Hey Rob,
From my understanding, you're looking for an explanation as to why 'nlinfit' and 'fitnlm' don't support exponential error models, whereas 'nlmefit' does. The key differences among nlinfit, fitnlm, and nlmefit in MATLAB are rooted in their intended purposes and the statistical models they accommodate.
The capability of 'nlmefit' to handle exponential error models, stems from its foundational design and the specific application domains it targets. 'nlinfit' and 'fitnlm' are designed for nonlinear least squares regression, which assumes a uniform error variance throughout all predictions. This assumption falls short in various real-world applications, such as pharmacokinetic (PK) analysis, where the error in measurements tends to grow with the size of the measurement. Conversely, 'nlmefit' is crafted for nonlinear mixed-effects models, which are essential in PK/PD analysis, enabling the model to include both fixed and random effects among individuals and to accommodate more intricate error structures, like those exponential in nature. This divergence in functionality reflects the distinct requirements of the user base each function is aimed at. While 'nlinfit' and 'fitnlm' are versatile tools for numerous nonlinear fitting tasks, 'nlmefit' is designed for specific scenarios where modeling the variance in data as a function of its magnitude (or other variables) is crucial.
One workaround for this can be to write custom error models using MATLAB optimization toolbox, where we can define our own likelihood function that included an exponential error model.
Please go through the following documentation to learn more,
Hope this helps.
