Linear Possibility Model with Interactions for Ordered Categorical Data

Amin I. Adam


The concern of this research is focussed with extending the idea of the linear possibility model for ordered categorical data to include the interactions between the categorical regressor variables. Besides the main differential effects of the categorical regressor variables, the model allow the differential effect for each level of variable to vary within the levels of other variables. This research shows how to estimate this type of model, how to resolve the problems surrounding it, and how to interpret it in a simple and straightforward way. The study also shows how to check and diagnose the estimated models using cross-validations, outliers and influential observations, and other tests. The application data for this research are collected from a random sample of students at the Omdurman Islamic University. The ordered response categorical variable for the study is the academic performance of students, which is assumed to be associated with three categorical variables and their interactions. These variables are: the specialization of the students, whether the students live with their families or not, and the educational level of their guardians. The results showed that the students whose their guardians have an intermediate level of education perform academically better when their specialization is social science and live with their families, but they seem to perform academically less than other students when they don’t live with their families and their specialization is not social science. Regardless of the educational level of the guardians, all students appear to perform academically less when their specialization is social science and live with their families or just being living with their families.  When they do not live with their families, their academic performance, however, seems to be the same regardless of their specialization (social or natural sciences). The data of the study are analysed by SPSS (Statistical Package for the Social Sciences) and Minitab.

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