A straightforward answer would have been possible had you phrased your question in terms of analyzing the extent of urbanization rather than the process of urbanization. Traditionally, analysts used a combination of two indices to measure the extent of urbanization within a given jurisdiction: size and land-use diversity. Cut-off values were set, and settlements were then sorted into 'urban' (the ones that met the minimum values on both indices) and 'non-urban' (the ones that that did not meet either or both). A ration was then established between the 'urban' and the 'non-urban', which, in turn was used as an indication of the extent of urbanization in a certain jurisdiction.
However, none of the above may be relevant to your question if you mean 'process' literally. If so, an answer can be given only if you specify the objectives of the analysis or the particular aspects of the 'process' (unfolding over time) in which you are interested.