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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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        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.