scholarly journals Nonlinear quantile regression to describe the dry matter accumulation of garlic plants

2020 ◽  
Vol 50 (1) ◽  
Author(s):  
Guilherme Alves Puiatti ◽  
Paulo Roberto Cecon ◽  
Moysés Nascimento ◽  
Ana Carolina Campana Nascimento ◽  
Antônio Policarpo Souza Carneiro ◽  
...  
Keyword(s):  
Quantile Regression ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Regression Models ◽  
Dry Matter ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Dry Matter Accumulation ◽  
Over Time

ABSTRACT: The objective of this study was to adjust nonlinear quantile regression models for the study of dry matter accumulation in garlic plants over time, and to compare them to models fitted by the ordinary least squares method. The total dry matter of nine garlic accessions belonging to the Vegetable Germplasm Bank of Universidade Federal de Viçosa (BGH/UFV) was measured in four stages (60, 90, 120 and 150 days after planting), and those values were used for the nonlinear regression models fitting. For each accession, there was an adjustment of one model of quantile regression (τ=0.5) and one based on the least squares method. The nonlinear regression model fitted was the Logistic. The Akaike Information Criterion was used to evaluate the goodness of fit of the models. Accessions were grouped using the UPGMA algorithm, with the estimates of the parameters with biological interpretation as variables. The nonlinear quantile regression is efficient for the adjustment of models for dry matter accumulation in garlic plants over time. The estimated parameters are more uniform and robust in the presence of asymmetry in the distribution of the data, heterogeneous variances, and outliers.

scholarly journals USE OF QUANTILE REGRESSION AND RANSAC ALGORITHM IN FITTING VOLUME EQUATIONS UNDER THE INFLUENCE OF DISCREPANT DATA

FLORESTA ◽  
2021 ◽  
Vol 51 (3) ◽  
pp. 596
Author(s):  
Jadson Coelho De Abreu ◽  
Carlos Pedro Boechat Soares ◽  
Helio Garcia Leite ◽  
Daniel Henrique Breda Binoti ◽  
Gilson Fernandes Da Silva
Keyword(s):  
Quantile Regression ◽  
Least Squares ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Ordinary Least Squares ◽  
Graphical Analysis ◽  
Estimation Methods ◽  
Volume Equations ◽  
Ransac Algorithm

The objective of this study was to evaluate three estimation methods to fit volume equations in the presence of influential or leverage data. To do so, data from the forest inventory carried out by the Centro Tecnológico de Minas Gerais Foundation were used to fit the Schumacher and Hall (1933) model in its nonlinear form for Cerradão forest, considering the quantile regression (QR), the RANSAC algorithm and the nonlinear Ordinary Least Squares (OLS) method. The correlation coefficient ( ) between the observed and estimated volumes, root-mean-square error (RMSE), as well as graphical analysis of the dispersion and distribution of the residuals were used as criteria to evaluate the performance of the methods. After the analysis, the nonlinear least squares method presented a slightly better result in terms of the goodness-of-fit statistics, however it altered the expected trend of the fitted curve due to the presence of influential data, which did not happen with the QR and the RANSAC algorithm, as these were more robust in the presence of discrepant data.

Calibration of stormwater quality regression models: a random process?

2010 ◽  
Vol 62 (4) ◽  
pp. 875-882 ◽  
Author(s):  
A. Dembélé ◽  
J.-L. Bertrand-Krajewski ◽  
B. Barillon
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Regression Models ◽  
Linear Models ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Data Sets ◽  
Data Set ◽  
Urban Catchments

Regression models are among the most frequently used models to estimate pollutants event mean concentrations (EMC) in wet weather discharges in urban catchments. Two main questions dealing with the calibration of EMC regression models are investigated: i) the sensitivity of models to the size and the content of data sets used for their calibration, ii) the change of modelling results when models are re-calibrated when data sets grow and change with time when new experimental data are collected. Based on an experimental data set of 64 rain events monitored in a densely urbanised catchment, four TSS EMC regression models (two log-linear and two linear models) with two or three explanatory variables have been derived and analysed. Model calibration with the iterative re-weighted least squares method is less sensitive and leads to more robust results than the ordinary least squares method. Three calibration options have been investigated: two options accounting for the chronological order of the observations, one option using random samples of events from the whole available data set. Results obtained with the best performing non linear model clearly indicate that the model is highly sensitive to the size and the content of the data set used for its calibration.

scholarly journals A Comparative Analysis on Some Estimators of Parameters of Linear Regression Models in Presence of Multicollinearity

2018 ◽  
pp. 1-8
Author(s):  
Warha, Abdulhamid Audu ◽  
Yusuf Abbakar Muhammad ◽  
Akeyede, Imam
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Models ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Linear Regression Models ◽  
Independent Variables ◽  
Different Levels

Linear regression is the measure of relationship between two or more variables known as dependent and independent variables. Classical least squares method for estimating regression models consist of minimising the sum of the squared residuals. Among the assumptions of Ordinary least squares method (OLS) is that there is no correlations (multicollinearity) between the independent variables. Violation of this assumptions arises most often in regression analysis and can lead to inefficiency of the least square method. This study, therefore, determined the efficient estimator between Least Absolute Deviation (LAD) and Weighted Least Square (WLS) in multiple linear regression models at different levels of multicollinearity in the explanatory variables. Simulation techniques were conducted using R Statistical software, to investigate the performance of the two estimators under violation of assumptions of lack of multicollinearity. Their performances were compared at different sample sizes. Finite properties of estimators’ criteria namely, mean absolute error, absolute bias and mean squared error were used for comparing the methods. The best estimator was selected based on minimum value of these criteria at a specified level of multicollinearity and sample size. The results showed that, LAD was the best at different levels of multicollinearity and was recommended as alternative to OLS under this condition. The performances of the two estimators decreased when the levels of multicollinearity was increased.

scholarly journals Quantile regression of nonlinear models to describe different levels of dry matter accumulation in garlic plants

2018 ◽  
Vol 48 (1) ◽  
Author(s):  
Guilherme Alves Puiatti ◽  
Paulo Roberto Cecon ◽  
Moysés Nascimento ◽  
Ana Carolina Campana Nascimento ◽  
Antônio Policarpo Souza Carneiro ◽  
...  
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Nonlinear Regression ◽  
Dry Matter ◽  
Nonlinear Models ◽  
Development Stage ◽  
Dry Matter Accumulation ◽  
Nonlinear Regression Models ◽  
Biological Interpretation ◽  
Quantile Estimates

ABSTRACT: Plant growth analyses are important because they generate information on the demand and necessary care for each development stage of a plant. Nonlinear regression models are appropriate for the description of curves of growth, since they include parameters with practical biological interpretation. However, these models present information in terms of the conditional mean, and they are subject to problems in the adjustment caused by possible outliers or asymmetry in the distribution of the data. Quantile regression can solve these problems, and it allows the estimation of different quantiles, generating more complete and robust results. The objective of this research was to adjust a nonlinear quantile regression model for the study of dry matter accumulation in garlic plants (Allium sativum L.) over time, estimating parameters at three different quantiles and classifying each garlic accession according to its growth rate and asymptotic weight. The nonlinear regression model fitted was a Logistic model, and 30 garlic accessions were evaluated. These 30 accessions were divided based on the model with the closest quantile estimates; 12 accessions were classified as of lesser interest for planting, 6 were classified as intermediate, and 12 were classified as of greater interest for planting.

scholarly journals Analysis of quantile regression as alternative to ordinary least squares

2015 ◽  
Vol 3 (2) ◽  
pp. 138
Author(s):  
Ibrahim Abdullahi ◽  
Abubakar Yahaya
Keyword(s):  
Analytical Solution ◽  
Quantile Regression ◽  
Least Squares ◽  
Fuel Consumption ◽  
Goodness Of Fit ◽  
Ordinary Least Squares ◽  
Coefficient Of Determination ◽  
Test Statistics ◽  
Least Absolute Deviation ◽  
Absolute Deviation

<p>In this article, an alternative to ordinary least squares (OLS) regression based on analytical solution in the Statgraphics software is considered, and this alternative is no other than quantile regression (QR) model. We also present goodness of fit statistic as well as approximate distributions of the associated test statistics for the parameters. Furthermore, we suggest a goodness of fit statistic called the least absolute deviation (LAD) coefficient of determination. The procedure is well presented, illustrated and validated by a numerical example based on publicly available dataset on fuel consumption in miles per gallon in highway driving.</p>

scholarly journals The Simulation Study to Test the Performance of Quantile Regression Method With Heteroscedastic Error Variance

CAUCHY ◽  
2017 ◽  
Vol 5 (1) ◽  
pp. 36
Author(s):  
Ferra Yanuar
Keyword(s):  
Quantile Regression ◽  
Least Squares ◽  
Least Squares Method ◽  
Simulated Data ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Regression Method ◽  
Data Consistency ◽  
Interval Width ◽  
Quantile Regression Method

<div><p class="Keywords">The purpose of this article was to describe the ability of the quantile regression method in overcoming the violation of classical assumptions. The classical assumptions that are violated in this study are variations of non-homogeneous error or heteroscedasticity. To achieve this goal, the simulated data generated with the design of certain data distribution. This study did a comparison between the models resulting from the use of the ordinary least squares and the quantile regression method to the same simulated data. Consistency of both methods was compared with conducting simulation studies as well. This study proved that the quantile regression method had standard error, confidence interval width and mean square error (MSE) value smaller than the ordinary least squares method. Thus it can be concluded that the quantile regression method is able to solve the problem of heteroscedasticity and produce better model than the ordinary least squares. In addition the ordinary least squares is not able to solve the problem of heteroscedasticity.</p></div>

scholarly journals Least Squares Estimations for the General Linear Model Parameters with Epsilon Skew Normal Error Term

2020 ◽  
pp. 636-645
Author(s):  
Hussain Karim Nashoor ◽  
Ebtisam Karim Abdulah
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Least Squares Method ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
Skewed Distribution ◽  
General Linear ◽  
Average Error ◽  
Model Parameters ◽  
Skew Normal

Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calculate these estimates can be obtained. Practically, values for these estimates can be obtained only by referring to numerical methods. This research paper is dedicated to estimate parameters of the Epsilon Skew Normal General Linear Model (ESNGLM) using an adaptive least squares method, as along with the employment of the ordinary least squares method for estimating parameters of the General Linear Model (GLM). In addition, the coefficient of determination was used as a criterion to compare the models’ preference. These methods were applied to real data represented by dollar exchange rates. The Matlab software was applied in this work and the results showed that the ESNGLM represents a satisfactory model. 

scholarly journals GM(1,1;λ) with Constrained Linear Least Squares

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 278
Author(s):  
Ming-Feng Yeh ◽  
Ming-Hung Chang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Model Fitting ◽  
Ordinary Least Squares ◽  
Linear Least Squares ◽  
Unknown Parameters ◽  
Constrained Problems ◽  
Linear Least Squares Problems ◽  
Ordinary Least Squares Method ◽  
Better Than

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters, and can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.

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