A pair of polychotomous random variables (Y1,Y2)⊤=:Y
Polychotomous ordinal data arise in many areas of statistical analysis and are particularly frequent in surveys and observational studies. Several questions may be asked to measure people’s feelings on a matter of interest, as well as some relevant information reported on a monotonic scale. Examples include individuals’ perceived social class or their educational attainments. Since it is usually acknowledged that these types of data possess levels that can be “naturally” ordered, it is desirable to account for this feature in the model’s representation and estimation. Specific methodologies were developed to address this issue, starting from the seminal works of Aitchison and Silvey (1957) and Snell (1964), up to their modern forms of the cumulative link models (CLM; McCullagh 1980) in which ordinal responses are expressed within the wider class of generalized linear models (GLMs; Nelder and Wedderburn 1972). An interesting historical review discussing merits (and limits) of each of the above contributions can be found in the monograph of Greene and Hensher (2010).
