نموذج القياسات المتكررة المتعدد المتغيرات ذو الاتجاه الواحد والاختبار الكروي == One - Way Multivariate Repeated Measurements Model And Sphericity Test
Author name:
فاطمة هاشم فلحي نور
Supervisor name:
عبد الحسين صبر المويل
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Master
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T92 - p.pdf
Abstract:
Repeated Measurement model is one of the most models widely used in field of Experimental Design especially in Agricultural Researches, Biomedical and Epidemiology that is involving in this field. This thesis is devoted to the study of One - Way Multivariate repeated measurement model. Three aspects of work are considered : The first aspect : we consider the multivariate repeated measurements analysis of variance ( MRM ANOVA ) model for complete data.The multivariate repeated measurements generalize repeated measurements in the sense that it allows a vector ofobservations at each measurement; we will consider the case of multivariate response variables. The terminology we use for the various MRM designs in this aspect is a one - way MRM ANOVA refers to the situation with only one within - units factor , which welabel as "Time" for convenience while we label as "Group" for between - units factor. For such model, the observations are transformed by an orthogonal matrix. The ANOVA which is based on the first set of transformed observations provides the ANOVA for the between - units factor effects, while ANOVA which is based on the th k set of transformed observations, for each k=2,3,…,p provides the ANOVA for within - units effect. The problem of the testing hypothesis of multivariate repeated measurements ANOVA model for complete data are studied in this aspect. The test statistics of various hypotheses on between - units factor, within - units factor, and interaction between.The second aspect : we study the sphericity test for one - way MRM ANOVA model.Also we obtain the likelihood ratio criterion and the th h Moment of this criteria. As well as the asymptotic expansion and limiting distribution of its test, statistics are obtained. These aspects are represented in the second chapter of this thesis.The third aspect : we applied the one - way MRM ANOVA model for the chemistry experiment data in order to investigates the possibility of environment pollution in the water of Shatt ALBasrah Khor AL - Zubair.Also we obtain the likelihood ratio criteria from the variance - covariance matrix which is obtain after transformed observations by using orthogonal matrix. The result have shown that is MRM is a best used because it care with the correlation between observations in the model. In addition, we have shown through likelihood ratio criterion is satisfying the spherical hypothesis in the theory aspect with practice aspect which is represented in third chapter of this thesis.
