Mathematical and statistical models may be of differing complexity. Their most usual use is to estimate parameters and calculate test statistics for relatively standard and general hypotheses. Such very general tests have the advantage that the assumptions for the model are simple and rela­ tively easy to check, but the disadvantage that they may be of relatively low power (in a statistical sense). Where the data are expensive or time consuming to collect, as in studies of ego identity status using interview methods, the question arises as to whether including more of the salient features of the study in a more sophisticated model may allow stronger conclusions to be drawn. The advantages and disadvantages of more com­ plex statistical models are discussed in this chapter, with reference to some particular aspects of ego identity status development studies.