Diagnostic procedures in Birnbaum–Saunders nonlinear regression models

This paper proposes a general definition of residuals for Birnbaum–Saunders nonlinear regression models by studying their statistical properties analytically and using Monte Carlo experiments. Also, some diagnostic procedures are derived based on case-deletion and mean-shift outlier models such as one-step approximation, likelihood displacement, generalized Cook’s distance, outlier tests and some measures for identifying influential observations on partial F-test. A test for homogeneity of shape parameter is also developed. Residuals and influence diagnostic tools are illustrated by means of an example that allows us to relate the response variable lifetime of a metal piece and the explanatory variable work per cycle. Three models were compared to fit the dataset, two of them with nonlinear systematic components.