastic 5mL-syringes as an alternative material to disposable columns, which are normally used in the liquid-solid extraction phase of n-alkanes. For both methods, the n-alkane extracts (carbon chain length between 31 and 36 atoms) were identified using gas chromatography. The linear regression between methods were: 1) feces: column Alkane=2.63+0.92×syringeAlkane [r²=0.94, square root of the mean square error (RMSE)=13.7mg kg-1, n=30] from which the intercept and the slope did not simultaneously differ from zero and unity (P>0.05), respectively; 2) feeds: column Alkane=0.36+1.12×syringeAlkane (r²=0.85, RMSE=1.9mg kg-1, n=21) from which the intercept and the slope did not simultaneously differ from zero and unity (P>0.05), respectively; 3) orts: column Alkane=0.49+0.92×syringeAlkane (r²=0.98, RMSE=1.2mg kg-1, n=15) from which the intercept and the slope did not simultaneously differ from zero and unity (P>0.05), respectively. Materials with low concentration of n-alkanes may affect the values obtained in both methods. These results suggested that disposable plastic syringes might be a viable alternative to columns thus, reducing analytical costs.

Performance of the empirical Bayes estimator for fixed parameters

When the unbiased estimators of a set of parameters are independently and normally distributed, the Empirical Bayes Estimator (EB) for each of the parameters depends on all the parameters. When these parameters are considered to be fixed, Rao and Shinozaki (1978) [7] compared the mean square error (MSE) of this estimator for an individual parameter with the variance of its unbiased estimator, and cautioned that its bias may be large. In this article, the conditions required for (a) the MSE of the EB to be smaller than the variance of the unbiased estimator and (b) at the same time, for its bias to be smaller than a specified fraction of the square root of the MSE are evaluated. To satisfy these conditions, critical limits for the difference of the parameter from the average of all the parameters and the sum of such differences over all the parameters are determined. As an illustration, for the daily inpatient hospital expenses in the Metropolitan Statistical Areas (MSAs) of 15 states in the US, the sample means and EBs are compared through the estimates of these limits.

Simulação do balanço de água no solo cultivado com trigo com modificação de dois modelos

O trigo é a principal cultura de inverno do estado do Rio Grande do Sul e o cálculo do balanço de água no solo é parte importante de modelos de crescimento, desenvolvimento e rendimento de culturas. O objetivo deste trabalho foi obter melhor estimativa do balanço de água no solo cultivado com trigo, modificando dois modelos de balanço de água nesse solo. Mediu-se o conteúdo de água no solo pelo método gravimétrico durante a estação de cultivo de dois cultivares de trigo em três datas de semeadura, em Santa Maria - RS, e a água disponível para a cultura foi representada pela fração de água no solo disponível para as plantas (FADS). O desempenho das versões originais e modificadas dos modelos de balanço de água no solo de Campbell & Diaz e de Amir & Sinclair foi avaliado pela raiz do quadrado médio do erro (RQME). O modelo de Campbell & Diaz modificado é mais realístico e com maior possibilidade de desempenho satisfatório em regiões de clima distinto daquele em que foi desenvolvido, mas o modelo de Amir & Sinclair modificado estimou melhor a água disponível no solo para a cultura do trigo na região do estudo. A profundidade máxima do sistema radicular de 0,30 m é mais apropriada para a simulação da fração de água disponível no solo, para a unidade de mapeamento de solo São Pedro.

Methods of Covariate Selection: Directed Acyclic Graphs and the Change-in-Estimate Procedure

Four covariate selection approaches were compared: a directed acyclic graph (DAG) full model and 3 DAG and change-in-estimate combined procedures. Twenty-five scenarios with case-control samples were generated from 10 simulated populations in order to address the performance of these covariate selection procedures in the presence of confounders of various strengths and under DAG misspecification with omission of confounders or inclusion of nonconfounders. Performance was evaluated by standard error, bias, square root of the mean-squared error, and 95% confidence interval coverage. In most scenarios, the DAG full model without further covariate selection performed as well as or better than the other procedures when the DAGs were correctly specified, as well as when confounders were omitted. Model reduction by using change-in-estimate procedures showed potential gains in precision when the DAGs included nonconfounders, but underestimation of regression-based standard error might cause reduction in 95% confidence interval coverage. For modeling binary outcomes in a case-control study, the authors recommend construction of a "conservative" DAG, determination of all potential confounders, and then change-in-estimate procedures to simplify this full model. The authors advocate that, under the conditions investigated, the selection of final model should be based on changes in precision: Adopt the reduced model if its standard error (derived from logistic regression) is substantially smaller; otherwise, the full DAG-based model is appropriate.