Local Influence Analysis for Skew-Normal Linear Mixed Models

Montenegro, Lourdes C.; Lachos, Víctor H.; Bolfarine, Heleno

doi:10.1080/03610920802238647

Cited by 17 publications

(5 citation statements)

References 17 publications

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“…One of the simplest MSN distributions is the restricted multivariate skew-normal (rSN) distribution. According to Arellano-Valle and Genton (2005) and Bolfarine et al (2007), the probability density function (PDF) of rSN distribution is…”

Section: Preliminariesmentioning

confidence: 99%

Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions

Sepahdar

Madadi

Jamalizadeh

2022

Stat

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The mixture‐of‐experts (MoE) paradigm attempts to learn complex models by combining several “experts” via probabilistic mixture models. Each expert in the MoE model handles a small area of the data space in which a gating function controls the data‐to‐expert assignment. The MoE framework has been used extensively in designing non‐linear models in machine learning and statistics to model the heterogeneity in data for the purpose of regression, classification and clustering. The existing MoE of multi‐target regression (MoE‐MTR) models for continuous data is based on multivariate normal distributions. However, in many practical situations, for a set of data, a group or groups of observations may exhibit asymmetric and heavy‐tailed behaviour, and inference based on symmetric distributions in such situations can unduly affect the fit of the regression model. We introduce here a novel robust multivariate non‐normal MoE model by the use of mean mixture of normal distributions. The proposed model can handle the issues of MoE‐MTR models regarding possibly skewed, heavy‐tailed and noisy data. Maximum likelihood estimates of model parameters are developed based on an expectation‐maximization (EM)‐type algorithm. Parsimony is also obtained by imposing suitable constraints on the expert dispersion matrices. The usefulness of the proposed methodology is illustrated using simulated and real data sets.

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Section: Preliminariesmentioning

confidence: 99%

Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions

Sepahdar

Madadi

Jamalizadeh

2022

Stat

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“…Similar to Montenegro et al, [33] c = ζ + 3.0 × SD(ζ ) is used as a benchmark. Their corresponding index plots are presented in Figure 7.…”

Section: A Real Data Examplementioning

confidence: 99%

Maximum-likelihood estimation and influence analysis in multivariate skew-normal reproductive dispersion mixed models for longitudinal data

Zhao

Tang

2015

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Various mixed models were developed to capture the features of between-and within-individual variation for longitudinal data under the normality assumption of the random effect and the within-individual random error. However, the normality assumption may be violated in some applications. To this end, this article assumes that the random effect follows a skew-normal distribution and the within-individual error is distributed as a reproductive dispersion model. An expectation conditional maximization (ECME) algorithm together with the Metropolis-Hastings (MH) algorithm within the Gibbs sampler is presented to simultaneously obtain estimates of parameters and random effects. Several diagnostic measures are developed to identify the potentially influential cases and assess the effect of minor perturbation to model assumptions via the case-deletion method and local influence analysis. To reduce the computational burden, we derive the first-order approximations to case-deletion diagnostics. Several simulation studies and a real data example are presented to illustrate the newly developed methodologies.

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“…The technique proposed by was successfully applied to nonlinear structural equation models (Lee et al, 2006), multilevel models (Shi and Chen, 2008), skewnormal linear mixed models (Montenegro et al, 2009), the Grubbs' model (Osorio et al, 2009), and skew-normal/independent linear mixed models (Zeller et al, 2010), to name just a few recent works.…”

Section: Introductionmentioning

confidence: 99%

Influence Assessment in an Heteroscedastic Errors-in-Variables Model

Galea

Castro

2012

Communications in Statistics - Theory and Methods

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The main goal of this article is to consider influence assessment in models with error-prone observations and variances of the measurement errors changing across observations. The techniques enable to identify potential influential elements and also to quantify the effects of perturbations in these elements on some results of interest. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.

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Local Influence Analysis for Skew-Normal Linear Mixed Models

Cited by 17 publications

References 17 publications

Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions

Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions

Maximum-likelihood estimation and influence analysis in multivariate skew-normal reproductive dispersion mixed models for longitudinal data

Influence Assessment in an Heteroscedastic Errors-in-Variables Model

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