Electron probe microanalysis (EPMA) is a well-established and practical technique for the microchemical analysis of materials. Although the physical processes that take place in microprobe analysis are relatively well understood, most of the commercially available approaches for data correction are still empirical or semi-empirical or make use of numerical calculations. Recently, a so-called Invariant Embedding Approach to Microanalysis, which is free of the disadvantage of the empirical methods, has been reported. This paper critically assesses the capabilities and limitations of this new approach when different values for the energies of the incident electrons, the atomic number and size and the sample tilt are considered. The theoretical results follow the general trends of the experimental data and Monte Carlo calculations, although a more in-depth study of the physical parameters involved in the model is still needed.