طرائق تقدير انموذج راش للبيانات المصنف متعددة القياسات مع تطبيق عملي == Methods of Estimating The Rasch Model For Multiple Categorical Data Measurements With Practical Application
Author name:
وضاح صبري ابراهيم المناصير
Supervisor name:
دجلة ابراهيم مهدي العزاوي
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Doctorate
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T4169 - p.pdf
Abstract:
يعتبر انموذج راش (The Rasch model)، من اهم نماذج نظرية السمة الكامنة (Latent Trait Theory) للنظرية المعاصرة لقياس سلوك الفرد، المبني على البيانات المصنفة، وهو احد نماذج الاستجابة للفقرة الاحادية البعد، بمعنى ان درجة الفرد في الاختبار لا يجب ان تكون دالة ( | Rasch Model is considered as one of the important models in Latent Trait Theory for the contemporary Theory to measuring human behavior that depends on categorized data. It is one of the response models for one dimension point i.e., the mark of an individual within test mustn’t be regarded as an evaluation for other individual’s samples that are used within Item Calibration.Therefore, the thesis aims at comparing some methods for Rasch Model’s parameters for Categorical Data Measurement by using Mean Absolute Percentage Error (MAPE).The following methods are also used : The Joint function of Maximum Likelihood Estimation Method (JML), The Maximum Likelihood Estimation Method (MLE), Cohen’s Approximation Estimation Method (CAE), and Bayesian Estimation Method ( BEM ) and the first adjusted Bayesian Estimation Method ( BEMFS ) and the second adjusted Bayesian Estimation Method ( BEMSS ). The thesis includes a suggestion for a method to find the initial values of Rasch model’s parameters that are used in the previous mentioned methods and simulation is also used for overgeneralizing the results for the methods within various sizes levels, in which n : (n=10 , n=25 , n=75 , n=150 , n=300 , n=500 ) and ( n ) represents the individuals and (m) represents the number of the items ( m= 10 , m= 25 , m=35 , m= 45 ) and four different distributions are used ( Binomial , Poisson , Normal , Beta ). It is found that the best method for estimating the parameter of item difficulty (?_j), is The Joint function of Maximum Likelihood Estimation Method (JML) and the best method for estimating the parameter of individual’s ability (B_i), is the Bayesian Estimation Method of the Second Adjusted. Danial’s test for intelligence is used in AL - Mustansyria University, College of Administration and Economics, Fourth year, morning studies only and the number of students are (531). The main conclusions are : By comparing all the methods with the suggested ones to estimate Rasch model’s parameters , it is found that the best estimating for the parameter of individual’s ability (B_i), is the Bayesian Estimation Method of the Second Adjusted by depending on the smallest value for Mean Absolute Percentage Error (MAPE) and all the distributions are concrete and constant. It is found by comparing the methods to estimate the parameter of item difficulty (?_j) that the Joint function of Maximum Likelihood Estimation Method is the best for estimation , in which Mean Absolute Percentage Error (MAPE) is appeared with the smallest value and for all the concrete and constant distributions. It is found from the average of the correct answers of the testes that the tests items are within a closed level for each item and this gives the opportunity to students to answer the items. It is found from the average of the correct answers of the testes that the average of response is very good and it is between ( 0.47 - 0. 26 ) for more than 500 students from the total 531. This shows the similarity between students to have Danial’s test for intelligence. It is found from standards statistics ( T ) for the test items after comparing them with the tabled value for the natural distribution of the moral connotation ( a = 0.05 ) and the value ( 1.6449 ) that all the values without moral connotation and this confirms the acceptance of the test’s items to apply it on students’ sample which has different levels of difficulty but still parallel.
