Time versus rate in parameter estimation of nonlinear temperature-dependent development models

A potential problem exists when rate (1/time) is used for parameter estimation instead of time in least-squares estimation of nonlinear development models, because the squared error is the quantity, that is minimized by this technique. Minimizing the squared error in the rates is not equivalent to minimizing the squared error in time. This is of particular significance in modeling insect development because, when development times are largest, rates are small and squared errors in the rates produce large errors in time predictions. The purpose of this study was to show that, in many cases, parameters should be evaluated in terms of the observed data. Using least-squares techniques on rates did not allow for the minimization of the absolute squared error in time at low temperatures. Least-squares techniques applied to development time produced good predicted values throughout the temperature range in particular cases. These results show that when parameters are not evaluated in terms of the observed data but rather in some modified form such as rate, erroneous predictions may result.