Influence diagnostics in semiparametric regression models

Mei

Acta Mathematicae Applicatae Sinica, English Series

2007

When a real-world data set is fitted to a specific type of models, it is often encountered that one or a set of observations have undue influence on the model fitting, which may lead to misleading conclusions. Therefore, it is necessary for data analysts to identify these influential observations and assess their impact on various aspects of model fitting. In this paper, one type of modified Cook's distances is defined to gauge the influence of one or a set observations on the estimate of the constant coefficient part in partially varyingcoefficient models, and the Cook's distances are expressed as functions of the corresponding residuals and leverages. Meanwhile, a bootstrap procedure is suggested to derive the reference values for the proposed Cook's distances. Some simulations are conducted, and a real-world data set is further analyzed to examine the performance of the proposed method. The experimental results are satisfactory.

Section: Analysis Of Diabetes Datamentioning

confidence: 99%

“…It should be noted that the semiparametric model considered in [13] is a special case of the partially varying-coefficient model (1). Considering that the constant γ 0 in (16) can be included in the nonparametric part, we also fit the data with n = 41 observations to a partially varying-coefficient model…”

Section: Analysis Of Diabetes Datamentioning

confidence: 99%

Influence Diagnostics in Partially Varying-Coefficient Models

Mei

Acta Mathematicae Applicatae Sinica, English Series

2007

“…In the spline smoothing model, Eubank (1985), Kim (1996), and Silverman (1985) suggested versions of Cook's distance, and Kim et al (2001) suggested Cook's distance in the local polynomial regression, and Fung et al (2002) and Kim et al (2002) studied detection of influential observations in the semiparametric model. Bae et al (2008) also studied diagnostic issues in the varying coefficient model.…”

Section: Introductionmentioning

confidence: 99%

Case influence diagnostics for the significance of the linear regression model

Bae

Noh

Kim

2017

CSAM

Self Cite

In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination R 2 and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in R 2 and F-statistic.

“…Fung et al (2002) considered the role of influence diagnostics in the maximum penalised likelihood estimators by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a non-parametric component. Kim et al (2002) studied the influence of observations on some estimators of the parametric and the non-parametric components in the semiparametric model and observed that the influence diagnostics in the semiparametric model have different aspects from those in the parametric and non-parametric models. Ortega et al (2003) discuss the application of influence diagnostics in generalized log-gamma regression models considering the possibility of censored observations.…”

Section: Introductionmentioning

confidence: 99%

A new approach to influence diagnostics in superpopulations

Fernández-Ponce

Infante-Macías

2005

Environmetrics

SUMMARYInfluence analysis on a model is one of the most studied topics from a frequentist viewpoint. Basically, disturbances are introduced into the model in order to measure the influence that one or a set of observations has on statistical analysis. The most common disturbance pattern is that of the omission of the observations whose influence is to be studied. In our model, we assume that there are only one or a few outliers because they may often be detected by deletion methods associated with regression diagnostics. However, these methods may fail in the presence of multiple outliers. In this case, the forward search can be used to avoid the masking and swamping problems.This article presents a Bayes approach for the influence analysis on a model in finite populations. Particularly, we develop a new approach to the study of influence in prediction theory, based on the given data rather than on the sampling design for data collection. We propose that the influence analysis on the superpopulation normal regression model and a measure based on the conditional bias from a Bayesian viewpoint is analyzed. Forward deletion formulae based on our influence measure can be defined, but this topic is beyond the scope of this article. Finally, we apply our proposed influence measure in a classic example for water contents of soil specimens.