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For the reliable results of regression analysis, influence diagnostic methods play an important role. The performance of various proposed residuals for the gamma-Pareto regression model (G-PRM) is presented in this study. These proposed residuals are partitioned into standardized and adjusted residual forms. For the detection of influential observations, difference of fits (DFFITS) was used in both standardized and adjusted residuals. To detect influential points, these residuals are compared through Monte Carlo Simulation also real data (Ardennes data) are analysed to show the benefits of the proposed methods. The likelihood residuals performed better for small dispersion than others. Additionally, all forms of adjusted residuals are the same, not much more efficient than the standardized form. All standardized residuals behave in the same way for wider dispersion, and they are superior to the likelihood residuals for the detection of influential points. [ABSTRACT FROM AUTHOR]

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 high-dimensional regression, the presence of influential observations may lead to inaccurate analysis results so that it is a prime and important issue to detect these unusual points before statistical regression analysis. Most of the traditional approaches are, however, based on single-case diagnostics, and they may fail due to the presence of multiple influential observations that suffer from masking effects. In this paper, an adaptive multiple-case deletion approach is proposed for detecting multiple influential observations in the presence of masking effects in high-dimensional regression. The procedure contains two stages. Firstly, we propose a multiple-case deletion technique, and obtain an approximate clean subset of the data that is presumably free of influential observations. To enhance efficiency, in the second stage, we refine the detection rule. Monte Carlo simulation studies and a real-life data analysis investigate the effective performance of the proposed procedure. [ABSTRACT FROM AUTHOR]

In this paper, we propose the zero-modified Poisson-Shanker regression model as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros in the presence of covariates. The zero modification has been incorporated using the zero-truncated Poisson-Shanker distribution. The zero-modified Poisson-Shanker distribution has been written as a hurdle model using a simple reparameterization of the probability function which leads to the fact that the proposed model can be fitted without any previous information about the zero modification present in a given dataset. The standard Bayesian procedures have been considered for estimation and inference. A simulation study has been presented to illustrate the performance of the developed methodology. The usefulness of the proposed model has been evaluated using a real dataset on fetal deaths notification data in Bahia State, Brazil. A sensitivity study to detect points which can influence the parameter estimates has been performed using Kullback-Leibler divergence measure. The randomized quantile residuals have been considered for the model validation issue. General comparison of the proposed model with some well-known discrete distributions has been provided. [ABSTRACT FROM AUTHOR]

In this article, we propose a new heteroskedastic consistent covariance matrix estimator, HC6, which is based on deviance measure. We have studied the finite sample behavior of the test statistic based on this new HC estimator. We compare its performance with other HC estimators namely HC1, HC3 and HC4m, which are also used in case of leverage observations. Extensive simulation studies are used to study the effect of various levels of heteroskedasticity on the performance of the quasi tests based on HC estimators. Results showed that the test statistic based on new suggested estimator has better asymptotic approximation and have less size distortion in small samples especially when high level heteroskedasticity is present in the data. [ABSTRACT FROM AUTHOR]

In model-based clustering based on normal-mixture models, a few outlying observations can influence the cluster structure and number. This paper develops a method to identify these, however it does not attempt to identify clusters amidst a large field of noisy observations. We identify outliers as those observations in a cluster with minimal membership proportion or for which the cluster-specific variance with and without the observation is very different. Results from a simulation study demonstrate the ability of our method to detect true outliers without falsely identifying many non-outliers and improved performance over other approaches, under most scenarios. We use the contributed R package MCLUST for model-based clustering, but propose a modified prior for the cluster-specific variance which avoids degeneracies in estimation procedures. We also compare results from our outlier method to published results on National Hockey League data. [ABSTRACT FROM AUTHOR]

In this paper, a Bayesian method for inference is developed for the zero-modified Poisson (ZMP) regression model. This model is very flexible for analyzing count data without requiring any information about inflation or deflation of zeros in the sample. A general class of prior densities based on an information matrix is considered for the model parameters. A sensitivity study to detect influential cases that can change the results is performed based on the Kullback-Leibler divergence. Simulation studies are presented in order to illustrate the performance of the developed methodology. Two real datasets on leptospirosis notification in Bahia State (Brazil) are analyzed using the proposed methodology for the ZMP model. [ABSTRACT FROM AUTHOR]

Getting a robust regression requires the detection of abnormal points. In this article we give a solution to this problem based on Cook’s distance, DFFITS, DFBETAS, among others. We then compare the bounds for those distances which are used to detect abnormal point. [ABSTRACT FROM AUTHOR]

Analysis of covariance (ANCOVA) is a powerful statistical method which incorporates one or more covariates into the analysis to reduce error associated with measurement. ANCOVA (modeling response as a function of fish size) is frequently used to analyze environmental effects monitoring (EEM) fish survey data. In approximately 12% of fish survey data sets taken from cycles 1 to 3 of Environment Canada’s EEM database for pulp and paper mills, the standard assumption of parallel regression slopes is not met. For the first three cycles of the EEM program, these data sets were classified as indicating a mill effect, but for the most part were excluded from subsequent analyses aimed at quantifying the effect. We present two different methods for initially dealing with data sets that exhibit heterogeneous slopes so that they can be analyzed using the parallel slope model. The first method identifies data sets where heterogeneous slopes are forced by a few high-influence observations. The second approach identifies data sets where a model with heterogeneous slopes is statistically, but not practically, significant: with a high coefficient of determination for the parallel slope model. These new methodologies are applied to EEM pulp and paper data sets and about 55% of cases with heterogeneous slopes can be described by a parallel slope model. We also discuss a third method that can be used to describe mill effects when regression slopes remain heterogeneous even after applying the above two methods, enabling comparison with a critical effect size. These new methodologies could benefit the EEM program by enabling more data sets to be incorporated into meta-analyses and be used to make more equitable mill monitoring decisions in the future. [ABSTRACT FROM AUTHOR]

Single-case deletion regression diagnostics have been used widely to discover unusual data points, but such approaches can fail in the presence of multiple unusual data points and as a result of masking. We propose a new approach to the use of single-case deletion diagnostics that involves applying these diagnostics to delete-2 and delete-3 jackknife replicates of the data, and considering the percentage of times among these replicates that points are flagged as unusual as an indicator of their influence. By considering replicates that exclude certain collections of points, subtle masking effects can be uncovered. [ABSTRACT FROM AUTHOR]

A method for the determination of 1-hydroxypyrene in urine and hexachlorbenzene in water applying the regression triplet in the calibration procedure of chromatographic data has been applied. The detection limit and quantification limit are currently calculated on the basis of the standard deviation of replicate analyses at a single concentration. However, since the standard deviation depends on concentration, these single-concentration techniques result in limits that are directly dependent on spiking concentration. A more rigorous approach requires first careful attention to the three components of the regression triplet (data, model, method), examining (1) the data quality of the proposed model, (2) the model quality and (3) the least-squares method to be used for fulfilment of all least-squares assumptions. For high-performance liquid chromatography determination of 1-hydroxypyrene in urine and gas chromatography analysis of hexachlorbenzene in water, this paper describes the effects of deviations from five basic assumptions The paper considers the correction of deviations: identifying influential points, namely, outliers, the calibration task depends on the regression model used, and the least-squares method is based on the assumptions of the normality of the errors, homoscedasticity and the independence of errors. Results show that the approach developed provides improved estimates of analytical limits and that the single-concentration approaches currently in wide use are seriously flawed. [ABSTRACT FROM AUTHOR]

In geographically weighted regression, one must determine a window size which will be used to subset the data locally. Typically, a cross-validation procedure is used to determine a globally optimal window size. Preliminary investigations indicate that the global cross-validation score is heavily influenced by a small number of observations in the dataset. At present, the ramifications of this behaviour in cross-validation are unknown. The research reported here explores the extent to which individual and groups of observations impact optimal window size determination, and whether one can explain why some points are more influential than others. In addition, we strive to examine the impact neighbourhood specification has on model quality in terms of predictive capabilities and the ability of the method to retrieve spatially varying processes. The analysis is based on several datasets and using simulated data in order to compare and validate results. The results provide some practical guidelines for the use of cross-validation. [ABSTRACT FROM AUTHOR]

The REGDIA regression diagnostics algorithm in S-Plus is introduced in order to examine the accuracy of p K a predictions made with four updated programs: PALLAS, MARVIN, ACD/pKa and SPARC. This report reviews the current status of computational tools for predicting the p K a values of organic drug-like compounds. Outlier predicted p K a values correspond to molecules that are poorly characterized by the p K a prediction program concerned. The statistical detection of outliers can fail because of masking and swamping effects. The Williams graph was selected to give the most reliable detection of outliers. Six statistical characteristics ( F exp, R 2, $$ {\text{R}}^{2}_{{\text{P}}} $$ , MEP, AIC, and s( e) in p K a units) of the results obtained when four selected p K a prediction algorithms were applied to three datasets were examined. The highest values of F exp, R 2, $$ {\text{R}}^{2}_{{\text{P}}} $$ , the lowest values of MEP and s( e), and the most negative AIC were found using the ACD/p K a algorithm for p K a prediction, so this algorithm achieves the best predictive power and the most accurate results. The proposed accuracy test performed by the REGDIA program can also be applied to test the accuracy of other predicted values, such as log P, log D, aqueous solubility or certain physicochemical properties of drug molecules. [ABSTRACT FROM AUTHOR]

When drugs are poorly soluble then, instead of the potentiometric determination of dissociation constants, pH-spectrophotometric titration can be used along with nonlinear regression of the absorbance response surface data. Generally, regression models are extremely useful for extracting the essential features from a multiwavelength set of data. Regression diagnostics represent procedures for examining the regression triplet ( data, model, method) in order to check (a) the data quality for a proposed model; (b) the model quality for a given set of data; and (c) that all of the assumptions used for least squares hold. In the interactive, PC-assisted diagnosis of data, models and estimation methods, the examination of data quality involves the detection of influential points, outliers and high leverages, that cause many problems when regression fitting the absorbance response hyperplane. All graphically oriented techniques are suitable for the rapid estimation of influential points. The reliability of the dissociation constants for the acid drug silybin may be proven with goodness-of-fit tests of the multiwavelength spectrophotometric pH-titration data. The uncertainty in the measurement of the p K a of a weak acid obtained by the least squares nonlinear regression analysis of absorption spectra is calculated. The procedure takes into account the drift in pH measurement, the drift in spectral measurement, and all of the drifts in analytical operations, as well as the relative importance of each source of uncertainty. The most important source of uncertainty in the experimental set-up for the example is the uncertainty in the pH measurement. The influences of various sources of uncertainty on the accuracy and precision are discussed using the example of the mixed dissociation constants of silybin, obtained using the SQUAD(84) and SPECFIT/32 regression programs. [ABSTRACT FROM AUTHOR]

The weighted bootstrap is a bootstrapping scheme that is valid under heteroskedasticity of unknown form. It is often used in linear regression analysis to obtain variance estimates of the ordinary least squares estimators of the linear parameters, especially when heteroskedasticity is suspected to be present in the data. Monte Carlo studies have shown, however, that its finite-sample performance can be poor when the data include points of high leverage. In this paper, we propose alternative bootstrap methods that take into the account the effect of possibly influential observations on the resulting inference via quasi-t tests. Our numerical results show that some of the proposed bootstrapping schemes generally outperform the weighted bootstrap when there are points of high leverage in the data. It is also shown that the potential gains from using the bootstrap inference we propose can be substantial. An application is presented. [ABSTRACT FROM AUTHOR]

Building a calibration model with detection and quantification capabilities is identical to the task of building a regression model. Although commonly used by analysts, an application of the calibration model requires at first careful attention to the three components of the regression triplet (data, model, method), examining (a) the data quality of the proposed model; (b) the model quality; (c) the LS method to be used or a fulfillment of all least-squares assumptions. This paper summarizes these components, describes the effects of deviations from assumptions and considers the correction of such deviations: identifying influential points is the first step in least-squares model building, the calibration task depends on the regression model used, and finally the least squares LS method is based on assumptions of normality of errors, homoscedasticity, independence of errors, overly influential data points and independent variables being subject to error. When some assumptions are violated, the ordinary LS is inconvenient and robust M-estimates with the iterative method of reweighted least-squares must be used. The effects of influential points, heteroscedasticity and non-normality on the calibration precision limits are also elucidated. This paper also considers the proper construction of the statistical uncertainty expressed as confidence limits predicting an unknown concentration (or amount) value, and its dependence on the regression triplet. The authors’ objectives were to provide a thorough treatment that includes pertinent references, consistent nomeclature, and related mathematical formulae to show by theory and illustrative examples those approaches best suited to typical problems in analytical chemistry. Two new algorithms, calibration and linear regression written in s-plus and enabling regression triplet analysis, the estimation of calibration precision limits, critical levels, detection limits and quantification limits with the statistical uncertainty of unknown concentrations, form the goal of this paper. [Copyright &y& Elsevier]

• Derivatives of nonlinear models help to better understand growth curves. • Influential points contribute to discussions of the animal growth curve. • Gompertz model is the better for the description of the Campolina breed growth curve. • The Campolina development at withers height was more accelerated than in body weight. The Campolina horse breed stands out for its gait, its tall size, harmonious and curvaceous features, it is used in sports, leisure and service. The study of animal growth curves based on nonlinear models has often been used as a method for analyzing the development of several species, however, there are no reports of a study on modeling the growth curve in this breed. This present study aimed to evaluate the fit of the Logistical, Gompertz, von Bertalanffy and Brody models for the withers height (WH) and body weight (BW) in males and females, in addition to study the first to fourth order derivatives of the growth model aiming to identify relevant points of the growth curve. The experimental data were obtained from an agricultural show in Belo Horizonte, State of Minas Gerais, in 2012. A total of 356 Campolina horses were measured, 114 males and 242 non-pregnant females, which were divided into 16 age classes (7 to 203 months) and sex. Each animal was measured only once, characterizing a cross-sectional data collection study. The models were compared according to the following criteria for quality of fit: R2, AIC c and MAPE. All adjustments and graphs constructed were analyzed by the statistical software R. The estimated asymptotic parameter for females in body weight were higher than those for males, indicating that they reach a higher adult weight, which may be due to different dietary practices, physiological conditions and physical conditioning between sexes. The maturity index of males was higher than for females, suggesting that the growth of males is more accelerated for withers height. The Gompertz model was chosen as the most suitable for the description of the growth curve in body weight and withers height of the Campolina breed horses because it presents best evaluators of quality and captures more influential points from its 1st to 4th order derivatives. Withers height develops faster than body weight. Some of the relevant points of equine growth still occur in the prenatal and lactation stages of foals. [Display omitted] [ABSTRACT FROM AUTHOR]

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