Regression Metamodels for Simulation with Common Random Numbers: Comparison of Validation Tests and Confidence Intervals

Linear regression analysis is important in many fields. In the analysis of simulation results, a regression (meta)model can be applied, even when common pseudorandom numbers are used. To test the validity of the specified regression model, Rao (1959) generalized the F statistic for lack of fit, whereas Kleijnen (1983) proposed a cross-validation procedure using a Student's t statistic combined with Bonferroni's inequality. This paper reports on an extensive Monte Carlo experiment designed to compare these two methods. Under the normality assumption, cross-validation is conservative, whereas Rao's test realizes its nominal type I error and has high power. Robustness is investigated through lognormal and uniform distributions. When simulation responses are distributed lognormally, then cross-validation using Ordinary Least Squares is the only technique that has acceptable type I error. Uniform distributions give results similar to the normal case. Once the regression model is validated, confidence intervals for the individual regression parameters are computed. The Monte Carlo experiment compares several confidence interval procedures. Under normality, Rao's procedure is preferred since it has good coverage probability and acceptable half-length. Under lognormality, Ordinary Least Squares achieves nominal coverage probability. Uniform distributions again give results similar to the normal case.