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Linear models are particularly vulnerable to influential observations which disproportionately affect the model's parameter estimates. Multiple statistics and numerous cut-off values have been proposed to detect highly influential observations including Cook’s Distance (CD), Standardized Difference of Fits (DFFITS) and Standardized Difference of Beta (DFBETAS). This paper reports on a Monte Carlo simulation study that assesses the effectiveness of these methods and recommended cut-off values under various conditions, including different sample sizes, numbers of predictors, strengths of variable associations, and non-sequential versus sequential analysis approaches within a multiple linear regression framework. The findings suggest that the proportion of observations identified as highly influential varies significantly based on the chosen diagnostic method and the thresholds used for detection. Consequently, researchers should consider the implications of their methodological choices and the thresholds they apply when identifying influential data points.

This study compares the performance of link functions for diagnostic methods to diagnose influential observations in the logistic regression model. Four link functions, i.e. logit, probit, clog-log and cauchit are considered to identify which link function gives the best results. We used Cook's distance, DIFFITS and CVR as diagnostic methods. We compare the performance of influence diagnostics with the link functions using the simulation study and a real-life application. Results show that the CVR with logit link function is a good method for small explanatory variables. For large explanatory variables and small sample sizes, the performance of the cook's distance and DIFFITS with probit and logit link function is better than the CVR method. Similarly, for large explanatory variables and sample sizes, the cook's distance (with probit and logit link functions) and CVR with cauchit link function give the same performance and are better than the DFFITS method. [ABSTRACT FROM AUTHOR]

Abstract Background Collection of intensive longitudinal health outcomes allows joint modeling of their mean (location) and variability (scale). Focusing on the location of the outcome, measures to detect influential subjects in longitudinal data using standard mixed-effects regression models (MRMs) have been widely discussed. However, no existing approach enables the detection of subjects that heavily influence the scale of the outcome. Methods We propose applying mixed-effects location scale (MELS) modeling combined with commonly used influence measures such as Cook’s distance and DFBETAS to fill this gap. In this paper, we provide a framework for researchers to follow when trying to detect influential subjects for both the scale and location of the outcome. The framework allows detailed examination of each subject’s influence on model fit as well as point estimates and precision of coefficients in different components of a MELS model. Results We simulated two common scenarios in longitudinal healthcare studies and found that influence measures in our framework successfully capture influential subjects over 99% of the time. We also re-analyzed data from a health behavior study and found 4 particularly influential subjects, among which two cannot be detected by influence analyses via regular MRMs. Conclusion The proposed framework can help researchers detect influential subject(s) that will be otherwise overlooked by influential analysis using regular MRMs and analyze all data in one model despite influential subjects.

The Underhill–Zucchini model of avian moult is a statistical simplification for the analysis of primary moult, a complex biological system in birds. As with all such models, conclusions can be biased if a subset of the data used to fit the model is strongly influential on the results. In the analysis of primary moult of a species, it is standard practice to assemble as many records as possible, frequently from different years or localities. We developed an approach, based on the concepts underpinning Cook's distance in regression, to evaluate the influence on the estimated moult parameters of groups of records that differ from the bulk of the data. The method is applied to a simulated dataset. [ABSTRACT FROM AUTHOR]

Little is known about the biology of the Red-headed Finch Amadina erythrocephala. This study investigates its primary moult, the first aspect of its life history to be looked at in depth. Additionally, we used a modified Cook's distance algorithm to explore the influence of individual years on the moult parameter estimates. Lastly, the primary moult of Red-headed Finches is compared to that of other passerines resident in the Highveld region of South Africa. Red-headed Finches breed through the Highveld winter, and start moult on 22 August, on average. Moult extends through spring and most of the summer, reaching completion on 22 February, on average. However, the moult started unusually early in the years 1988, 2005, 2008 and 2019, whereas in 2017 moult started unusually late. The duration of moult was estimated to be 185 days. The majority of other passerines resident in the central Highveld breed through summer, undergo primary moult in autumn, and complete moult before the regular frosts start to occur during the Highveld winter. The moult duration of the Red-headed Finch is substantially longer than that of other resident passerines. [ABSTRACT FROM AUTHOR]

Background: Collection of intensive longitudinal health outcomes allows joint modeling of their mean (location) and variability (scale). Focusing on the location of the outcome, measures to detect influential subjects in longitudinal data using standard mixed-effects regression models (MRMs) have been widely discussed. However, no existing approach enables the detection of subjects that heavily influence the scale of the outcome. Methods: We propose applying mixed-effects location scale (MELS) modeling combined with commonly used influence measures such as Cook's distance and DFBETAS to fill this gap. In this paper, we provide a framework for researchers to follow when trying to detect influential subjects for both the scale and location of the outcome. The framework allows detailed examination of each subject's influence on model fit as well as point estimates and precision of coefficients in different components of a MELS model. Results: We simulated two common scenarios in longitudinal healthcare studies and found that influence measures in our framework successfully capture influential subjects over 99% of the time. We also re-analyzed data from a health behavior study and found 4 particularly influential subjects, among which two cannot be detected by influence analyses via regular MRMs. Conclusion: The proposed framework can help researchers detect influential subject(s) that will be otherwise overlooked by influential analysis using regular MRMs and analyze all data in one model despite influential subjects. [ABSTRACT FROM AUTHOR]

Brain cancer is one of the most deadly cancers, with a very low survival rate. By understanding the factors that lead to cancer spreading, practitioners can concentrate their efforts on providing the most effective treatment, and they can modify the treatment plan as necessary. Also, knowing the likelihood of a patient’s survival over a specified time period can enable them to make informed decisions about adjusting their routines, future investments, and other health-related decisions. The use of data-driven models in cancer research has gained increased popularity over the past several decades. Moreover, there is still much uncertainty surrounding the factors that contribute to survival of cancer, making it difficult to develop a model. The existing literature on brain cancer contains a variety of machine learning models. However, many of them lack a high degree of accuracy, and, in medical research, accuracy is essential to the proper guidance of treatment decisions. Therefore, we have proposed a framework comprising multiple phases of classical statistics and machine learning methods to find a parsimonious model with a high degree of accuracy (98.9%) for predicting brain cancer survivability. Furthermore, we develop a prototype web-based interactive tool to facilitate the practical implementation of the proposed model and provide a deeper understanding of how a particular factor affects survival when other factors remain unchanged. By integrating this tool into healthcare settings, medical professionals can rapidly detect potentially vulnerable patients, and it can also be useful in determining the most effective treatment plan.

Abstract The presence of influential observations affect the accuracy of the model results. Similarly, the multicollinearity is the other problem that affect accuracy. Literature has shown that both the presence of influential observations and multicollinearity can arise in the model at the same time. This situation is also encountered in the geographically weighted regression. This study introduces the case-deletion diagnostics for the ridge estimator in geographically weighted regression model. To identify the influential observations, Cook’s Distance and Pena’s Statistics are adapted for the geographically weighted ridge regression model. The proposed diagnostics have been applied through a well-known real data. The influential observations have been detected by Cook’s Distance and Pena’s Statistics plots in real data. In addition, the simulated data has been used to reveal the performance of the proposed diagnostics. The results of the simulation showed that Pena’s Statistics has been very good at detecting high leverage outliers in the large data sets, especially. [ABSTRACT FROM AUTHOR]

This article investigates the performance of several residuals for the Cox proportional hazards regression model to diagnose the influential observations. The standardized and adjusted forms of residuals are proposed for Cox proportional hazards regression model. In addition, Cook's distance is proposed for both standardized and adjusted residuals. The assessment of different residuals for the identification of influential observations is made through the Monte Carlo simulation. A real dataset of bone marrow transplant Leukaemia is analyzed to show the benefit of the proposed methods. Simulation and application results show that the standardized and adjusted residuals based on the Cox–Snell method perform best for the detection of influential points. Furthermore, the standardized, and adjusted Martingale and deviance residuals work better when the sample size is large. [ABSTRACT FROM AUTHOR]

In this paper we present several diagnostic measures for the class of nonparametric regression models with symmetric random errors, which includes all continuous and symmetric distributions. In particular, we derive some diagnostic measures of global influence such as residuals, leverage values, Cook's distance and the influence measure proposed by Peña (Technometrics 47(1):1–12, 2005) to measure the influence of an observation when it is influenced by the rest of the observations. A simulation study to evaluate the effectiveness of the diagnostic measures is presented. In addition, we develop the local influence measure to assess the sensitivity of the maximum penalized likelihood estimator of smooth function. Finally, an example with real data is given for illustration. [ABSTRACT FROM AUTHOR]

In this article, we propose some diagnostic techniques for the inverse Gaussian regression model (IGRM), which are appropriate for modeling the response variable that undertakes positively skewed continuous dataset. Moreover, two new diagnostic methods are mainly proposed for the IGRM, which named as covariance ratio (CVR) and Welsch's distance (WD). The comparison of our proposed methods of influence diagnostics with the existing approaches has been made through Monte Carlo simulation under different factors. In addition, the benefit of the proposed methods is assessed using a real application. Based on the simulation and empirical application results, we observed that the performance of the proposed method is better than the existing methods for detection of influential observations. [ABSTRACT FROM AUTHOR]

The subject of the thesis concerns the application of selected statistical methods searching for outliers in the process of determining the value of real estate, based on a functional model adjusted to market data.

The Generalised linear mixed model (GLMM) is widely used for modelling environmental data. However, such data are prone to influential observations, which can distort the estimated exposure-response curve particularly in regions of high exposure. Deletion diagnostics for iterative estimation schemes commonly derive the deleted estimates based on a single iteration of the full system holding certain pivotal quantities such as the information matrix to be constant. In this paper, we present an approximate formula for the deleted estimates and Cook's distance for the GLMM, which does not assume that the estimates of variance parameters are unaffected by deletion. The procedure allows the user to calculate standardised DFBETAs for mean as well as variance parameters. In certain cases such as when using the GLMM as a device for smoothing, such residuals for the variance parameters are interesting in their own right. In general, the procedure leads to deleted estimates of mean parameters, which are corrected for the effect of deletion on variance components as estimation of the two sets of parameters is interdependent. The probabilistic behaviour of these residuals is investigated and a simulation based procedure suggested for their standardisation. The method is used to identify influential individuals in an occupational cohort exposed to silica. The results show that failure to conduct post model fitting diagnostics for variance components can lead to erroneous conclusions about the fitted curve and unstable confidence intervals.

This paper investigates the impact of gender on the individual probability of being unemployed and makes a cross‑country comparison across 13 European countries during the European recession. Applying a general logit model for each country and capital, whilst controlling for the year, as well as for individual and regional characteristics, the probability of unemployment was estimated using individual labour force data from 2011 to 2014. Cook’s distance is used to examine the differences between labour markets of capital regions (or cities) and non‑capital regions. Using the size of Cook’s distance, models are calibrated, and models which include the degree of urbanization and occupation type are evaluated. The results are presented in the form of a spatial map and show that gender affects the probability of unemployment in the majority of the analysed countries. Overall, the effect is lower in capital than in non‑capital regions.

Detecting anomalous changes in remote sensing images is a challenging problem, where many approaches and techniques have been presented so far. We rely on the standard field of multivariate statistics of diagnostic measures, which are concerned about the characterization of distributions, detection of anomalies, extreme events, and changes. One useful tool to detect multivariate anomalies is the celebrated Cook's distance. Instead of assuming a linear relationship, we present a novel kernelized version of the Cook's distance to address anomalous change detection in remote sensing images. Due to the large computational burden involved in the direct kernelization, and the lack of out-of-sample formulas, we introduce and compare both random Fourier features and Nyström implementations to approximate the solution. We study the kernel Cook's distance for anomalous change detection in a chronochrome scheme, where the anomalousness indicator comes from evaluating the statistical leverage of the residuals of regressors between time acquisitions. We illustrate the performance of all algorithms in a representative number of multispectral and very high resolution satellite images involving changes due to droughts, urbanization, wildfires, and floods. Very good results and computational efficiency confirm the validity of the approach.

In a linear regression model, the estimation of regression parameters is affected by some anomalous observations in the data set. Thus, identification of these observations is one of the essential steps in regression analysis. Detection of these influential observations becomes more complex when serious multicollinearity among regressors is also observed. In the present article, we formulated Pena's statistic for each point while considering the modified ridge regression (MRR) estimator. Using this statistic, we showed that when MRR was used to mitigate the effects of multicollinearity, the influence of some observations could be significantly changed. The normality of this statistic was also discussed and it was proved that it could detect a subset of high modified ridge leverage outliers. The Monte Carlo simulations were used for empirical results and an example of real data was presented for illustration. [ABSTRACT FROM AUTHOR]

In a quantitative synthesis of studies via meta‐analysis, it is possible that some studies provide a markedly different relative treatment effect or have a large impact on the summary estimate and/or heterogeneity. Extreme study effects (outliers) can be detected visually with forest/funnel plots and by using statistical outlying detection methods. A forward search (FS) algorithm is a common outlying diagnostic tool recently extended to meta‐analysis. FS starts by fitting the assumed model to a subset of the data which is gradually incremented by adding the remaining studies according to their closeness to the postulated data‐generating model. At each step of the algorithm, parameter estimates, measures of fit (residuals, likelihood contributions), and test statistics are being monitored and their sharp changes are used as an indication for outliers. In this article, we extend the FS algorithm to network meta‐analysis (NMA). In NMA, visualization of outliers is more challenging due to the multivariate nature of the data and the fact that studies contribute both directly and indirectly to the network estimates. Outliers are expected to contribute not only to heterogeneity but also to inconsistency, compromising the NMA results. The FS algorithm was applied to real and artificial networks of interventions that include outliers. We developed an R package (NMAoutlier) to allow replication and dissemination of the proposed method. We conclude that the FS algorithm is a visual diagnostic tool that helps to identify studies that are a potential source of heterogeneity and inconsistency. [ABSTRACT FROM AUTHOR]

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In the process of building a linear regression model, the essential part is to identify influential observations. Various influence measures involving Cook's distance and DFFITS are designed to detect the linear regression's influential observations using the Least Squares (LS). The existence of influential observations in the data is complicated by the presence of severe collinearity and affects the efficiency of the detection measures. This paper proposes new diagnostic methods based on the Liu type estimator (LTE) defined by Liu [1]. The Cook's distance and DFFITS for the LTE are introduced. Moreover, approximate formulas for Cook's distance and DFFITS are also proposed for LTE. Two real data sets with a high level of multicollinearity among the explanatory variables as well as the simulation study are used to illustrate and evaluate performance of the methodologies presented in this paper.

In many practical classification problems, datasets would have a portion of outliers, which could greatly affect the performance of the constructed models. In order to address this issue, we apply the group method of data handing (GMDH) neural network in outlier detection. This study builds a GMDH-based outlier detection (GOD) model. This model first implements feature selection in the training set L using GMDH neural network. Then a new training set L′ can be obtained by mapping the selected key feature subset. Next, a linear regression model can be constructed in the set L′ by ordinary least squares estimation. Further, it eliminates a sample from the set L′ randomly every time, and then rebuilds a linear regression model. Finally, outlier detection is realized by calculating Cook's distance for each sample. Four different customer classification datasets are used to conduct experiments. Results show that GOD model can effectively eliminate outliers, and compared with the five existing outlier detection models, it generally performs significantly better. This indicates that eliminating outliers can effectively enhance classification accuracy of the trained classification model. [ABSTRACT FROM AUTHOR]

Support vector machines (SVM) is very efficient and popular tool for classification, however, its non-robustness to outliers is a critical drawback. In fact, SVM is more sensitive to outliers than other classifiers since the optimal separating hyperplane obtained by SVM is solely determined by support vectors. So far all the studies about outliers in SVM are done by trying to minimize the effect of outliers by specifying robust loss functions. In this paper, we propose a version of Cook's distance based on the deletion method and the infinitesimal perturbation method. Also, we express the Cook's distance in terms of basic building blocks such as residual and leverage. Further, we propose a simple measure which can be used as either descriptive statistics in SVM diagnostics or approximate measure when the Cook's distance cannot be computed due to the high-dimensionality. [ABSTRACT FROM AUTHOR]

Probability of default (PD) estimation is essential to the calculation of expected credit loss under the Basel III framework and the International Financial Reporting Standard 9. Gross domestic product (GDP) growth has been adopted as a key determinant in PD estimation models. However, PD models with a GDP covariate may not perform well under aberrant (i.e., outlier) conditions such as the COVID-19 pandemic. This study explored the robustness of a PD model with a GDP determinant (the test model) in comparison with that of a PD model with a credit default swap index (CDX) determinant (the alternative model). The test model had a significantly greater ratio of increase in Akaike information criterion than the alternative model in comparisons of the fit performance of models including 2020 data with that of models excluding 2020 data (i.e., that do not cover the COVID-19 pandemic). Furthermore, the Cook’s distance of the 2020 data of the test model was significantly greater than that of the alternative model. Therefore, the test model exhibited a serious robustness issue in outlier scenarios, such as the COVID-19 pandemic, whereas the alternative model was more robust. This finding opens the prospect for the CDX to potentially serve as an alternative to GDP in PD estimation models.

Linear models where the response is a function and the predictors are vectors are useful in analyzing data from designed experiments and other situations with functional observations. Residual analysis and diagnostics are considered for such models. Studentized residuals are defined and their properties are studied. Chi-square quantile-quantile plots are proposed to check the assumption of Gaussian error process and outliers. Jackknife residuals and an associated test are proposed to detect outliers. Cook’s distance is defined to detect influential cases. The methodology is illustrated by an example from a robust design study.

In this paper, two new multiple influential observation detection methods, GCD.GSPR and mCD*, are introduced for logistic regression. The proposed diagnostic measures are compared with the generalized difference in fits (GDFFITS) and the generalized squared difference in beta (GSDFBETA), which are multiple influential diagnostics. The simulation study is conducted with one, two and five independent variable logistic regression models. The performance of the diagnostic measures is examined for a single contaminated independent variable for each model and in the case where all the independent variables are contaminated with certain contamination rates and intensity. In addition, the performance of the diagnostic measures is compared in terms of the correct identification rate and swamping rate via a frequently referred to data set in the literature. [ABSTRACT FROM AUTHOR]

Statistical methods are effectively used in the evaluation of pharmaceutical formulations instead of laborious liquid chromatography. However, signal overlapping, nonlinearity, multicollinearity and presence of outliers deteriorate the performance of statistical methods. The Partial Least Squares Regression (PLSR) is a very popular method in the quantification of high dimensional spectrally overlapped drug formulations. The SIMPLS is the mostly used PLSR algorithm, but it is highly sensitive to outliers that also effect the diagnostics. In this paper, we propose new robust multivariate diagnostics to identify outliers, influential observations and points causing non-normality for a PLSR model. We study performances of the proposed diagnostics on two everyday use highly overlapping drug systems: Paracetamol-Caffeine and Doxylamine Succinate-Pyridoxine Hydrochloride. [ABSTRACT FROM AUTHOR]

Abstract Influence diagnostics are used to identify data points that have a disproportionate impact on model parameters, performance and/or predictions, providing valuable information for use in model calibration. Regression-theory influence diagnostics identify influential data by combining the leverage and the standardised residuals, and are computationally more efficient than case-deletion approaches. This study evaluates the performance of a range of regression-theory influence diagnostics on ten case studies with a variety of model structures and inference scenarios including: nonlinear model response, heteroscedastic residual errors, data uncertainty and Bayesian priors. A new technique is developed, generalised Cook's distance, that is able to accurately identify the same influential data as standard case deletion approaches (Spearman rank correlation: 0.93–1.00) at a fraction of the computational cost (<1%). This is because generalised Cook's distance uses a generalised leverage formulation which outperforms linear and nonlinear leverage formulations due to less restrictive assumptions. Generalised Cook's distance has the potential to enable influential data to be efficiently identified on a wide variety of hydrological and environmental modelling problems. Highlights • Influential data points have a disproportionate impact on model predictions. • A new generalised Cook's distance accurately identifies influential data points. • More efficient (<1% computational cost) than standard case-deletion approaches. • Applies to nonlinear regression and hydrological models with heteroscedastic errors. • Can be used in a Bayesian framework with priors or data uncertainty. [ABSTRACT FROM AUTHOR]

This study examines regional variations in spatial inequality measured by consumption expenditure using National Sample Survey Office data and social indicators from the census of India. It classifies rural people from survey-based, unit-level household data into bottom 25%, middle 50%, and top 25% economic quartiles. The observations include 559 common districts over time across rural India. Contemporary studies on regional development are based on the 'state' as the unit of analysis. The main objective of this study is to investigate whether sub-state disparities increased during the highest growth phase in India since 2004/2005, thereby helping determine whether the Mahatma Gandhi National Rural Employment Guarantee Act had any lasting impact on the living standards of utterly deprived people beyond the state capitals. In addition to some non-parametric tests, the study conducts alternative multivariate regressions to investigate the factors responsible for rising deprivation and the impact of policy. The statistical evidence is highly alarming and warrant urgent policy initiatives to reach the poor living in alienated regions. [ABSTRACT FROM AUTHOR]

In fitting regression model, one or more observations may have substantial effects on estimators. These unusual observations are precisely detected by a new diagnostic measure, Pena's statistic. In this article, we introduce a type of Pena's statistic for each point in Liu regression. Using the forecast change property, we simplify the Pena's statistic in a numerical sense. It is found that the simplified Pena's statistic behaves quite well as far as detection of influential observations is concerned. We express Pena's statistic in terms of the Liu leverages and residuals. The normality of this statistic is also discussed and it is demonstrated that it can identify a subset of high Liu leverage outliers. For numerical evaluation, simulated studies are given and a real data set has been analysed for illustration. [ABSTRACT FROM AUTHOR]

Influence diagnostics aim to identify a small number of influential data points that have a disproportionate impact on the model parameters and/or predictions. The key issues with current influence diagnostic techniques are that the regression-theory approaches do not provide hydrologically relevant influence metrics, while the case-deletion approaches are computationally expensive to calculate. The main objective of this study is to introduce a new two-stage hybrid framework that overcomes these challenges, by delivering hydrologically relevant influence metrics in a computationally efficient manner. Stage one uses computationally efficient regression-theory influence diagnostics to identify the most influential points based on Cook’s distance. Stage two then uses case-deletion influence diagnostics to quantify the influence of points using hydrologically relevant metrics. To illustrate the application of the hybrid framework, we conducted three experiments on 11 hydro-climatologically diverse Australian catchments using the GR4J hydrological model. The first experiment investigated how many data points from stage one need to be retained in order to reliably identify those points that have the hightest influence on hydrologically relevant metrics. We found that a choice of 30–50 is suitable for hydrological applications similar to those explored in this study (30 points identified the most influential data 98% of the time and reduced the required recalibrations by 99% for a 10 year calibration period). The second experiment found little evidence of a change in the magnitude of influence with increasing calibration period length from 1, 2, 5 to 10 years. Even for 10 years the impact of influential points can still be high (>30% influence on maximum predicted flows). The third experiment compared the standard least squares (SLS) objective function with the weighted least squares (WLS) objective function on a 10 year calibration period. In two out of three flow metrics there was evidence that SLS, with the assumption of homoscedastic residual error, identified data points with higher influence (largest changes of 40%, 10%, and 44% for the maximum, mean, and low flows, respectively) than WLS, with the assumption of heteroscedastic residual errors (largest changes of 26%, 6%, and 6% for the maximum, mean, and low flows, respectively). The hybrid framework complements existing model diagnostic tools and can be applied to a wide range of hydrological modelling scenarios. [ABSTRACT FROM AUTHOR]

Birds play an important role in modern and historic Puebloan ceremonialism, with feathers, wings, stuffed birds, and live birds used for ceremonies, sacrifices, and creation of ritual paraphernalia. Archaeological evidence suggests birds played an ideological and ritual role for some prehispanic Southwestern groups as well. Here, we explore the use of avian remains for ritual purposes at Pueblo Bonito by presenting new evidence from the northern burial cluster. Drawing on multiple quantitative measures, we establish the dissimilarity of this assemblage to other Chacoan sites. We demonstrate that an unusually wide variety of avian species was deposited in the northern burial cluster, particularly wing elements that may reflect wing fan deposition. These findings improve our understanding of ritual life at Pueblo Bonito and also show the utility of using both qualitative and quantitative data to create a more accurate understanding of past ceremonial activity. [ABSTRACT FROM PUBLISHER]

The classical assumption in generalized linear measurement error models (GLMEMs) is that measurement errors (MEs) for covariates are distributed as a fully parametric distribution such as the multivariate normal distribution. This paper uses a centered Dirichlet process mixture model to relax the fully parametric distributional assumption of MEs, and develops a semiparametric Bayesian approach to simultaneously obtain Bayesian estimations of parameters and covariates subject to MEs by combining the stick-breaking prior and the Gibbs sampler together with the Metropolis-Hastings algorithm. Two Bayesian case-deletion diagnostics are proposed to identify influential observations in GLMEMs via the Kullback-Leibler divergence and Cook's distance. Computationally feasible formulae for evaluating Bayesian case-deletion diagnostics are presented. Several simulation studies and a real example are used to illustrate our proposed methodologies. [ABSTRACT FROM AUTHOR]

Quasi-likelihood nonlinear models (QLNMs) are an extension of generalized linear model and include a widen class of models as special cases. This article investigates some diagnostic methods in QLNMs. An equivalency between a case-deletion model and a mean-shift outlier model in QLNM is established. Two simulation study and a real dataset are used to illustrate the proposed diagnostic methods. [ABSTRACT FROM AUTHOR]

An outlier is defined as an observation that is significantly different from the others in its dataset. In high-dimensional regression analysis, datasets often contain a portion of outliers. It is important to identify and eliminate the outliers for fitting a model to a dataset. In this paper, a novel outlier detection method is proposed for high-dimensional regression problems. The leave-one-out idea is utilized to construct a novel outlier detection measure based on distance correlation, and then an outlier detection procedure is proposed. The proposed method enjoys several advantages. First, the outlier detection measure can be simply calculated, and the detection procedure works efficiently even for high-dimensional regression data. Moreover, it can deal with a general regression, which does not require specification of a linear regression model. Finally, simulation studies show that the proposed method behaves well for detecting outliers in high-dimensional regression model and performs better than some other competing methods. [ABSTRACT FROM AUTHOR]

A method for detecting outliers in axial data has been proposed by Best and Fisher (1986). For extending that work, we propose four new methods. Two of them are suitable for outlier detection and they depend on the classic geodesic distance and a modified version of this distance. The other two procedures, which are designed for influential observation detection, are based on the Kullback–Leibler and Cook’s distances. Some simulation experiments are performed to compare all considered methods. Detection and error rates are used as comparison criteria. Numerical results provide evidence in favor of the KL distance. [ABSTRACT FROM AUTHOR]

When considering data from many trials, it is likely that some of them present a markedly different intervention effect or exert an undue influence on the summary results. We develop a forward search algorithm for identifying outlying and influential studies in meta-analysis models. The forward search algorithm starts by fitting the hypothesized model to a small subset of likely outlier-free studies and proceeds by adding studies into the set one-by-one that are determined to be closest to the fitted model of the existing set. As each study is added to the set, plots of estimated parameters and measures of fit are monitored to identify outliers by sharp changes in the forward plots. We apply the proposed outlier detection method to two real data sets; a meta-analysis of 26 studies that examines the effect of writing-to-learn interventions on academic achievement adjusting for three possible effect modifiers, and a meta-analysis of 70 studies that compares a fluoride toothpaste treatment to placebo for preventing dental caries in children. A simple simulated example is used to illustrate the steps of the proposed methodology, and a small-scale simulation study is conducted to evaluate the performance of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An influence measure known as Cook's distance has been used for judging the influence of each observation on the least squares estimate of the parameter vector. The distance does not reflect the distributional property of the change in the least squares estimator of the regression coefficients due to case deletions: the distribution has a covariance matrix of rank one and thus it has a support set determined by a line in the multidimensional Euclidean space. As a result, the use of Cook's distance may fail to correctly provide information about influential observations, and we study some reasons for the failure. Three illustrative examples will be provided, in which the use of Cook's distance fails to give the right information about influential observations or it provides the right information about the most influential observation. We will seek some reasons for the wrong or right provision of information. [ABSTRACT FROM AUTHOR]

Interaction orientation reflects the ability of a company to interact with the individual customer and to gather information from successful interactions. Four dimensions of interaction orientation are identified in the literature: customer concept, interaction response capacity, customer empowerment and customer value management (Ramani and Kumar, 2008). This study shows that indeed a fifth dimension of interaction orientation exists and investigates the determinants, moderators and consequences of this construct. The first notable finding is that B2B companies exhibit a greater degree of interaction orientation than B2C firms. Ramani and Kumar hypothesized that in their study. We show that there are B2C industries such as financial services, whose companies also have a greater interaction orientation. This could be the reason why the authors could not prove their hypothesis. Furthermore, we examine the influence of strategic orientations on organizational performances and compare various orientations with each other.