Robust Regression Analysis Study for Data with Outliers at Some Significance Levels

Nugroho, Waego Hadi; Wardhani, Ni Wayan Surya; Fernandes, Adji Achmad Rinaldo; Solimun, Solimun

doi:10.13189/ms.2020.080401

Cited by 4 publications

(5 citation statements)

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“…This study investigates performances regression in big data. Regression is a method used to build the predictive model [20]. Regression analysis is a supervised machine learning technique for building a model and evaluating its performance for a continuous response based on the relationship among several variables.…”

Section: Regression Learningmentioning

confidence: 99%

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Hybrid model in machine learning–robust regression applied for sustainability agriculture and food security

Mukhtar

Ali

Ismail

et al. 2022

IJECE

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<span lang="EN-US">A dataset containing 1924 observations used in this study to evaluate the effect of 435 different independent variables on one dependent variable. Big data has some issues such as irrelevant variables and outliers. Therefore, this study focused on analysing and comparing the impact of three different variable selection based on machine learning techniques, including random forest (RF), support vector machines (SVM), and Boosting. Further, the M robust regression was applied to address the outliers using M–bi square, M–Hampel, and M–Huber. Random forest and M-Hampel results revealed the significant comparing from the other methods such as mean absolute error (MAE) 175.33995, mean square error (MSE) 31.8608, mean average percentage error (MAPE) 9.16091, sum of square error (SSE) 89270.45, R–square 0.829511, and R–square adjusted 0.82670. Also, these techniques indicated that the 8 selection criteria were lower than the other techniques including Akaike information criterion (AIC) 47.25915, generalized cross validation (GCV) 47.27169, hannan-quinn (HQ) 47.60351, RICE (47.2845), SCHWARZ 51.7099, sigma square (SGMASQ) 46.50605, SHIBATA 47.23489, and final prediction error (FPE) 47.25929. Therefore, the study recommended that the best random forest and M-Hampel models are helpful to show the minimum issues and efficient validation for analysing and comparing big data.</span>

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Section: Regression Learningmentioning

confidence: 99%

“…Several robust-to outliers have been proposed in the statistical literature [18], [19]. M-robust regressions can handle outliers [20]. M-robust regressions include M-bi square Tukey, M-Hampel, and M-Huber.…”

Section: Introductionmentioning

confidence: 99%

Hybrid model in machine learning–robust regression applied for sustainability agriculture and food security

Mukhtar

Ali

Ismail

et al. 2022

IJECE

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“…This research proposes the use of a robust method to overcome the problems faced by the ML estimator for POM. Among the popular robust estimates of the regression model are the least absolute deviations, the least median of squares, the M-estimator, and the MM-estimator Abu-Shawiesh, Riaz, and Khaliq [19], Nugroho, Wardhani, Fernandes, and Solimun [20].…”

Section: Robust Estimationmentioning

confidence: 99%

Robust Estimation for Proportional Odds Model through Monte Carlo Simulation

Zulkifli¹,

Mohamed²,

Azmee³

et al. 2021

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Ordinal regression is used to model the ordinal response variable as functions of several explanatory variables. The most commonly used model for ordinal regression is the proportional odds model (POM). The classical technique for estimating the unknown parameters of this model is the maximum likelihood (ML) estimator. However, this method is not suitable for solving problems with extreme observations. A robust regression method is needed to handle the problem of extreme points in the data. This study proposes Huber M-estimator as a robust method to estimate the parameters of the POM with a logistic link function and polytomous explanatory variables. This study assesses ML estimator performance and the robust method proposed through an extensive Monte Carlo simulation study conducted using statistical software, R. Measurement for comparisons are bias, RMSE, and Lipsitzs' goodness of fit test. Various sample sizes, percentages of contamination, and residual standard deviations are considered in the simulation study. Preliminary results show that Huber estimates provide the best results for parameter estimation and overall model fitting. Huber's estimator has reached a 50% breakdown point for data containing extreme points that are quite far from most points. In addition, the presence of extreme points that have only a distance of two times far from most points has no major impact on ML estimates. This means that the estimates for ML and Huber may yield the same results if the model's residual values are between -2 and 2. This situation may also occur for data with a percentage of contamination below 5%.

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“…One method for estimating parameters in the GWPR is weighted least squares (Bruna and Yu (2016); Li and Managi (2022)), which is susceptible to outliers (Zhang and Mei, 2011). The existence of outliers causes the parameter estimation of the regression model using Least Squares method to be biased, and parameter estimation results become inefficient because of large residual values (Nugroho et al, 2020). Outliers can have a significant impact on the estimation parameters of the regression model.…”

Section: Introductionmentioning

confidence: 99%

Applied fixed effect of Geographically Weighted Panel Regression (GWPR) with M- Estimator approach to estimate sugarcane yield data in East Java

Mondiana,

Pramoedyo,

Iriany

et al. 2024

JANS

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Geographically Weighted Panel Regression (GWPR), a combination of panel regression and geographically weighted regression (GWR), is used to analyze panel data and capture diverse relationship between locations. GWPR was developed on data with panel-fixed effects and applied to modeling data with spatial heterogeneity and time series. One method for estimating parameters in the GWPR is weighted least squares (WLS), which are sensitive to outliers. The present study aimed to use the M- method to estimate GWPR model parameters in data containing outliers using fixed-effect GWPR modeling for the sugar cane yield in East Java of Indonesia from 2019 to 2021. Sugarcane yield data in East Java contained outliers in several areas, including Malang, Blitar, and Ngawi Districts. Because the data contains outliers, a robust method with the M estimator was applied. The results showed that plantation areas significantly affected production in all districts.The R2 of the model was 0.87, showing that GWPR model with M estimation was appropriate in predicting sugarcane yield. Based on the Akaike Information Criterion (AIC) value, the GWPR model with M estimation had better performance than GWPR model alone.

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Robust Regression Analysis Study for Data with Outliers at Some Significance Levels

Cited by 4 publications

References 1 publication

Hybrid model in machine learning–robust regression applied for sustainability agriculture and food security

Hybrid model in machine learning–robust regression applied for sustainability agriculture and food security

Robust Estimation for Proportional Odds Model through Monte Carlo Simulation

Applied fixed effect of Geographically Weighted Panel Regression (GWPR) with M- Estimator approach to estimate sugarcane yield data in East Java

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