Assessment Of Local Influence Research Articles

Inference and Local Influence Assessment in a Multifactor Skew-Normal Linear Mixed Model

This work considers a multifactor linear mixed model under heteroscedasticity in random-effect factors and the skew-normal errors for modeling the correlated datasets. We implement an expectation–maximization (EM) algorithm to achieve the maximum likelihood estimates using conditional distributions of the skew-normal distribution. The EM algorithm is also implemented to extend the local influence approach under three model perturbation schemes in this model. Furthermore, a Monte Carlo simulation is conducted to evaluate the efficiency of the estimators. Finally, a real data set is used to make an illustrative comparison among the following four scenarios: normal/skew-normal errors and heteroscedasticity/homoscedasticity in random-effect factors. The empirical studies show our methodology can improve the estimates when the model errors follow from a skew-normal distribution. In addition, the local influence analysis indicates that our model can decrease the effects of anomalous observations in comparison to normal ones.

Assessment of local influence in spatial elliptical linear measurement error models

In this paper, we consider estimation and inference procedures in spatial linear models when some of the covariates are measured with errors. It is assumed that the additive error distributed according to the law belonging to the class of elliptically contoured distributions. The development of the corrected score function with the family of elliptical distributions is the basis for derivation of the estimators. For sensitivity analysis, the local influence approach is used for assessing influence of small perturbations on the parameter estimates. A simulation study is presented illustrating the good performance of the proposed approach, including the robustness property for the heavier tail models. We further illustrate the proposed procedures by an application in a real dataset.

Assessment of local influence for the analysis of agreement.

The concordance correlation coefficient (CCC) and the probabilityof agreement (PA) are two frequently used measures for evaluating the degree ofagreement between measurements generated by two different methods. In this paper, weconsider the CCC and the PA using the bivariate normal distribution formodeling the observations obtained by two measurement methods. The main aim of thispaper is to develop diagnostic tools for the detection of those observations thatare influential on the maximum likelihood estimators of the CCC and thePA using the local influence methodology but not based on the likelihood displacement.Thus, we derive first- and second-order measures considering the case-weight perturbationscheme. The proposed methodology is illustrated through a Monte Carlo simulation study andusing a dataset from a clinical study on transient sleep disorder. Empirical resultssuggest that under certain circumstances first-order local influencemeasures may be more powerful than second-order measures for the detection of influentialobservations.

Cook's Local Influence in Generalized Linear Models via the Shape Operator

In this paper we develop an algorithm for assessing the effect of small perturbations of the data on the validity of a postulated generalized linear model. The procedure is based on the geometric notion of shape operator, a single mathematical object that gathers together all the normal curvatures of a given influence graph or hypersurface. In addition to introducing relevant theoretical notions and explaining the foundations of the local influence assessment method in a generalized linear model with a canonical link, we provide a detailed example of application together with the explicit $R$ code implementing the algorithm.

Influence diagnostics in a vector autoregressive model

In this paper, we use a likelihood approach and the local influence method introduced by Cook [Assessment of local influence (with discussion). J Roy Statist Soc Ser B. 1986;48:133–149] to study a vector autoregressive (VAR) model. We present the maximum likelihood estimators and the information matrix. We establish the normal curvature and slope diagnostics for the VAR model under several perturbation schemes and use the Monte Carlo method to obtain benchmark values for determining the influence of directional diagnostics and possible influential observations. An empirical study using the VAR model to fit real data of monthly returns of IBM and S&P500 index illustrates the effectiveness of our proposed diagnostics.

Local Influence Diagnostics in the Modified Ridge Regression

Calculations of local influence curvatures have been well developed when the ordinary least squares method is applied. In this article, we discuss the assessment of local influence under the modified ridge regression. Using a pseudo-likelihood function, we express the normal curvatures of local influence for three useful perturbation schemes in interpretable forms. Two illustrative examples are analyzed by the methodology developed in the article.

Influential observations in GARCH models

This paper examines local influence assessment in generalized autoregressive conditional heteroscesdasticity models with Gaussian and Student-t errors, where influence is examined via the likelihood displacement. The analysis of local influence is discussed under three perturbation schemes: data perturbation, innovative model perturbation and additive model perturbation. For each case, expressions for slope and curvature diagnostics are derived. Monte Carlo experiments are presented to determine the threshold values for locating influential observations. The empirical study of daily returns of the New York Stock Exchange composite index shows that local influence analysis is a useful technique for detecting influential observations; most of the observations detected as influential are associated with historical shocks in the market. Finally, based on this empirical study and the analysis of simulated data, some advice is given on how to use the discussed methodology.

Influence measures on corrected score estimators in functional heteroscedastic measurement error models

This paper deals with the local influence assessment of the effects of minor perturbations of data on corrected score estimators in the functional heteroscedastic measurement error models with known variances. By extending to the context of measurement error models the differential-geometrical framework proposed by Zhu et al. [H.T. Zhu, J.G. Ibrahim, S. Lee, H. Zhang, Perturbation selection and influence measures in local influence analysis, The Annals of Statistics 35 (2007) 2565–2588], an n-dimensional Riemannian manifold is defined. The associated metric tensor is utilized for the selection of appropriate perturbation schemes. The Levi-Civita connection and first and second derivatives of the corrected score estimators are used to construct influence measures. Simple formulas are obtained under different perturbation schemes. A comparison with the slope and curvature based diagnostics defined from the surface of the corrected score estimators formed by perturbation is included. A real data application and a simulated example illustrate the performance of the proposed diagnostics.

Local influence analysis for semiparametric reproductive dispersion nonlinear models

The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the Δ matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms.

Local Influence Under Parameter Constraints

Calculations of local influence curvatures and leverage have been well developed when the parameters are unrestricted. In this article, we discuss the assessment of local influence and leverage under linear equality parameter constraints with extensions to inequality constraints. Using a penalized quadratic function we express the normal curvature of local influence for arbitrary perturbation schemes and the generalized leverage matrix in interpretable forms, which depend on restricted and unrestricted components. The results are quite general and can be applied in various statistical models. In particular, we derive the normal curvature under three useful perturbation schemes for generalized linear models. Four illustrative examples are analyzed by the methodology developed in the article.

Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. Journal of the Royal Statistical Society - Series B 48 (2), 133–169; Cook D., 1987. Influence assessment. Journal of Applied Statistics 14 (2), 117–131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507–528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1–17], which was analyzed under the assumption of normality.

Local influence analysis of nonlinear structural equation models with nonignorable missing outcomes from reproductive dispersion models

Nonlinear structural equation models with nonignorable missing outcomes from reproductive dispersion models are proposed to identify the relationship between manifest variables and latent variables in modern educational, medical, social and psychological studies. The nonignorable missing mechanism is specified by a logistic regression model. An EM algorithm is developed to obtain the maximum likelihood estimates of the structural parameters and parameters in the logistic regression model. Assessment of local influence is investigated in nonlinear structural equation models with nonignorable missing outcomes from reproductive dispersion models on the basis of the conditional expectation of the complete-data log-likelihood function. Some local influence diagnostics are obtained via observations of missing data and latent variables that are generated by the Gibbs sampler and Metropolis–Hastings algorithm on the basis of the conformal normal curvature. A simulation study and a real example are used to illustrate the application of the proposed methodologies.

Inference and local influence assessment in skew-normal null intercept measurement error model

In this article, we discuss inferential aspects of the measurement error regression models with null intercepts when the unknown quantity x (latent variable) follows a skew normal distribution. We examine first the maximum-likelihood approach to estimation via the EM algorithm by exploring statistical properties of the model considered. Then, the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. In order to discuss some diagnostics techniques in this type of models, we derive the appropriate matrices to assessing the local influence on the parameter estimates under different perturbation schemes. The results and methods developed in this paper are illustrated considering part of a real data set used by Hadgu and Koch [1999, Application of generalized estimating equations to a dental randomized clinical trial. Journal of Biopharmaceutical Statistics, 9, 161–178].

Local influence assessment in heteroscedastic measurement error models

Functional heteroscedastic measurement error models are investigated aiming to assess the effects of perturbations of data on some inferential procedures. This goal is accomplished by resorting to methods of local influence. The techniques provide to the practitioner a valuable tool that enables to identify potential influential elements and to quantify the effects of perturbations in these elements on results of interest. An illustrative example with a real data set is also reported.

Assessment of local influence in elliptical linear models with longitudinal structure

The aim of this paper is to derive local influence curvatures under various perturbation schemes for elliptical linear models with longitudinal structure. The elliptical class provides a useful generalization of the normal model since it covers both light- and heavy-tailed distributions for the errors, such as Student- t, power exponential, contaminated normal, among others. It is well known that elliptical models with longer-than-normal tails may present robust parameter estimates against outlying observations. However, little has been investigated on the robustness aspects of the parameter estimates against perturbation schemes. We use appropriate derivative operators to express the normal curvatures in tractable forms for any correlation structure. Estimation procedures for the position and variance–covariance parameters are also presented. A data set previously analyzed under a normal linear mixed model is reanalyzed under elliptical models. Local influence graphics are used to select less sensitive models with respect to some perturbation schemes.

Influence diagnostics in nonlinear reproductive dispersion mixed models

The class of nonlinear reproductive dispersion mixed models (NRDMMs) is an extension of nonlinear reproductive dispersion models and generalized linear mixed models. This paper discusses the influence analysis of the model based on Laplace approximation. The equivalence of case-deletion models and mean-shift outlier models in NRDMMs is investigated, and some diagnostic measures are proposed via the case-deletion method. We also investigate the assessment of local influence of various perturbation schemes. The proposed method is illustrated with an example.

Local influence analysis of nonlinear structural equation models

By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis are computed via observations of the latent variables generated by the Metropolis-Hastings algorithm, while the diagnostic measures are obtained via the conformal normal curvature. Seven perturbation schemes, including some perturbation schemes on latent vectors, are investigated. The proposed procedure is illustrated by a simulation study and a real example.

Assessment of Local Influence in GARCH Processes

Abstract. This paper investigates the problem of assessing local influence of small perturbations in GARCH processes. First, we examine the local influence on the Lagrange multiplier (LM) statistic. Second, we assess the local influence on the pseudo‐likelihood of the GARCH model. We find that short patches of high volatility observations that have a strong influence on the LM statistic may not necessarily be influential on the pseudo‐likelihood. This is mainly due to the fact that the effects of high volatility could be incorporated through GARCH modeling. An empirical example is presented to illustrate the effectiveness of the proposed methods. It is interesting to note that observations which have a very strong influence on the LM statistic are far less influential on the GARCH pseudo‐likelihood, suggesting that under the GARCH model they should not be regarded as outliers.

On diagnostics in conditionally heteroskedastic time series models under elliptical distributions

In statistical diagnostics and sensitivity analysis, the local influence method plays an important rôle. In the present paper, we use this method to study financial time series data and conditionally heteroskedastic models under elliptical distributions. We start with a likelihood displacement, and consider data- and model-perturbation schemes. We obtain corresponding matrices of derivatives, and measures of slope and normal curvature, and then discuss the assessment of local influence.