Bayesian estimation of ordinal logistic regression

A thesis
Submitted to the council of the college of administration and Economic\ University of Karbala, as partial fulfillment of the requirements for the degree of Master of Science in statistic

By

Ahmed Saeed Jabar Salah

Super vised by

Asist-Prof. Dr. Einas Abdul Haffuod M.

Abstract

The models that are hypothesized represent the effect of a number of independent variables on the response variable that can be affected by a number of hypothesized factors whose effects are different depending on the circumstances of the experiment.

Regression models that have a response variable of a descriptive type suffer from special cases that must be taken into account, which is represented by (contrary to the possession of a response variable of a normal distribution), and for this this study came in an attempt to employ four different Bayesian methods :

Expected A Posteriori (EAP )

Maximum A posteriori (MAP)

Generalized Maximum Entropy  (GME)

Bayesian Reg. With Category Prior Informing ( BRCPI )

With the study of the effect of these methods and the results of the mean squares of error related to them, the efficiency of each method was examined for comparison with a number of factors, namely:

Within the factors {number of explanatory variables (p), percentages of pollution (Prop), percentage of the number of explanatory variables of descriptive type within the total number of these variables (Gate), number of items (n), value of the initial distribution parameter (Sig) }

The results showed the effect of having Bayesian methods for orderly logistic regression on the aforementioned factors .

1- The method (Bayesian Regressions With Category Prior Informing) was the best because it gave the least mean squares of error, while the method (Maximum A posteriori) was the worst because it gave the largest mean squares of error.

2- The estimation results from the models were affected by the sample size, because ( ) gave the best results, while the sample size () gave the worst results.

3- The estimation models were affected by (the value of the initial distribution parameter), as () gave the best results versus () which gave the worst results.

4- There is an effect of pollution rates on the results of the estimation, as the pollution rate () was the best because it gave the mean squares of error that is closest to zero, while () was the worst because it gave the largest average.