Filidor V. Labra

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

HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays, and consequently the responses are either left or right censored. Linear and nonlinear mixed-effects models, with modifications to accommodate censoring (LMEC and NLMEC), are routinely used to analyze this type of data. Recently, Vaida and Liu (2009) proposed an exact EM-type algorithm for LMEC/NLMEC, called the SAGE algorithm (Meng and Van Dyk, 1997), that uses closed-form expressions at the E-step, as opposed to Monte Carlo simulations. Motivated by this algorithm, we propose here an exact ECM algorithm (Meng and Rubin, 1993) for LMEC/NLMEC, which enables us to develop local influence analysis for mixed-effects models on the basis of conditional expectation of the complete-data log-likelihood function. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex which makes it difficult to directly apply the approach of Cook (1977, 1986). Some useful perturbation schemes are also discussed. Finally, the results obtained from the analyses of two HIV AIDS studies on viral loads are presented to illustrate the newly developed methodology.

Influence analyses of skew-normal/independent linear mixed models

A extension of some diagnostic procedures to skew-normal/independent linear mixed models is discussed. This class provides a useful generalization of normal (and skew-normal) linear mixed models since it is assumed that the random effects and the random error terms follow jointly a multivariate skew-normal/independent distribution. Inspired by the EM algorithm, a local influence analysis for linear mixed models, following Zhu and Lees approach is developed. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex and Cooks well-known approach can be very difficult for obtaining measures of local influence. Moreover, the local influence measures obtained under this approach are invariant under reparameterization. Four specific perturbation schemes are also discussed. Finally, a real data set is analyzed in order to illustrate the usefulness of the proposed methodology.

Statistical diagnostics for nonlinear regression models based on scale mixtures of skew-normal distributions

The purpose of this paper is to develop diagnostics analysis for nonlinear regression models (NLMs) under scale mixtures of skew-normal (SMSN) distributions introduced by Garay et al. [Nonlinear regression models based on SMSN distributions. J. Korean Statist. Soc. 2011;40:115–124]. This novel class of models provides a useful generalization of the symmetrical NLM [Vanegas LH, Cysneiros FJA. Assessment of diagnostic procedures in symmetrical nonlinear regression models. Comput. Statist. Data Anal. 2010;54:1002–1016] since the random terms distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as the skew-t, skew-slash, skew-contaminated normal distributions, among others. Motivated by the results given in Garay et al. [Nonlinear regression models based on SMSN distributions. J. Korean Statist. Soc. 2011;40:115–124], we presented a score test for testing the homogeneity of the scale parameter and its properties are investigated through Monte Carlo simulations studies. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. The newly developed procedures are illustrated considering a real data set.

An application of the local influence diagnostics to ridge regression under elliptical model

In this article, we study the effect of a minor perturbation on the ridge estimator considering the elliptical distribution for the errors. The necessary matrices for assessing the local influence under the perturbation of the explanatory variables and the scale matrix are derived. The Longley data is analyzed for illustration.

Local influence in null intercept measurement error regression under a student_t model

Abstract In this paper we discuss the application of local influence in a measurement error regression model with null intercepts under a Student_t model with dependent populations. The Student_t distribution is a robust alternative to modelling data sets involving errors with longer than Normal tails. We derive the appropriate matrices for assessing the local influence for different perturbation schemes and use real data as an illustration of the usefulness of the application.