Hyperspectral imaging is an important asset of modern spectroscopy. It allows us to perform optical metrology at a high spatial resolution, for example in cathodoluminescence in scanning electron microscopy. However, hyperspectral datasets present added challenges in their analysis compared to individually taken spectra due to their lower signal to noise ratio and specific aberrations. On the other hand, the large volume of information in a hyperspectral dataset allows the application of advanced statistical analysis methods derived from machine-learning. In this article, we present a methodology to perform model fitting on hyperspectral maps, leveraging principal component analysis to perform a thorough noise analysis of the dataset. We explain how to correct the imaging shift artifact, specific to imaging spectroscopy, by directly evaluating it from the data. The impact of goodness-of-fit-indicators and parameter uncertainties is discussed. We provide indications on how to apply this technique to a variety of hyperspectral datasets acquired using other experimental techniques. As a practical example, we provide an implementation of this analysis using the open-source Python library hyperspy, which is implemented using the well established Jupyter Notebook framework in the scientific community. (C)& nbsp;2022 Author(s). & nbsp;