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Response Surface Methodology
CASOS Technical Report
Kathleen M. Carley, Natalia Y. Kamneva, Jeff Reminga
October 2004
CMU-ISRI-04-136
Carnegie Mellon University
School of Computer Science
ISRI - Institute for Software Research International
CASOS - Center for Computational Analysis of Social and Organizational Systems
1 This work was supported in part by NASA # NAG-2-1569, Office of Naval Research Grant N00014-02-1-
0973, “Dynamic Network Analysis: Estimating Their Size, Shape and Potential Weaknesses”, Office of Naval
Research, N00014-97-1-0037, “Constraint Based Team Transformation and Flexibility Analysis” under “Adaptive
Architectures”, the DOD and the National Science Foundation under MKIDS. Additional support was provided by
the center for Computational Analysis of Social and Organizational Systems (CASOS)
(http://www.casos.cs.cmu.edu) and the Institute for Software Research International at Carnegie Mellon University.
The views and conclusions contained in this document are those of the authors and should not be interpreted as
representing the official policies, either expressed or implied, of the National Science Foundation, or the U.S.
government.
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Response Surface Methodology 5b. GRANT NUMBER
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Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
Keywords: Response Surface Methodology (RSM), regression analysis, linear regression
model, regressors, variable selection, model building, full model, multicollinearity, ridge
regression, unit length scaling, condition number, optimization, Simulated Annealing, global
optimum
Abstract
There is a problem faced by experimenters in many technical fields, where, in general, the
response variable of interest is y and there is a set of predictor variablesx ,x ,...,x . For
1 2 k
example, in Dynamic Network Analysis (DNA) Response Surface Methodology (RSM) might be
useful for sensitivity analysis of various DNA measures for different kinds of random graphs and
errors.
In Social Network Problems usually the underlying mechanism is not fully understood, and
the experimenter must approximate the unknown function g with appropriate empirical model
y = f( x ,x ,..., x ) + ε, where the term ε represents the error in the system.
1 2 k
Usually the function f is a first-order or second-order polynomial. This empirical model is
called a response surface model.
Identifying and fitting from experimental data an appropriate response surface model
requires some use of statistical experimental design fundamentals, regression modeling
techniques, and optimization methods. All three of these topics are usually combined into
Response Surface Methodology (RSM).
Also the experimenter may encounter situations where the full model may not be appropriate.
Then variable selection or model-building techniques may be used to identify the best subset of
regressors to include in a regression model. In our approach we use the simulated annealing
method of optimization for searching the best subset of regressors. In some response surface
experiments, there can be one or more near-linear dependences among regressor variables in the
model. Regression model builders refer to this as multicollinearity among the regressors.
Multicollinearity can have serious effects on the estimates of the model parameters and on the
general applicability of the final model.
The RSM is also extremely useful as an automated tool for model calibration and validation
especially for modern computational multi-agent large-scale social-networks systems that are
becoming heavily used in modeling and simulation of complex social networks.
The RSM can be integrated in many large-scale simulation systems such as BioWar, ORA
and is currently integrating in Vista, Construct, and DyNet.
This report describes the theoretical approach for solving of these problems and the
implementation of chosen methods.
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