Journal of Applied Statistics, Vol. 31, No. 9, 1049–1064, November 2004 Influence Diagnostics in log-Birnbaum– Saunders Regression Models MANUEL GALEA*, VI ´ CTOR LEIVA-SA ´ NCHEZ** AND GILBERTO A. PAULA† *Departamento de Estadı ´stica, Universidad de Valparaı ´so, Chile, **Departamento de Estadı ´sticayCa ´lculo, Universidad Auto ´noma Agraria Antonio Narro, Me ´xico, †Departamento de Estatı ´stica, Universidade de Sa ˜o Paulo, Brasil A In this paper we present various diagnostic methods for a linear regression model under a logarithmic Birnbaum–Saunders distribution for the errors, which may be applied for accelerated life testing or to compare the median lives of several populations. Some influence methods,suchasthelocalinfluence,totallocalinfluenceofanindividualandgeneralizedleverage are derived, analysed and discussed. We also present a connection between the local influence andgeneralizedleveragemethods.Adiscussionofthecomputationofthelikelihooddisplacement as well as the normal curvature in the local influence method are presented. Finally, an example withrealdataisgiven for illustration. K W: Birnbaum–Saunders distribution, life distributions, sinh-normal distribution, fatigue life, log-linear models, influence diagnostic, generalized leverage, local influence, maximum likelihood estimator Introduction Diagnostic methods for normal linear regression models have been investigated in the statistical literature (see, for instance, Belsley etal., 1980; Cook & Weisberg, 1982; Chatterjee & Hadi, 1988). The majority of the works have put an emphasis on studying the effect of eliminating observations on the results from the fitted model, particularly the parameter estimates. Alternatively, Cook (1986) has proposed an interesting method, named local influence, to assess the effect of small perturbations in the model on the parameter estimates. Several authors have extended the local influence method to various regression models (see, for example, Lawrence, 1988; Escobar & Meeker, 1992; Paula, 1993; Galea et al., 1997, 2000; Ortega etal., 2003; Dı ´az-Garcı ´a etal., 2003). On the other hand, fatigue is the structural damage that results when a material is exposed to fluctuating stresses and strains. It was first recognized as a cause of failure in carriage axles in the early 1800s. It was blamed in the 1950s for the crashes of British Comet aeroplanes. This problem of fatigue of materials is also presented in other cases. Correspondence Address: M. Galea, Departamento de Estadı ´stica, Universidad de Valparaı ´so, Casilla 5030, Valparaı ´so, Chile. Email: manuel.galea@uv.cl 0266-4763 Print/ 1360-0532 Online/04/091049-16 ©2004 Taylor & Francis Ltd DOI: 10.1080/0266476042000280409