Testing for Varying Dispersion in Exponential Family Nonlinear Models

Wei, Bo‐Cheng; Shi, Jian-Qing; Fung, Wing K.; Hu, Yue‐Qing

doi:10.1023/a:1003491131768

Cited by 40 publications

(33 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Then the Fisher-scoring iteration method can be used for computinĝby iteratively solving the following equation (see [14,24]):…”

Section: Theorem 1 For the Model Defined By (1)-(3) Conditional Oñ mentioning

confidence: 99%

“…The local influence analysis has become a general tool for detecting a group of points with great influence on the fitted model through perturbation schemes [9]. This approach has been successfully applied in many models, such as mixed models [10,11], generalized linear models [12], generalized linear mixed models [13], exponential family nonlinear models [14], nonlinear reproductive dispersion mixed model [15], nonlinear mixed-effect models [16,17], and multivariate threshold time series models [1]. However, in these references the local influence method severely depends on the likelihood displacement, which is rarely known in practice.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Local Influence Analysis for Quasi-Likelihood Nonlinear Models with Random Effects

Xia

Jiang

2018

Journal of Probability and Statistics

View full text Add to dashboard Cite

We propose a quasi-likelihood nonlinear model with random effects, which is a hybrid extension of quasi-likelihood nonlinear models and generalized linear mixed models. It includes a wide class of existing models as examples. A novel penalized quasilikelihood estimation method is introduced. Based on the Laplace approximation and a penalized quasi-likelihood displacement, local influence of minor perturbations on the data set is investigated for the proposed model. Four concrete perturbation schemes are considered in the local influence analysis. The effectiveness of the proposed methodology is illustrated by some numerical examinations on a pharmacokinetics dataset.

show abstract

“…Then the Fisher-scoring iteration method can be used for computinĝby iteratively solving the following equation (see [14,24]):…”

Section: Theorem 1 For the Model Defined By (1)-(3) Conditional Oñ mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Local Influence Analysis for Quasi-Likelihood Nonlinear Models with Random Effects

Xia

Jiang

2018

Journal of Probability and Statistics

View full text Add to dashboard Cite

show abstract

“…However, most of their work were considered under normal error structures (see [3,12,13,23,24]). Moving away from normal errors, Wei et al [25] presented the likelihood ratio and score tests in exponential family nonlinear models. Cysneiros et al [6] discussed diagnostic methods in symmetrical heteroscedastic linear models.…”

Section: Introductionmentioning

confidence: 99%

Heteroscedasticity and/or autocorrelation checks in longitudinal nonlinear models with elliptical and AR(1) errors

Cao

Lin

2011

Acta Math. Appl. Sin. Engl. Ser.

View full text Add to dashboard Cite

The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR(1) errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-t, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.

show abstract

“…From refs. [3][4][5][6][7][8][9][10], both the variability of dispersion parameter (varying dispersion) and the presence of random effects might cause the departures from nominal dispersion. Several authors have discussed tests for departures from nominal dispersion through testing for the necessity of random effects.…”

Section: Introductionmentioning

confidence: 99%

“…Hall and Berenhaut [16] presented a general score test for heterogeneity and overdispersion in zero-inflated Poisson and binomial regression models. On the other hand, Wei et al [8] proposed several diagnostic statistics for departures from nominal dispersion through the test for varying dispersion in GNLMs based on the continuous exponential family distributions.…”

Section: Introductionmentioning

confidence: 99%

Testing for departures from nominal dispersion in generalized nonlinear models with varying dispersion and/or additive random effects

Lin

2008

Journal of Statistical Computation and Simulation

View full text Add to dashboard Cite

This paper discusses the tests for departures from nominal dispersion in the framework of generalized nonlinear models with varying dispersion and/or additive random effects. We consider two classes of exponential family distributions. The first is discrete exponential family distributions, such as Poisson, binomial, and negative binomial distributions. The second is continuous exponential family distributions, such as normal, gamma, and inverse Gaussian distributions. Correspondingly, we develop a unifying approach and propose several tests for testing for departures from nominal dispersion in two classes of generalized nonlinear models. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas, so that the tests can easily be implemented using existing statistical software. The properties of test statistics are investigated through Monte Carlo simulations.

show abstract

Testing for Varying Dispersion in Exponential Family Nonlinear Models

Cited by 40 publications

References 22 publications

Local Influence Analysis for Quasi-Likelihood Nonlinear Models with Random Effects

Local Influence Analysis for Quasi-Likelihood Nonlinear Models with Random Effects

Heteroscedasticity and/or autocorrelation checks in longitudinal nonlinear models with elliptical and AR(1) errors

Testing for departures from nominal dispersion in generalized nonlinear models with varying dispersion and/or additive random effects

Contact Info

Product

Resources

About