Local influence assessment in canonical correlation analysis

The local influence method is adapted to canonical correlation analysis for the purpose of investigating the influence of observations. We consider a perturbation based on the empirical distribution function. An illustrative example is given to show the effectiveness of the local influence method for the identification of influential observations.     

Local influence in multivariate regression

The method of local influence is generalized to the multivariate regression. The scheme of perturbations adopted in multivariate regression is similar in spirit to the perturbation of case-weights in univariate regression case. The method developed here is useful for identifying influential observations in multivariate regression as an exploratory or confirmatory data analysis. An illustrative example is given for the effectiveness of the local influence approach in multivariate regression.     

An application of the local influence approach to ridge regression

In this study, the method of local influence, which was introduced by Cook as a general tool for assessing the influence of local departures from the underlying assumptions, is applied to ridge regression, by defining the maximum pseudo-likelihood ridge estimator obtained using the augmentation approach, because this method is suitable for likelihood-based models. In addition, an alternative local influence approach suggested by Billor and Loynes is applied to ridge regression. A comparison of these approaches and an example are given.     

Influence diagnostic analysis in the possibly heteroskedastic linear model with exact restrictions

The local influence method has proven to be a useful and powerful tool for detecting influential observations on the estimation of model parameters. This method has been widely applied in different studies related to econometric and statistical modelling. We propose a methodology based on the Lagrange multiplier method with a linear penalty function to assess local influence in the possibly heteroskedastic linear regression model with exact restrictions. The restricted maximum likelihood estimators and information matrices are presented for the postulated model. Several perturbation schemes for the local influence method are investigated to identify potentially influential observations. Three real-world examples are included to illustrate and validate our methodology.     

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.     

Local influence on a test of linear hypothesis in multiple regression model

SUMMARY The local influence method is adapted to investigate the influence of observations on testing the linear hypothesis. The method provides information about individually or jointly influential observations in performing the test, which the usual diagnostic methods do not yield. An example is presented for illustration of the method.     

Influence Diagnostics in log-Birnbaum-Saunders Regression Models

In this paper we present various diagnostic methods for a linear regression model under a logarithmic Birnbaum-Saunders distribution for the errors, which may be applied for accelerated life testing or to compare the median lives of several populations. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are derived, analysed and discussed. We also present a connection between the local influence and generalized leverage methods. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.     

A Diagnostic Method for Principal Components Tests

The local influence method is adapted to testing hypotheses about principal components for investigating the influence of observations on the test statistic. Simultaneous perturbations on all observations are considered. The main diagnostic is the direction vector of the maximum slope of the surface formed by the perturbed test statistic. A perturbation is constructed whose result is the same as that of the influence function method. An example is given for illustration.     

Local influence in multilevel models

The authors study the local influence of observations in multilevel regression models. To this end, they perturb simultaneously the variances, responses and design matrix. To measure the local change caused by these perturbations, they use generalized Cook statistics for the fixed and random parameter estimates. Closed form local influence measures also allow them to assess the joint influence of various observations. They suggest a simple computation method and illustrate their results using two examples.     

Influence diagnostics for polyhazard models in the presence of covariates

In this paper, we present various diagnostic methods for polyhazard models. Polyhazard models are a flexible family for fitting lifetime data. Their main advantage over the single hazard models, such as the Weibull and the log-logistic models, is to include a large amount of nonmonotone hazard shapes, as bathtub and multimodal curves. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.     

Local influence for incomplete data models

This paper proposes a method to assess the local influence in a minor perturbation of a statistical model with incomplete data. The idea is to utilize Cook's approach to the conditional expectation of the complete-data log-likelihood function in the EM algorithm. It is shown that the method proposed produces analytic results that are very similar to those obtained from a classical local influence approach based on the observed data likelihood function and has the potential to assess a variety of complicated models that cannot be handled by existing methods. An application to the generalized linear mixed model is investigated. Some illustrative artificial and real examples are presented.     

Stepwise local influence in generalized autoregressive conditional heteroskedasticity models

Detection of outliers or influential observations is an important work in statistical modeling, especially for the correlated time series data. In this paper we propose a new procedure to detect patch of influential observations in the generalized autoregressive conditional heteroskedasticity (GARCH) model. Firstly we compare the performance of innovative perturbation scheme, additive perturbation scheme and data perturbation scheme in local influence analysis. We find that the innovative perturbation scheme give better result than other two schemes although this perturbation scheme may suffer from masking effects. Then we use the stepwise local influence method under innovative perturbation scheme to detect patch of influential observations and uncover the masking effects. The simulated studies show that the new technique can successfully detect a patch of influential observations or outliers under innovative perturbation scheme. The analysis based on simulation studies and two real data sets show that the stepwise local influence method under innovative perturbation scheme is efficient for detecting multiple influential observations and dealing with masking effects in the GARCH model.     

Bayesian local influence for survival models

The aim of this paper is to develop a Bayesian local influence method (Zhu et al. 2009, submitted) for assessing minor perturbations to the prior, the sampling distribution, and individual observations in survival analysis. We introduce a perturbation model to characterize simultaneous (or individual) perturbations to the data, the prior distribution, and the sampling distribution. We construct a Bayesian perturbation manifold to the perturbation model and calculate its associated geometric quantities including the metric tensor to characterize the intrinsic structure of the perturbation model (or perturbation scheme). We develop local influence measures based on several objective functions to quantify the degree of various perturbations to statistical models. We carry out several simulation studies and analyze two real data sets to illustrate our Bayesian local influence method in detecting influential observations, and for characterizing the sensitivity to the prior distribution and hazard function.     

Outliers and influential observations in the structural errors-in-variables model

The influence of observations on the parameter estimates for the simple structural errors-in-variables model with no equation error is investigated using the local influence method. Residuals themselves are not sufficient for detecting outliers. The likelihood displacement approach is useful for outlier detection especially when a masking phenomenon is present. An illustrative example is provided.     

Local influence in multivariate normal data

The local influence method introduced by Cook is adapted to multivariate normal data for the purpose of detecting outliers. The method allows simultaneous perturbations on all observations, so that it can identify multiple outliers. An illustrative example is given to show the e ectiveness of the method for the identification of influential observations.     

Local influence of nonlinear mixed effects model based on M-estimation

Abstract

In this work we mainly study the local influence in nonlinear mixed effects model with M-estimation. A robust method to obtain maximum likelihood estimates for parameters is presented, and the local influence of nonlinear mixed models based on robust estimation (M-estimation) by use of the curvature method is systematically discussed. The counting formulas of curvature for case weights perturbation, response variable perturbation and random error covariance perturbation are derived. Simulation studies are carried to access performance of the methods we proposed. We illustrate the diagnostics by an example presented in Davidian and Giltinan, which was analyzed under the non-robust situation.     

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.     

Influence Diagnostics for Simultaneous Equations Models

This paper presents influence diagnostics for simultaneous equations models. It proposes residuals, leverage and other influence measures. A missing data method is adopted to minimize the masking effect due to case deletions. The assessment of local influence is also considered. The paper shows how to evaluate the effects that perturbations to the endogenous variables, predetermined variables and case weights may have on the parameter estimates. The diagnostics are illustrated with two examples.     

Influence measure in maximum likelihood estimate for models of lifetime data

We use the local influence approach to develop influence measures for identifying observations that strike a disproportionate effect on the maximum likelihood estimate of parameters in models for lifetime data. The proposed method for developing influence measures can be applied to a wide variety of models and we use the exponential model to illustrate the details. In particular, we show that the proposed measure is equivalent to the martingale residual under the exponential model.