Beyond Least Squares: Estimation of Dynamic Models With Alternative Likelihoods and Kalman Filtering

Abstract

From business to healthcare and operations to strategy, grounding system dynamics models in data is indispensable for theory and practice. However, formal estimation is difficult due to incomplete data, model mis-specification, process noise, and measurement error. This complexity has limited the quantity and quality of formal estimation. We argue that comparing generic and easy-to-apply estimation methods for common models is fruitful for identifying methods that work well for SD practitioners. Using the classical SEIR model, we compare standard least squares against maximum likelihood estimators including variance-scaled Gaussian, log Gaussian, Poisson, and negative binomial estimators, and assess the value of (extended) Kalman filtering. Under different assumptions about data availability and noise, we find that least squares, log Gaussian, and scaled Gaussian likelihoods perform poorly in estimating confidence intervals. The negative binomial and Kalman filtering with variance scaling and auto-correlated process noise are promising across different setups. Implications for modelers are discussed.