Regression-based approaches for simulation meta-modelling in the presence of heterogeneity and correlation
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Date
2021
Authors
Garces, L.P.D.M.
Bogomolov, T.
Chiera, B.A.
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Conference paper
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Proceedings of the International Congress on Modelling and Simulation, MODSIM, 2021, pp.827-833
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24th International Congress on Modelling and Simulation, MODSIM 2021 (5 Dec 2021 - 10 Dec 2021 : Sydney, Australia)
Abstract
We discuss several regression-based methods for simulation meta-modelling and illustrate these methods using combat simulator data. Since the use of common random numbers (CRNs) as a variance reduction technique induces correlations in the outputs generated by different simulation inputs, it is crucial to accommodate the possibility of heterogeneity, heteroskedasticity, and correlation when building metamodels. Furthermore, mainstream combat simulators produces a variety of output types, including continuous, binary, and count data. While extensive work has been done towards the development of simulation meta-modelling methods for continuous outputs, the meta-modelling of discrete, binary, and count data seems to be less understood. To this end, we consider the use of estimated generalized least squares (EGLS), finite mixture generalized linear models (GLMs), and heteroskedastic binary regression, which specifically incorporate correlation, heteroskedasticity, and heterogeneity, for meta-modelling with continuous, binary, and count output data. EGLS extends the ordinary least squares (OLS) model by allowing the errors to have a non-diagonal covariance matrix. Finite mixture GLMs capture the possible heterogeneity in regression intercepts and slopes due to the possible existence of latent clusters in the simulation inputs.
Heteroskedastic binary regression is a latent variable approach for binary data which jointly models the conditional mean and the scale parameter of the distribution of the latent error term. An analysis of combat simulator data using the aforementioned methods shows that there is significant heterogeneity in the base mean levels and in the marginal effects of individual input variables for continuous and binary output data. Furthermore, likelihood ratio tests suggest an improved fit to the data when using heteroskedastic probit and logistic regression models over their homoskedastic counterparts. However, the analysis of count output data points to severe underdispersion in the data rather than heterogeneity in the sense of the finite mixture GLMs. This also suggests that approaches which jointly model the mean and dispersion may be viable alternatives.
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Copyright 2021 Proceedings of the International Congress on Modelling and Simulation, MODSIM