Generalized Leverage and its Applications

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

doi:10.1111/1467-9469.00086

Cited by 97 publications

(73 citation statements)

References 26 publications

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“…Next, we shall be concerned with the identification of influential observations and residual analysis. In what follows we shall use the generalized leverage proposed by Wei, Hu and Fung (1998), which is defined as…”

Section: Diagnostic Measuresmentioning

confidence: 99%

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Beta Regression for Modelling Rates and Proportions

Ferrari

Cribari‐Neto

2004

Journal of Applied Statistics

2,257

1,822

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Abstract. This paper proposes a regression model where the response is beta distributed using a parameterization of the beta law that is indexed by mean and dispersion parameters. The proposed model is useful for situations where the variable of interest is continuous and restricted to the interval (0, 1) and is related to other variables through a regression structure. The regression parameters of the beta regression model are interpretable in terms of the mean of the response and, when the logit link is used, of an odds ratio, unlike the parameters of a linear regression that employs a transformed response. Estimation is performed by maximum likelihood. We provide closed-form expressions for the score function, for Fisher's information matrix and its inverse. Hypothesis testing is performed using approximations obtained from the asymptotic normality of the maximum likelihood estimator. Some diagnostic measures are introduced. Finally, practical applications that employ real data are presented and discussed.

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Section: Diagnostic Measuresmentioning

confidence: 99%

“…Let θ be the maximum likelihood estimator of θ, assumed to exist and be unique, and assume that the log-likelihood function has second-order continuous derivatives with respect to θ and y. Wei, Hu and Fung (1998) have shown that the generalized leverage is obtained by evaluating…”

Section: Diagnostic Measuresmentioning

confidence: 99%

Beta Regression for Modelling Rates and Proportions

Ferrari

Cribari‐Neto

2004

Journal of Applied Statistics

2,257

1,822

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“…The main idea behind the concept of leverage (see, for instance, Emerson, Hoaglin and Kempthorne, 1984;St. Laurent and Cook, 1992;Wei, Hu and Fung, 1998) is that of evaluating the influence of y i on its own predicted value. This influence may be well represented by the derivative ∂ŷ i /∂y i that equals h ii in the normal linear case, where h ii is the ith principal diagonal element of the projection matrix H = X(X T X) −1 X T and X is the model matrix.…”

Section: Generalized Leveragementioning

confidence: 99%

“…Laurent and Cook (1992) and Wei et al(1998). Using equation (2.6) of Wei et al (1998) the (n × n) matrix (∂ŷ/∂y) of generalized leverage in univariate elliptical nonlinear regression models may be expressed as…”

Section: Generalized Leveragementioning

confidence: 99%

The Use of Score Tests for Inference on Variance Components

Verbeke¹,

Molenberghs²

2003

Biometrics

203

144

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Summary Whenever inference for variance components is required, the choice between one‐sided and two‐sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two‐sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one‐sided tests, however, one‐sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two‐sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well‐chosen one‐sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.

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“…A medida de alavancagem proposta por Wei et al (1998), generaliza a definição de pontos de alavanca usados em modelos de regressão linear múltipla para outros modelos lineares pertencentes a classe dos MLG, sendo desenvolvida a partir dos elementos h ij da matriz H que é conhecida como matriz de projeção ou "matriz chapéu" (H = X(X'X) -1 X'). Supondo que todos os pontos exerçam a mesma influência sobre os valores ajustados, pode-se esperar que os elementos h ii da diagonal da matriz H sejam definidos por w / n, onde w é o somatório dos elementos h ii definido pelos coeficientes dos modelos e n é o número de observações.…”

Section: Critérios De Adequaçãounclassified

Modelagem da fração de não-conformes em processos industriais

Sant’Anna

Caten

2010

Pesqui. Oper.

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ResumoEm qualquer processo industrial, pode ser definido um conjunto de causas ou fatores que produzem determinado efeito sobre uma ou mais características de qualidade de um produto que pode ou não satisfazer às especificações do cliente, gerando a produção de produtos não-conformes. A modelagem da proporção ou fração de produtos não-conformes utilizando-se o modelo de regressão linear não é adequada por pelo menos duas razões: (i) pressupõe que as proporções seguem a distribuição normal, que não é correto; e (ii) possibilita a previsão de valores fora do intervalo [0,1]. Alternativas à modelagem da proporção de não-conformes são os Modelos Lineares Generalizados e os Modelos de Regressão Beta. O objetivo deste artigo é modelar a fração de não-conformes às especificações de uma indústria curtidora com enfoque nos Modelos de Regressão Beta e Modelo Linear Generalizado. Esses modelos podem ser estendidos a processos industriais que envolvam a produção de produtos não-conformes às especificações de manufatura.Palavras-chave: modelo linear generalizado; modelo de regressão beta; fração de não-conformes. AbstractIn any industrial process, one can enumerate causes or factors that act on one or more quality characteristics of the resulting product such that they fail to meet customers' specifications, generating items deemed as nonconforming. Modeling the fraction or proportion of nonconforming items using linear regression models is not adequate for at least two reasons: (i) proportions are assumed to follow a Normal distribution, which is not correct, and (ii) predicted responses will not necessarily be confined in the [0,1]-interval. Alternative approaches to the modeling of nonconforming proportions are based on Generalized Linear Models and Beta Regression Models. In this paper we present a case study where the objective is to model the nonconforming fraction of items emerging from a tanning process; our analysis uses Generalized Linear Models and Beta Regression Models. The developments presented in the paper may be extended to other industrial process where the proportion of nonconforming items is easily accessible.

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Generalized Leverage and its Applications

Cited by 97 publications

References 26 publications

Beta Regression for Modelling Rates and Proportions

Beta Regression for Modelling Rates and Proportions

The Use of Score Tests for Inference on Variance Components

Modelagem da fração de não-conformes em processos industriais

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