Fitting multiple models to multiple data sets

• Published in: Journal of sea research Vol. 143; pp. 48 - 56
• Main Authors: Marques, Gonçalo M., Lika, Konstadia, Augustine, Starrlight, Pecquerie, Laure, Kooijman, Sebastiaan A.L.M.
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.01.2019; Elsevier BV; Elsevier
• Subjects: Biodiversity and Ecology; Biological activity; Biology; Case studies; Computer simulation; Confidence intervals; Data; Datasets; Energy budget; Environmental Sciences; Fitting models; Interval estimates; Loss function; Mathematical models; Modelling; Monte Carlo simulation; Monte Carlo simulation studies; Parameter estimation; Parameters; Point estimates; Scattering; Solutions; Water treatment; Loss function; Parameter estimation; Point estimates; Monte Carlo simulation studies; Interval estimates; Fitting models; covariation method; ACL; parameters
• ISSN: 1385-1101; 1873-1414
• DOI: 10.1016/j.seares.2018.07.004

Dynamic Energy Budget (DEB) theory constitutes a coherent set of universal biological processes that have been used as building blocks for modeling biological systems over the last 40 years in many applied disciplines. In the context of extracting parameters for DEB models from data, we discuss the methodology of fitting multiple models, which share parameters, to multiple data sets in a single parameter estimation. This problem is not specific to DEB models, and is (or should be) really general in biology. We discovered that a lot of estimation problems that we suffered from in the past originated from the use of a loss function that was not symmetric in the role of data and predictions. We here propose two much better symmetric candidates, that proved to work well in practice. We illustrate estimation problems and their solutions with a Monte-Carlo case study for increasing amount of scatter, which decreased the amount of information in the data about one or more parameter values. We here validate the method using a set of models with known parameters and different scatter structures. We compare the loss functions on the basis of convergence, point and interval estimates. We also discuss the use of pseudo-data, i.e. realistic values for parameters that we treat as data from which predictions can differ. These pseudo-data are used to avoid that a good fit results in parameter values that make no biological sense. We discuss our new method for estimating confidence intervals and present a list of concrete recommendations for parameter estimation. We conclude that the proposed method performs very well in recovering parameter values of a set of models, applied to a set of data. This is consistent with our large-scale applications in practice. •A new method of fitting multiple models to multiple datasets is proposed.•General methodology to arrive at interval estimates for parameter values is proposed.•Two loss functions are compared on the basis of convergence and parameter estimates.•The amount of scatter, but not its cause, strongly affects parameter estimates.•Pseudo-data are used to increase identifiability of parameters.