Examples of polytomous data include blood type (A, B, AB, O,…), food testing, measures of mental and physical well-being, variables arising in social science research.
Based on these investigations it will be established that simply some models of a class of models for polytomous variables can be distinct as stochastic dimension models.
In summary, the two main aims of this paper are (1) to describe models for polytomous variables as stochastic dimension models and to examine the depiction, uniqueness, and meaningfulness trouble in this division of models; (2) to show how stochastic measurement theory can direct the collection of a model for polytomous variables. Therefore, the class of models developed by Marsh and Grayson is described in the next section and is transferred to an analogous class of models for polytomous response variables. Then, the probabilistic foundations of models for polytomous variables are explained. After that, models for polytomous variables are defined as stochastic measurement models and the representation, distinctiveness, and meaningfulness problems are examined. Furthermore, the meaning of different models will be explained on the basis of the measurement theoretical investigations and a small empirical example. Finally, the consequences of these investigations will be discussed.