Comparison of 1-step and 2-step methods of fitting microbiological models

Previous conclusions that a 1-step fitting method gives more precise coefficients than the traditional 2-step method are confirmed by application to three different data sets. It is also shown that, in comparison to 2-step fits, the 1-step method gives better fits to the data (often substantially) with directly interpretable regression diagnostics and standard errors. The improvement is greatest at extremes of environmental conditions and it is shown that 1-step fits can indicate inappropriate functional forms when 2-step fits do not. 1-step fits are better at estimating primary parameters (e.g. lag, growth rate) as well as concentrations, and are much more data efficient, allowing the construction of more robust models on smaller data sets. The 1-step method can be straightforwardly applied to any data set for which the 2-step method can be used and additionally to some data sets where the 2-step method fails. A 2-step approach is appropriate for visual assessment in the early stages of model development, and may be a convenient way to generate starting values for a 1-step fit, but the 1-step approach should be used for any quantitative assessment.