Empirical evaluation of the inverse Gaussian regression residuals for the assessment of influential points

Amin, Muhammad; Amanullah, M. Mohamed; Aslam, Muhammad

doi:10.1002/cem.2805

Cited by 27 publications

(14 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…GLM has three components: a response variable distribution, a linear predictor η = X ′ β that involves the regression variables, and a link function η i = g ( μ i ) that connects the linear predictor to the natural mean of the response variable. The data we are using follows the inverse Gaussian distribution, and resultantly the IGRM . For inverse Gaussian regression, inverse squared canonical link function is used:

Link function ((), Xβ) = μ^{- 2}

and

Mean function ((), μ) = {(Xβ)}^{- \frac{1}{2}}

…”

Section: Methodsmentioning

confidence: 99%

“…This data set is already used by Meloun and Mility, for detection of influential observations in LRM and found observation numbers 12, 14, 29, 33, and 34 as influential. Amin et al also used this data and detect influential points through IGRM as GLM because response variable follows inverse Gaussian distribution. They have shown that observations 5, 12, 14, 26, 27, 28, 29, and 30 are influential.…”

Section: Empirical Evaluationsmentioning

confidence: 99%

“…We include five influential points in all covariates, and the following Monte Carlo scheme with 1000 replications is considered to compare performance. The data generation is as follows: y i ~ IG ( μ , σ ), where μ = E ( y i ) = 0.5, is the arbitrary mean and σ is dispersion parameter that is assumed to follow arbitrary values σ = 0.005,0.05,0.5,3,9 (also used in Amin et al). Here, the design matrix X with no influential points of the sample sizes n = 25,50,100,and 200 is generated as X ij ~ U (0,0.5), i = 1,2, … , n ; j = 1,2,3,4, and then we make 5th, 10th, 15th, 20th, and 25th points as influential points in the X as x ij = a 0 + x ij , for i = 5,10,15,20,25; j = 1,2,3,4, where

a_{0} = {\overset{true¯}{x}}_{j} + 100

.…”

Section: Empirical Evaluationsmentioning

confidence: 99%

“…The present study is motivated by the lack of research on the performance of NPR on data contaminated by outliers, when such data are modeled particularly by IGRM and LRM. Usually, outliers are detected by some specific manner and then deleted followed by remodeling of the data . Here, we are going to handle such data by NPR method and model the data without deletion of outlying observations.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Empirical performance of nonparametric regression over LRM and IGRM addressing influential observations

Khan

Akbar

2019

Journal of Chemometrics

View full text Add to dashboard Cite

Nonparametric regression is commonly used for summarizing the relationship between variables without requiring the assumptions of model. Generalized linear model and linear regression model are usually used to examine the relationship of variables, but both are badly affected by influential observations. Due to this, detection and removal of outliers attain a lot of attention of researchers to obtain reliable estimates. We focus on such robust technique whose performance is acceptable in the presence of outliers. The present article empirically compared the performance of linear regression model and generalized linear model with multivariate nonparametric kernel regression. Here, multivariate nonparametric kernel regression is used with Gaussian kernel and six different bandwidths on Aerial biomass data. The performance of nonparametric regression with Bayesian bandwidth was found to be better as compared with other methods.

show abstract

Link function ((), Xβ) = μ^{- 2}

and

Mean function ((), μ) = {(Xβ)}^{- \frac{1}{2}}

…”

Section: Methodsmentioning

confidence: 99%

Section: Empirical Evaluationsmentioning

confidence: 99%

a_{0} = {\overset{true¯}{x}}_{j} + 100

.…”

Section: Empirical Evaluationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Empirical performance of nonparametric regression over LRM and IGRM addressing influential observations

Khan

Akbar

2019

Journal of Chemometrics

View full text Add to dashboard Cite

show abstract

“…However, according to Amin et al , in the GLM approach, the PRs are defined as

χ = \frac{y - \overset{μ}{true}}{\sqrt{Var (\overset{μ}{true})}}

. Therefore, the PR of the IG regression can be written as follows:

χ = \frac{y - \frac{1}{\sqrt{X^{'} β}}}{\sqrt{{(\frac{1}{\sqrt{X^{'} β}})}^{3}}} .

…”

Section: The Data Model For the Glm‐based Control Chartmentioning

confidence: 99%

GLM‐based control charts for the inverse Gaussian distributed response variable

Kinat

Amin

Mahmood

2019

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

In the modern era of digitalization, manufacturing industries needed monitoring methods to timely detect an abrupt change in the process. Control charts are widely used online monitoring method and used in several sectors for the surveillance of the process. Usually, control charts are developed for a single study variable, but there exists auxiliary information along with the study variable. Because of the linear relation between the study variable and auxiliary variable, several control chart studies are designed based on the simple linear regression model, but they are restricted to the normally distributed response variable. When the response variable follows an exponential family distribution, then the generalized linear modeling (GLM) approach provides better estimates. Hence, this study is designed to propose GLM‐based control charts when the response variable follows the inverse Gaussian (IG) distribution. In GLM‐based control charts, deviance and Pearson residuals of the IG regression are considered as plotting statistics. For the evaluation purpose, a simulation study is designed, and the performance of the proposed methods is compared with existing counterparts in terms of the run length properties. Moreover, run‐rules are also implemented to gain the efficiency of the Shewhart type GLM‐based control charts under small‐to‐moderate shifts. Finally, an example related to the yarn manufacturing industry is also used to highlight the importance of the stated proposal.

show abstract

The generalized linear model‐based exponentially weighted moving average and cumulative sum charts for the monitoring of high‐quality processes

Mahmood

Xie

2021

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

In this industry 4.0 revolution, most of the manufacturing processes are equipped with the digital devices which are continuously recording the data. To monitor the quality of a manufacturing system, variable about number of conforming or nonconforming items is usually used and statistical analysis based on it is further utilized for developing the policies. In this era of sophisticated and modern technology, most of the manufacturing systems are producing near zero‐defect items. Such processes are known as high‐quality processes, and their dataset consists of excess number of zeros. Generally, the zero excess or near zero‐defect dataset is well fitted by the zero‐inflated distributions, and the zero‐inflated Poisson (ZIP) and zero‐inflated Negative Binomial (ZINB) distributions are the most common models. Most of the time, in high‐quality processes, few covariates are also measured along with defect counts. Hence, to model such processes, generalized linear model (GLM) based on ZIP and ZINB distributions are used to fit the data. In monitoring perspective, data‐based control charts are designed to monitor high‐quality datasets while the GLM‐based control charts based on the residuals of the GLM models are used to monitor a change in the mean of the zero excess datasets. In this study, we have developed memory‐type data‐based and GLM‐based control charts (i.e., exponentially weighted moving average and cumulative sum) to monitor the increasing average defect counts in a high‐quality process. Further, the proposed methods are evaluated using run‐length properties and compared with its competitive charts. Furthermore, to highlight the importance of the study, the proposed methods are implemented on a dataset concerning the number of flight delays between Atlanta and Orlando airports.

show abstract

Empirical evaluation of the inverse Gaussian regression residuals for the assessment of influential points

Cited by 27 publications

References 44 publications

Empirical performance of nonparametric regression over LRM and IGRM addressing influential observations

Empirical performance of nonparametric regression over LRM and IGRM addressing influential observations

GLM‐based control charts for the inverse Gaussian distributed response variable

The generalized linear model‐based exponentially weighted moving average and cumulative sum charts for the monitoring of high‐quality processes

Contact Info

Product

Resources

About