Local Influence Measures Research Articles

A Bimodal Exponential Regression Model for Analyzing Dengue Fever Case Rates in the Federal District of Brazil

Dengue fever remains a significant epidemiological challenge globally, particularly in Brazil, where recurring outbreaks strain healthcare systems. Traditional statistical models often struggle to accurately capture the complexities of dengue case distributions, especially when data exhibit bimodal patterns. This study introduces a novel bimodal regression model based on the log-generalized odd log-logistic exponential distribution, offering enhanced flexibility and precision for analyzing epidemiological data. By effectively addressing multimodal distributions, the proposed model overcomes the limitations of unimodal models, making it well suited for public health applications. Through regression analysis of dengue case data from the Federal District of Brazil during the epidemiological weeks of 2022, the model demonstrates its capacity to improve the fit of the disease rate. The model’s parameters are estimated using maximum likelihood estimation, and Monte Carlo simulations validate their accuracy. Additionally, local influence measures and residual analysis ensure the proposed model’s goodness-of-fit. While this innovative regression model offers substantial advantages, its effectiveness depends on the availability of high-quality data, and further validation is necessary to confirm its applicability across diverse diseases and regions with varying epidemiological characteristics.

Diagnostic tools for a multivariate negative binomial model for fitting correlated data with overdispersion

We focus on the development of diagnostic tools and an R package called MNB for a multivariate negative binomial (MNB) regression model for detecting atypical and influential subjects. The MNB model is deduced from a Poisson mixed model in which the random intercept follows the generalized log-gamma (GLG) distribution. The MNB model for correlated count data leads to an MNB regression model that inherits the features of a hierarchical model to accommodate the intraclass correlation and the occurrence of overdispersion simultaneously. The asymptotic consistency of the dispersion parameter estimator depends on the asymmetry of the GLG distribution. Inferential procedures for the MNB regression model are simple, although it can provide inconsistent estimates of the asymptotic variance when the correlation structure is misspecified. We propose the randomized quantile residual for checking the adequacy of the multivariate model and derive global and local influence measures from the multivariate model to assess influential subjects. Finally, two applications are presented in the data analysis section. The code for installing the MNB package and the code used in the two examples is exhibited in the Appendices.

Residual and local influence analyses for unit gamma regressions

AbstractWe obtain local influence measures and residuals for the unit gamma regression model. In particular, we introduce four residuals that are based on Fisher's iterative scoring parameter estimation algorithm and develop local influence analysis based on several different perturbation schemes: cases weighting, response additive perturbation, and covariate(s) additive perturbation. An empirical application in which variables related to education and investment in research and development are used to explain the proportion of nonpoor people in a set of countries is presented and discussed. Residual and local influence analyses show that the unit gamma regression model yields a good fit to the data, even outperforming the beta regression model. The diagnostic analysis singles out countries whose data are worthy of further investigation. Our results reveal that lower poverty levels are associated with higher shares of investment in high technology. The statistical significance of such a relationship is not sensitive to atypical data points.

Centrality-Based Opinion Modeling on Temporal Networks

While most of opinion formation models consider static networks, a dynamic opinion formation model is proposed in this work. The so-called Temporal Threshold Page Rank Opinion Formation model (TTPROF) integrates temporal evolution in two ways. First, the opinion of the agents evolve with time. Second, the network structure is also time varying. More precisely, the relations between agents evolve with time. In the TTPROF model, a node is affected by part of its neighbor's opinions weighted by their Page Rank values. A threshold is introduced in order to limit the neighbors that can share their opinion. In other words, a neighbor influences a node if the difference between their opinions is below the threshold. Finally, a fraction of top ranked nodes in the neighborhood are considered influential nodes irrespective of the threshold value. Experiments have been performed on random temporal networks in order to analyze how opinions propagate and converge to consensus or multiple clusters. Preliminary results have been presented [1]. In this paper, this work is extended in two directions. First, the impact of various centrality measures on the model behavior is investigated. Indeed, in earlier work, the influence of a node is measured using Page Rank. New results using Directed Degree centrality and Closeness Centrality are derived. They allow to compare global against local influence measures as well as distance-based centrality, and to better understand the impact of the weighting parameter on the model convergence. Second, the results of an extensive experimental investigation are reported and analyzed in order to characterize the model convergence in various situations.

Bayesian Local Influence of Generalized Failure Time Models with Latent Variables and Multivariate Censored Data

We develop a Bayesian local influence procedure for generalized failure time models with latent variables and multivariate censored data. We propose to use the penalized splines (P-splines) approach to formulate the unknown functions of the proposed models. We assess the effects of minor perturbations to individual observations, the prior distributions of parameters, and the sampling distribution on statistical inference through various perturbation schemes. The first-order local influence measure is used to quantify the degree of minor perturbations to different aspects of a statistical model with the use of Bayes factor as an objective function. Simulation studies show that the empirical performance of the Bayesian local influence procedure is satisfactory. An application to a study of renal disease for type 2 diabetes patients is presented.

Estimation and diagnostic analysis in skew-generalized-normal regression models

ABSTRACTThe skew-generalized-normal distribution [Arellano-Valle, RB, Gómez, HW, Quintana, FA. A new class of skew-normal distributions. Comm Statist Theory Methods 2004;33(7):1465–1480] is a class of asymmetric normal distributions, which contains the normal and skew-normal distributions as special cases. The main virtues of this distribution is that it is easy to simulate from and it also supplies a genuine expectation–maximization (EM) algorithm for maximum likelihood estimation. In this paper, we extend the EM algorithm for linear regression models assuming skew-generalized-normal random errors and we develop a diagnostics analyses via local influence and generalized leverage, following Zhu and Lee's approach. This is because Cook's well-known approach would be more complicated to use to obtain measures of local influence. Finally, results obtained for a real data set are reported, illustrating the usefulness of the proposed method.

Influence diagnostics in spatial models with censored response

Environmental data are often spatially correlated and sometimes include observations below or above detection limits (i.e., censored values reported as less or more than a level of detection). Existing research studies mainly concentrate on parameter estimation using Gibbs sampling, and most research studies conducted from a frequentist perspective in spatial censored models are elusive. In this paper, we propose an exact estimation procedure to obtain the maximum‐likelihood estimates of fixed effects and variance components, using a stochastic approximation of the expectation–maximization algorithm (Delyon, Lavielle, & Moulines). This approach permits estimation of the parameters of spatial linear models when censoring is present in an easy and fast way. As a by‐product, predictions of unobservable values of the response variable are possible. Motivated by this algorithm, we develop local and global influence measures on the basis of the conditional expectation of the complete‐data log‐likelihood function, which eliminates the complexity associated with the approach of Cook for spatial censored models. Some useful perturbation schemes are discussed. The newly developed method is illustrated using data from a dioxin‐contaminated site in Missouri that contain left‐censored data and a data set related to the depths of a geological horizon that contains both left‐ and right‐censored observations. In addition, a simulation study is presented that explores the accuracy of the proposed measures in detecting influential observations under different perturbation schemes. The methodology addressed in this paper is implemented in the R packageCensSpatial.

Influence diagnostics in meta-regression model.

This paper studies the influence diagnostics in meta-regression model including case deletion diagnostic and local influence analysis. We derive the subset deletion formulae for the estimation of regression coefficient and heterogeneity variance and obtain the corresponding influence measures. The DerSimonian and Laird estimation and maximum likelihood estimation methods in meta-regression are considered, respectively, to derive the results. Internal and external residual and leverage measure are defined. The local influence analysis based on case-weights perturbation scheme, responses perturbation scheme, covariate perturbation scheme, and within-variance perturbation scheme are explored. We introduce a method by simultaneous perturbing responses, covariate, and within-variance to obtain the local influence measure, which has an advantage of capable to compare the influence magnitude of influential studies from different perturbations. An example is used to illustrate the proposed methodology.

Log-symmetric regression models under the presence of non-informative left- or right-censored observations

In this paper, an extension to allow the presence of non-informative left- or right-censored observations in log-symmetric regression models is addressed. Under such models, the log-lifetime distribution belongs to the symmetric class and its location and scale parameters are described by semi-parametric functions of explanatory variables, whose nonparametric components are approximated using natural cubic splines or P-splines. An iterative process of parameter estimation by the maximum penalized likelihood method is presented. The large sample properties of the maximum penalized likelihood estimators are studied analytically and by simulation experiments. Diagnostic methods such as deviance-type residuals and local influence measures are derived. The package ssym, which includes an implementation in the computational environment R of the methodology addressed in this paper, is also discussed. The proposed methodology is illustrated by the analysis of a real data set.

Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model

In this paper we consider the capital asset pricing model under the multivariate normal distribution for modeling asset returns. We develop and implement local influence diagnostic techniques not based on likelihood displacement. The main interest is to consider the test of mean–variance efficiency of a given portfolio as objective function. Sensitivity of maximum likelihood estimators of slopes is also considered. For this purpose, first and second-order local influence measures are calculated under a case weights perturbation scheme. In particular, for our objective functions, which have nonzero first derivative at the critical point, the proposed second-order measures are scale invariant, unlike the normal curvature. The performance of the proposed measures is illustrated by using two real data sets as well as a simulation study and a simulated data set. Empirical results seem to indicate that the Wald test statistic is less sensitive to atypical returns than maximum likelihood estimators of the slopes. By the other hand, there is some evidence about the convenience of jointly using first and second-order influence measures, to detect months/days with outlying returns, principally in Wald test statistic.

Bayesian local influence analysis of general estimating equations with nonignorable missing data

Bayesian empirical likelihood (BEL) method with missing data depends heavily on the prior specification and missing data mechanism assumptions. It is well known that the resulting Bayesian estimations and tests may be sensitive to these assumptions and observations. To this end, a Bayesian local influence procedure is proposed to assess the effect of various perturbations to the individual observations, priors, estimating equations (EEs) and missing data mechanism in general EEs with nonignorable missing data. A perturbation model is introduced to simultaneously characterize various perturbations, and a Bayesian perturbation manifold is constructed to characterize the intrinsic structure of these perturbations. The first- and second-order adjusted local influence measures are developed to quantify the effect of various perturbations. The proposed methods are adopted to systematically investigate the tenability of nonignorable missing mechanism assumption, the sensitivity of the choice of the nonresponse instrumental variable and the sensitivity of EEs assumption, and goodness-of-fit statistics are presented to assess the plausibility of the posited EEs. Simulation studies are conducted to investigate the performance of the proposed methodologies. An example is analyzed.

Local influence diagnostics for hierarchical count data models with overdispersion and excess zeros.

We consider models for hierarchical count data, subject to overdispersion and/or excess zeros. Molenberghs etal. () and Molenberghs etal. () extend the Poisson-normal generalized linear-mixed model by including gamma random effects to accommodate overdispersion. Excess zeros are handled using either a zero-inflation or a hurdle component. These models were studied by Kassahun etal. (). While flexible, they are quite elaborate in parametric specification and therefore model assessment is imperative. We derive local influence measures to detect and examine influential subjects, that is subjects who have undue influence on either the fit of the model as a whole, or on specific important sub-vectors of the parameter vector. The latter include the fixed effects for the Poisson and for the excess-zeros components, the variance components for the normal random effects, and the parameters describing gamma random effects, included to accommodate overdispersion. Interpretable influence components are derived. The method is applied to data from a longitudinal clinical trial involving patients with epileptic seizures. Even though the data were extensively analyzed in earlier work, the insight gained from the proposed diagnostics, statistically and clinically, is considerable. Possibly, a small but important subgroup of patients has been identified.

Influence diagnostics in log-linear integer-valued GARCH models

Integer-valued generalized autoregressive conditional heteroscedasticity (GARCH) models have played an important role in time series analysis of count data. To model negatively autocorrelated time series and to accommodate covariates without restrictions, the log-linear integer-valued GARCH model has recently been proposed as an alternative to the existing models. In this paper, we study a local influence diagnostic analysis in the log-linear integer-valued GARCH models. The slope-based diagnostic and stepwise curvature-based diagnostics in a framework of the modified likelihood displacement are proposed. Under five perturbation schemes the corresponding local influence measures are derived. Two simulated data sets and a real-world example are analyzed to illustrate our method. In addition, the fitted model for this example has a negative coefficient for one of the two covariates, which is particularly illustrative of the extra flexibility of the considered model.

Influence in the Elliptical Modified Ridge Regression

In this article, we present diagnostic methods for the modified ridge regression under elliptical model based on the pseudo-likelihood function. The maximum likelihood estimators of the parameters in the modified ridge elliptical model are given and local influence measures are developed. Finally, illustration of our methodology is given through a numerical example.

Bayesian influence analysis of generalized partial linear mixed models for longitudinal data

This paper develops a Bayesian local influence approach to assess the effects of minor perturbations to the prior, sampling distribution and individual observations on the statistical inference in generalized partial linear mixed models (GPLMMs) with the distribution of random effects specified by a truncated and centered Dirichlet process (TCDP) prior. A perturbation manifold is defined. The metric tensor is employed to select an appropriate perturbation vector. Several Bayesian local influence measures are proposed to quantify the degree of various perturbations to statistical models based on the first and second-order approximations to the objective functions including the ϕ-divergence, the posterior mean distance and Bayes factor. We develop two Bayesian case influence measures to detect the influential observations in GPLMMs based on the ϕ-divergence and Cook’s posterior mean distance. The computationally feasible formulae for Bayesian influence analysis are given. Several simulation studies and a real example are presented to illustrate the proposed methodologies.

Inference and diagnostics in skew scale mixtures of normal regression models

Skew scale mixtures of normal distributions are often used for statistical procedures involving asymmetric data and heavy-tailed. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine expectation-maximization (EM) algorithms for maximum likelihood estimation. In this paper, we extend the EM algorithm for linear regression models and we develop diagnostics analyses via local influence and generalized leverage, following Zhu and Lee's approach. This is because Cook's well-known approach cannot be used to obtain measures of local influence. The EM-type algorithm has been discussed with an emphasis on the skew Student-t-normal, skew slash, skew-contaminated normal and skew power-exponential distributions. Finally, results obtained for a real data set are reported, illustrating the usefulness of the proposed method.

Bayesian diagnostics of transformation structural equation models

In the behavioral, social, psychological, and the medical sciences, the most widely used models in assessing latent variables are the structural equation models (SEMs). However, most of the existing statistical methods for analyzing SEMs have been developed for normally distributed data. Transformation SEMs are useful tools for tackling the non-normality of multidimensional data and simultaneously revealing the interrelationships among latent variables. The main objective of this paper is to develop a Bayesian diagnostic procedure for transformation SEMs. The first- and second-order local inference measures are established with the objective functions that are defined based on the logarithm of Bayes Factor. Markov chain Monte Carlo (MCMC) methods with the Bayesian P-splines approach are developed to compute the local influence measures and to estimate nonparametric transformations, latent variables, and unknown parameters. Compared with conventional maximum likelihood-based diagnostic procedures, the Bayesian diagnostic approach could detect outliers and/or influential points in the observed data, as well as conduct model comparison and sensitivity analysis through various perturbations of the data, sampling distributions, or prior distributions of the model parameters. Simulation studies reveal the empirical performance of the proposed Bayesian diagnostic procedure. An actual data set that is extracted from a study based on the Hong Kong Diabetes Registry is used to illustrate the application of our methodology.

Statistical diagnostics for nonlinear regression models based on scale mixtures of skew-normal distributions

The purpose of this paper is to develop diagnostics analysis for nonlinear regression models (NLMs) under scale mixtures of skew-normal (SMSN) distributions introduced by Garay et al. [Nonlinear regression models based on SMSN distributions. J. Korean Statist. Soc. 2011;40:115–124]. This novel class of models provides a useful generalization of the symmetrical NLM [Vanegas LH, Cysneiros FJA. Assessment of diagnostic procedures in symmetrical nonlinear regression models. Comput. Statist. Data Anal. 2010;54:1002–1016] since the random terms distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as the skew-t, skew-slash, skew-contaminated normal distributions, among others. Motivated by the results given in Garay et al. [Nonlinear regression models based on SMSN distributions. J. Korean Statist. Soc. 2011;40:115–124], we presented a score test for testing the homogeneity of the scale parameter and its properties are investigated through Monte Carlo simulations studies. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. The newly developed procedures are illustrated considering a real data set.

The (uncertain) invisible college of Spanish accounting scholars

Abstract In order to test empirically the invisible college thesis in an accounting academic community and evaluate the internal mechanisms that are embedded in its reproduction, we explore in this paper the social network of Spanish accounting scholars. The social network examined arises from one event that combines formal and informal aspects of interaction between scholars: the selection of members of Ph.D. panels for the period 1994–2003. Results are consistent with the existence of an oligarchic academic community that shows a strong and positive association with measures of local influence, but that is decoupled from measures of scholarly contribution. In this regard it is difficult to sustain that high profile scholars in this community generate a disproportionate volume of new ideas, which is the basic tenet of the invisible college hypothesis. This finding is also indicative of the schizophrenia in which non-tenured Spanish accounting scholars live, between increasing demands of refereed publications by academic institutions and a hierarchical academic community sponsoring very different values.

Local influence for functional comparative calibration models with replicated data

We investigate local influence analysis in functional comparative calibration models with replicated data. A method for selecting appropriate perturbation schemes based on the expected Fisher information matrix with respect to the perturbation vector is proposed. It is shown that arbitrarily perturbing these models may result in misleading inference about the influential subjects. First-order influence measures for identifying the correct influential subjects and replicates on corrected score estimators are defined. We introduce different perturbation schemes including perturbation of subjects and replicates on the corrected likelihood function and obtain the density of the perturbed model from which the methodology is based. Particularly, three perturbation of variances schemes could be a better way to handle badly modeled subjects or replicates. Two real data sets are analyzed to illustrate the use of our local influence measures.