Outliers In Regression Analysis Research Articles

Unpacking Outlier with Weight Least Square (Implemented on Pepper Plantations Data)

Outliers in regression analysis can cause large residuals, the diversity of the data becomes greater, causing the data to be heterogenous. If an outlier is caused by an error in recording observations or an error in preparing equipment, the outlier can be ignored or discarded before data analysis is carried out. However, if outliers exist not because of the researcher's error, but are indeed information that cannot be provided by other data, then the outlier data cannot be ignored and must be included in data analysis. There are several methods to deal with outliers. The Weight Least Square method produces good results and is quite resistive to outliers. The WLS method is used to overcome the regression model with non-constant error variance, because WLS has the ability to neutralize the consequences of violating the normality assumption caused by the presence of outliers and can eliminate the nature of unusualness and consistency of the OLS estimate. To compare the level of estimator accuracy between regression models, the mean absolute percentage error (MAPE) is used. Based on the results of this study, it was concluded that the WLS method produced a smaller Mean Absolute Percentage Error value so that the use of this method was more appropriate because it was not susceptible to the effect of outliers.

The Redescending M estimator For detection and deletion of Outliers in Regression analysis

Outliers in a statistical analysis strongly affect the performance of the ordinary least squares, such outliers need to be detected and extreme outliers deleted. Thisp is aimed at proposing a Redescending M-estimator which is more efficient and robust compared to other existing methods. The results show that the proposed method is effective in detection and deletion of extreme outliers compared to the other existing ones.

Analisis Regresi Komponen Utama Robust dengan Metode Minimum Covariance Determinant – Least Trimmed Square (MCD-LTS)

Principal Component Regression (PCR) is a method used to overcome multicollinearity problems by reducing the dimensions of independent variables to obtain new simpler variables without losing most of the information contained in the variables. If the data analyzed contain outliers, a robust method on PCR is required. In this paper we use a robust method which is a combination of Robust Principal Component Analysis using the Minimum Covariance Determinant (MCD) method and Robust Regression Analysis using Least Trimmed Square (LTS) method. The purpose of this study is to examine the robust PCR analysis using the MCD-LTS method and to know the robustness of the method by looking at its sensitivity to outliers. For this purpose we compared the MCD-LTS PCR to the classic PCR based on the bias and Mean Square Error (MSE) values on several different sample sizes and percentages of outliers. The results of this study indicate that robust PCR using MCD-LTS is effective and efficient in overcoming the problem of multicollinearity and outliers in regression analysis.

OWA Operator-Based Hybrid Framework for Outlier Reduction in Web Mining

Web mining is the process of extracting useful information from Web resources. Handling outliers is one of the primary challenges of present Web mining techniques. The complex nature of the Web, by virtue of both data and users, makes it very difficult to mine the information and convert to knowledge base with little outlier values. In this paper, a framework for reducing outliers in regression analysis with the help of ordered weighted operators (OWA) as a multicriteria decision-making problem is being formulated. First, a regression problem with a real-time Web data set will be formulated followed by solving the same with the help of a variant of OWA operators. Results, thus obtained are able to prove that outliers can be reduced significantly with the help of proposed approach.

Combining Some Biased Estimation Methods with Least Trimmed Squares Regression and its Application

<p>In the case of multicollinearity and outliers in regression analysis, the researchers are encouraged to deal with two problems simultaneously. Biased methods based on robust estimators are useful for estimating the regression coefficients for such cases. In this study we examine some robust biased estimators on the datasets with outliers in x direction and outliers in both x and y direction from literature by means of the R package ltsbase. Instead of a complete data analysis, robust biased estimators are evaluated using capabilities and features of this package.</p>

A New Algorithm for Detecting Outliers in Linear Regression

In this paper, we present a new algorithm for detecting multiple outliers in linear regression. The algorithm is based on a non-iterative robust covariance matrix and concentration steps used in LTS estimation. A robust covariance matrix is constructed to calculate Mahalanobis distances of independent variables which are then used as weights in weighted least squares estimation. A few concentration steps are then performed using the observations that have smallest residuals. We generate random data sets for $n=10^3, 10^4, 10^5$ and $p=5,10$ to show up the capabilities of the algorithm. In our Monte Carlo simulations, it is shown that our algorithm has very low masking and swamping ratios when the number of observations is up to $10^4$ in the case of maximum contamination in X-Space. It is also shown that, the algorithm is successful in the case of Y-Space outliers when the contamination level, sample size and number of parameters are up to $30\%$, $n=10^5$, and $p=10$, respectively. Bias, variance and MSE statistics are calculated for different scenarios. The reported computation time of our implementation is quite short. It is concluded that the presented algorithm is suitable and applicable for detecting multiple outliers in regression analysis with its small masking and swamping ratios, accurate estimates of regression parameters except the intercept, and short computation time in large data sets and high level of contamination. A future work is required for reducing bias and variance of the intercept estimator in the model.

PRM51 Nonparametric Regression Analysis Controls Cost Analysis in Data with Outliers

Cost analysis is often complicated to analyze because of skewed data caused by outliers in the upper tail of the distribution. Some of these outlier expenses are a result of extreme expenses before an observation period starts or during an episode of illness. Theil regression is a non-parametric linear regression method that provides accurate estimates of slope and intercept when outliers are present by calculating values based on the median. In a study intended to measure the length of time it took for patient costs to return to normal pre-episode costs after pneumonia, the Theil method was used and compared to Ordinary Least Squares (OLS) results on the same data. The baseline cost was computed as the mean cost for the six months prior to diagnosis, the study allowed for a three month episode period and the OLS and Theil regression methods were computed on the monthly costs for the six months after the episode. High cost outliers during the three month episode led to elevated costs for the first post episode period. This caused an underestimate of cost using the OLS method. Theil regression correctly estimated the increased time to return to normal in 11 of the 21 variables tracked. These differences ranged from 15 to 370 days. OLS found extended time over Theil for 5 of 21 comparisons. These differences ranged from 2 to 26 days. Agreement between OLS and Theil was found for 5 of 21 comparisons. Outliers in regression analysis frequently occur when the variable of interest is cost. Theil regression offers considerable advantages over OLS regression when the outlier is in one of the tails of the distribution. The advantages include more accurate results as well being able to use all the data without exclusion of any data elements.

A Hausman-type test to detect the presence of influential outliers in regression analysis

In regression analysis, classical estimations may be excessively influenced by a few atypical observations. We propose a Hausman-type test to balance robustness and efficiency and to check whether a robust method should be implemented. An economic application is presented.

Beware of ‘Good’ Outliers and Overoptimistic Conclusions*

AbstractThe main goal of this paper is to warn practitioners of the danger of neglecting outliers in regression analysis, in particular, good leverage points (i.e. points lying close to the regression hyperplane but outlying in the x‐dimension). While the types of outliers which do influence regression estimates (vertical outliers and bad leverage points) have been extensively investigated, good leverage points have been largely ignored, probably because they do not affect the estimated regression parameters. However, their effect on inference is far from negligible. We propose a step‐by‐step procedure to identify and treat all types of outliers. The paper of Persson and Tabellini [American Economic Review (2004) Vol. 94, pp. 25–46] linking the degree of proportionality of an electoral system to the size of government is discussed to illustrate how the choice of a measure and the existence of atypical observations may substantially influence results.

Diagnostic Methods for Detecting Outliers in Regression Analysis

Statistical modeling using linear regression in the presence of un usual observations, or outliers, is discussed and illustrated with an example from entomological field research. The effect of outliers on estimates of coefficients using least squares regression is discussed and compared with estimates using weighted least squares robust regression. The ability of the latter technique to detect outliers and estimate regression coefficients in their presence is demonstrated. Several other diagnostic displays for the objective detection of outliers and the evaluation of the fitted model are illustrated.