Linear Possibility Model for Ordered Categorical Data: A Similar Way of Analysis to Regression Analysis

Amin I. Adam

Abstract


This research is concerned with introducing the linear possibility model for ordered categorical data, a model which is extended from the idea of the probit model.  In linear possibility model the response variable for ordered categorical data is having a wider range of values, and consequently, the conditional expected values for this response given a number of regressors will be outside the range of 0-1. This research shows how the problems surrounding the linear possibility model can be solved, to a large extent, allowing the model to give simple and straight forward interpretations for the relationships between the categorical variables similar to regression analysis. The study gives empirical estimates of the effects between the variables and explains estimates corresponding to the ordering nature of the categorical variables under concerned. 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: the specialization of the students, whether the students live with their families or not, and the educational level of their guardians. The result showed that the conditional possibility of the academic performance of the students is lower by almost a third for all the students whose specialization is social science. Likewise, the conditional possibility of the academic performance of the students is higher by almost a third for all the students whose the educational level of their guardian is secondary. AS for those, whose  specialization is natural science and the educational level of their guardian is primary or lower, the conditional possibility of their academic performance is 3.791, which is "good". The data of the study is analysed with the aid of SPSS, (Statistical Package for the Social Sciences) and Minitab.


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