Bootstrapping for confidence interval estimation and hypothesis testing for parameters of system dynamics models

Methods for confidence interval estimation and hypothesis testing used in the literature and implemented in system dynamics software packages typically assume that the data are normally distributed, not autocorrelated and not heteroskedastic. In dynamic models these assumptions are often violated. Here we propose the bootstrapping method for confidence interval estimation and hypothesis testing in system dynamics models and provide an overview of the issues involved in applying bootstrapping properly in dynamic models. Bootstrapping is a widely used and robust method but its use in system dynamics models is rare. Bootstrapping can handle violations of the maintained assumptions of traditional methods. It is also valid for small samples whereas traditional methods are valid only asymptotically. Another advantage of bootstrapping is that it is a convenient tool for testing hypotheses including complicated functions of parameters (e.g., multiplication, division of parameters). We provide two examples for illustration, one in discrete time and one in continuous time, including experimental data from the beer distribution game and field data from a study of service quality in the banking industry. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

[2]  D. Freedman.  Bootstrapping Regression Models , 1981 .

[3]  Rogelio Oliva,et al.  Cutting Corners and Working Overtime: Quality Erosion in the Service Industry , 2001, Manag. Sci..

[4]  John D. Sterman,et al.  System Dynamics: Systems Thinking and Modeling for a Complex World , 2002 .

[5]  Qi Li.  Nonparametric testing of closeness between two unknown distribution functions , 1996 .

[6]  G. S. Hongyi Li,et al.  Bootstrapping time series models , 1996 .

[7]  B. Efron,et al.  Bootstrap confidence intervals , 1996 .

[8]  James D. Hamilton.  Time Series Analysis , 1994 .

[9]  D. Sterman,et al.  Misperceptions of Feedback in a Dynamic Decision Making Experiment , 1989 .

[10]  D. Freedman,et al.  Bootstrapping a Regression Equation: Some Empirical Results , 1984 .

[11]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[12]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[13]  J. Horowitz.  Bootstrap Methods in Econometrics: Theory and Numerical Performance , 1995 .

[14]  R. Fair.  Bootstrapping Macroeconometric Models , 2001 .

[15]  Rogelio Oliva,et al.  Model calibration as a testing strategy for system dynamics models , 2003, Eur. J. Oper. Res..

[16]  B. Efron.  The jackknife, the bootstrap, and other resampling plans , 1987 .

[17]  Y. Barlas.  Multiple tests for validation of system dynamics type of simulation models , 1989 .