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طرائق تقدير معلمات الانموذج المختلط الخطي الطبيعي الملتوي في حالة القياسات المكررة مع تطبيق عملي == Method of Estimating Parameters of The Skew - Normal Linear Mixed Model In The Case of Repeated Measures With Practical Application
Author name:
هند وليد عبد الرحمن الجبوري
Supervisor name:
محمود مهدي حسن البياتي
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:
07T4154 - p.pdf
Abstract:
تم في هذا البحث دراسة احد اهم النماذج الواسعة الاستعمال والتطبيق في تحليل البيانات التي تتصف بكون المشاهدات فيها تاخذ شكل قياسات مكررة Repeated Measures والذي يعد تعميم للانموذج المختلط الخطي (LMM) في حالة عدم تحقق الطبيعية Normality، وهو الانموذج المختل | In this research, the one of the most important widely used and application model was studied in analysis the data which are described by the observations take repeated measures form, which regarded as generalization of Linear Mixed Model (LMM) in the case of the lack normality, it is the Skew - Normal Linear Mixed Model (SN - LMM), which widely used to analysis the longitudinal data that characterized by the observations take repeated measures form and correlated among of them, this model express of these correlations by the random effect, it also achieved normality through the assumption that the data are distributed multivariate skew normal distribution.Also the research is concerned with the multivariate skew distribution generally and multivariate skew normal distribution specially with addressing the importance and used of these distributions, then dealing with the Skew - Normal Linear Mixed Model (SN - LMM) from its importance, used, properties, modeling, and parameters estimation methods Three important method are used for estimation the fixed effect parameters, random effect parameters and skewness parameters, in addition a proposed method by researcher, these methods are : 1) Maximum likelihood (ML) Method.2) Restricted Maximum Likelihood (RML) Method.3) Bayes Method.4) Proposed Method.A comparison among the best of these methods is made in the application aspect which contained the practical application on two clinical experiment including two samples of diabetic patients data, Who were given a new drug, the data of two samples are represent the repeated monthly measures for the level of sugar and some other variables which are taken for patient from the beginning of the experiment, after three months , and after six months from start to give them the new drug, in aim to study the effect of age and sex, which represented the fixed effect, also the visits times, that the repeated monthly measures are taken in these visits for the sugar level and other variables which represented the random effect, the comparison among the best method are held by using statistical standard the Mean Square Error (MSE), it was found in general that the proposed method is the best to estimate the fixed effects because of its lower mean square error compared to other methods, and the Bayes method is the best among these method to estimate the random effect and random errors because of its lower mean square error compared to other methods.
