A mixed effects log-linear model based on the Birnbaum-Saunders distribution

  • Authors:

  • A. F. Desmond;Carlos L. Cíntora González;R. S. Singh;Xuewen Lu

  • Affiliations:

  • Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada;Departamento de Estadistica, Matemática y Cómputo, Universidad Autónoma Chapingo, Km. 38.5 Carretera México Texcoco Chapingo, 56230, Mexico;Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada;Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, Canada

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2012

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Abstract

In lifetime data analysis and particularly in engineering reliability contexts, the Birnbaum-Saunders (BISA) density is often suggested as a suitable model; see Birnbaum and Saunders (1969), Mann et al. (1974), and Desmond (1985). A linear regression model, obtained from a logarithmic transformation of the response variable, is useful in studying the effect of covariates on the response variable; see Rieck and Nedelman (1991), Tsionas (2001) and Galea et al. (2004). In this paper, an extension of the log-linear regression model of Rieck and Nedelman (1991), which considers random effects, is introduced. From a Monte Carlo simulation study, the performance of various estimation and prediction methods are studied. The usefulness of the mixed log-linear model is stressed and compared to the pure fixed effects log-linear regression BISA model. The new model is used to analyze a real data set, for which a fixed effects model is inappropriate.