Influence diagnostics in linear and nonlinear mixed-effects models with censored data

Influence assessment in censored mixed-effects models using the multivariate Student’s-tdistribution

“…In order to quantify the influence of a case in the data, we follow the method based on the function $M{false(0false)}_l={\sum }_{k=1}^r{\stackrel{\sim }{\zeta }}_k{\mathrm{bold-italic\epsilon }}_{kl}^2$, where ζ̃ k = ζ k /( ζ 1 + … + ζ r ) and ${\mathit{\epsilon }}_k^2={false({\mathit{\epsilon }}_{k1}^2,\dots ,{\mathit{\epsilon }}_{kg}^{2}false)}^{\top }$ with {( ζ k , ε k ), k = 1, …, g } the eigenvalue-eigenvector pairs of −2 Q ­­ ¨ ω 0 , where ζ 1 ≥ …, ≥ ζ r > ζ r +1 = … = 0 and the eigenvectors { ε k , k = 1, …, g } are orthonormal (for details see Matos et al 2013a). The lth case may be regarded as influential if M (0) l is larger than the benchmark (cut-off).…”

“…Hence, developing influence diagnostics is a key in assessing the effect of a single observation on the predicted scores for other observations, and consequently the overall parameter estimates, all based on the mean function. Although diagnostics for the traditional normality based LME and LMEC (Matos et al 2013a) models exist, those for heavy-tailed LMEC/NLMEC models are not well developed. Influence analysis is generally conducted using two primary approaches.…”

“…This Q -function approach produces result similar to those obtained using the Cook’s approach. Recently, Matos et al (2013a) used this Q -function approach for developing influence diagnostics for LMEC/NLMEC models. Stemming from the same difficulty with intractable integrals (for example, the pdfs of truncated multivariate Student’s- t distributions) in implementing the Cook’s diagnostics for the t -LMEC/NLMEC model of Matos et al (2013b), we develop case-deletion and influence diagnostics measures using the approach of Zhu et al (2001) (see also Lee and Xu 2004).…”

The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis

“…Recently, some authors have investigated the assessment of local influence in different regression models, with the presence and absence of censored data, for instance, Lemonte and Patriota [3] considered the problem of assessing local influence in Birnbaum-Saunders nonlinear regression models; Rondon et al [4] adapted local influence methods to Birnbaum-Saunders nonlinear regression models; Matos et al [5] investigated local influence in linear and nonlinear mixedeffects models with censored data; Paula [6] derived curvature calculations under various perturbation schemes in double generalized linear models and Fachini et al [7] investigated local influence in location-scale models for bivariate survival times based on the copula to model the dependence of bivariate survival data with cure fraction. We develop a similar methodology to detect influential subjects in LOLLW regression models for censored data.…”

An extension of Birnbaum-Saunders distributions based on scale mixtures of skew-normal distributions with applications to regression models

“…ln this case, the method of Zhu and Lee (2001) and Zhu et al (2001) instead of the method of Cook (1986). The methods of Zhu and Lee (2001) and Zhu et al (2001) have also been successfully applied in models based on the class of scale mixture of skew-normal distributions, see for example Matos et al (2013) and Zeller et al (2010).…”