Exponential models are widely used in many chemistry, biology and ecology applications when analyzing data and fitting models. Examples include in chemical kinetics particularly for first order reaction rates when the rate at which the reactant is used up is proportional to its concentration; exponential growth of bacteria and invasive species; and the sum-of-exponentials models for time-resolved spectroscopy data. This poster is continued research of work presented at the ACS Spring 2021 virtual meeting by Johnson et al., 2021. Exponential models are fit to known linear functions of data. Simulations are used to compare models formed by taking the log of the exponential models examined and undoing the transformation after the models are fit. The linear models obtained on transformation are compared using the regression fitting criteria of ordinary least squares (OLS), reverse OLS, maximum likelihood estimation (MLE), orthogonal regression (OR), geometric mean regression (GMR), and robust regression (RR). The Bootstrap is also used to find an improved estimate by incorporating bias in estimation. 1,000 Monte Carlo simulations are used to compare the OLS, reverse-OLS, MLE, OR, GMR and RR estimates. Comparisons are made using the simulated data, with the introduction of data that has increased variability on the error terms and with the introduction of known influential/outlier observations.

Regression criteria comparing exponential models fit to data: Chemistry applications

ACS Fall 2021

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