Nonlinear regression metamodels: a systematic approach

This paper proposes an approach for systematic development of nonlinear regression metamodels for stochastic simulation. This approach provides the practitioner with a process for the construction of nonlinear metamodels in general, and includes statistical techniques for estimation and validation of nonlinear regression models. In order to ensure that the resulting metamodel is a valid substitute for the original simulation model, validation techniques are suggested. In a case study, the proposed application leads to simple function that adequately approximate the model's behaviour, while linear regression polynomials result in a poor fit.

[1]  Isabel R. Santos,et al.  Simulation metamodels for modeling output distribution parameters , 2007, 2007 Winter Simulation Conference.

[2]  M. I. R. D. Santos,et al.  ESTIMATION OF NONLINEAR SIMULATION METAMODELS USING CONTROL VARIATES , 2005 .

[3]  M. Isabel Reis dos Santos,et al.  Using subsystem linear regression metamodels in stochastic simulation , 2009, Eur. J. Oper. Res..

[4]  Jack P. C. Kleijnen,et al.  Generalization of simulation results practicality of statistical methods , 1979 .

[5]  Jack P. C. Kleijnen,et al.  A methodology for fitting and validating metamodels in simulation , 2000, Eur. J. Oper. Res..

[6]  Christos Alexopoulos,et al.  A Comprehensive Review of Methods for Simulation Output Analysis , 2006, Proceedings of the 2006 Winter Simulation Conference.

[7]  James R. Wilson,et al.  Validation of Simulation Analysis Methods for the Schruben-Margolin Correlation-Induction Strategy , 1992, Oper. Res..

[8]  M. Isabel Reis dos Santos,et al.  Estimating and Validating Nonlinear Regression Metamodels in Simulation , 2007, Commun. Stat. Simul. Comput..

[9]  Jack P. C. Kleijnen,et al.  Cross-validation using the t statistic☆ , 1983 .

[10]  Jack P. C. Kleijnen,et al.  State-of-the-Art Review: A User's Guide to the Brave New World of Designing Simulation Experiments , 2005, INFORMS J. Comput..

[11]  J. Kleijnen,et al.  Response surface methodology revisited , 2002, Proceedings of the Winter Simulation Conference.

[12]  Jack P. C. Kleijnen,et al.  Supply chain simulation tools and techniques: a survey , 2005, Int. J. Simul. Process. Model..

[13]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[14]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[15]  Jack P. C. Kleijnen,et al.  Simulation: A Statistical Perspective , 1992 .

[16]  Jack P. C. Kleijnen,et al.  Validation of regression metamodels in simulation: Bootstrap approach , 2006, Eur. J. Oper. Res..

[17]  Russell R. Barton,et al.  Metamodels for simulation input-output relations , 1992, WSC '92.

[18]  M. Isabel Reis dos Santos,et al.  Statistical fitting and validation of non-linear simulation metamodels: A case study , 2006, Eur. J. Oper. Res..

[19]  J. Kleijnen.  Statistical tools for simulation practitioners , 1986 .

[20]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[21]  Hershey H. Friedman,et al.  Validating the simulation metamodel: Some practical approaches , 1985 .

[22]  Bernard P. Zeigler,et al.  Theory of modeling and simulation , 1976 .

[23]  M. Bilodeau,et al.  Theory of multivariate statistics , 1999 .

[24]  Joan M. Donohue,et al.  Simulation Designs and Correlation Induction for Reducing Second-Order Bias in First-Order Response Surfaces , 1993, Oper. Res..

[25]  H. White,et al.  NONLINEAR REGRESSION ON CROSS-SECTION DATA , 1980 .

[26]  Russell R. Barton.  Design of experiments for fitting subsystem metamodels , 1997, WSC '97.

[27]  M. Isabel Reis dos Santos,et al.  Sequential designs for simulation experiments: nonlinear regression metamodeling , 2007 .

[28]  M. E. Johnson,et al.  A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data , 1981 .

[29]  J. Kleijnen.  Regression metamodels for simulation with common random numbers: comparison of validation tests and confidence intervals , 1992 .

[30]  Andrej Pázman,et al.  Nonlinear Regression , 2019, Handbook of Regression Analysis With Applications in R.

[31]  Enver Yücesan,et al.  Randomization tests for initialization bias in simulation output , 1993 .

[32]  M. F. Fuller,et al.  Practical Nonparametric Statistics; Nonparametric Statistical Inference , 1973 .

[33]  M. Isabel Reis dos Santos,et al.  Sequential experimental designs for nonlinear regression metamodels in simulation , 2008, Simul. Model. Pract. Theory.

[34]  Inci Batmaz,et al.  A metamodeling methodology involving both qualitative and quantitative input factors , 2003, Eur. J. Oper. Res..

[35]  Jack P. C. Kleijnen.  Design and Analysis of Simulation Experiments , 2007 .

[36]  Arjun K. Gupta.  The Theory of Linear Models and Multivariate Analysis , 1981 .

[37]  M. Isabel Reis dos Santos,et al.  The main issues in nonlinear simulation metamodel estimation , 1999, WSC '99.

[38]  M. Isabel Reis dos Santos,et al.  Construction of Stochastic Simulation Metamodels based on Unreplicated Smoothed Data , 2009, Simul..

[39]  Dep. Matemática,et al.  Validation of nonlinear simulation metamodels , 2022 .