Diagnostics for non-linear regression Articles uri icon

publication date

  • August 2009

start page

  • 1109

end page

  • 1128


  • 9


  • 79

International Standard Serial Number (ISSN)

  • 0094-9655

Electronic International Standard Serial Number (EISSN)

  • 1563-5163


  • Sensitivity analysis in regression is concerned with assessing the sensitivity of the results of a regression model (e.g., the objective function, the regression parameters, and the fitted values) to changes in the data. Sensitivity analysis in least squares linear regression has seen a great surge of research activities over the last three decades. By contrast, sensitivity analysis in non-linear regression has received very little attention. This paper deals with the problem of local sensitivity analysis in non-linear regression. Closed-form general formulas are provided for the sensitivities of three standard methods for the estimation of the parameters of a non-linear regression model based on a set of data. These methods are the least squares, the minimax, and the least absolute value methods. The effectiveness of the proposed measures is illustrated by application to several non-linear models including the ultrasonic data and the onion yield data. The proposed sensitivity measures are shown to deal effectively with the detection of influential observations in non-linear regression models.


  • Mathematics


  • dual optimization problem; influential observations; lagrangian function; least absolute value; least square; minimax method; outlier detection; primal optimization problem