Canonical correlation analysis and its application on animal science

ABSTRACTPhD THESISCANONICAL CORRELATION ANALYSIS AND ITS APPLICATION ONANIMAL SCIENCESoner ÇANKAYADEPARTMENT OF ANIMAL SCIENCEINSTITUTE OF NATURAL AND APPLIED SCIENCESÇUKUROVA ÜNİVERSİTESİSupervisor : Prof. Dr. G. Tamer KAYAALPYear: 2005, Pages :135Jury : Prof. Dr. G. Tamer KAYAALPProf. Dr. Yüksel BEKProf. Dr. Mustafa AKARProf. Dr. Zeynel CEBECİAssoc. Prof. Dr. Suat ŞAHİNLERIn animal breeding researches, generally more than one character or variable are taken formeasurement from the same animal. In order to determine the degree and direction of the linearrelationships belonging to these obtained measurements, simple correlation analysis is usuallypreferred by researchers. However, there may be many variables having effects on the chosen variableor variables, and these variables may also be interrelated. Most of the problems challenging thecontemporary researchers are related to whether there is any relationship between two or morevariables.The aims of this study are to explain canonical correlation analysis by taking intoconsideration main concepts which are simple correlation, multiple correlation, canonical correlation,partial canonical correlation, canonical variate, etc.; to present the test statistics which are used to testthe significance of canonical correlation coefficients (CCC?s); to put into practice the necessary pointsat stage both analysis and interpreting results. In order to illustrate its application, the relationshipbetween eight different morphologic characters (X set) and three different live weights (Y set)measured from 86 kids, German FawnxHair Crossbred, was investigated by canonical correlationanalysis. Moreover, both CCC?s and partial CCCs for meaningful sets, L and Y sets, obtained viaelimination of some variables, were estimated and compared the results of both analyses in the case ofa high canonical correlation coefficient between X and Y sets.The results showed that the CCC was higher than maximum Pearson correlation coefficientbetween chest depth and chest girth, 0.931 and 0.871 respectively, and statistically significant (p<0.01). Moreover, the CCC was estimated as 0.901 for L and Y sets. Instead of eliminating thevariables, the first partial CCC was estimated as 0.572 when the effect of the variables on L and Y setswere kept constant. According to the results, it was determined that there was a difference ofapproximately 33 % between the correlation coefficients estimated for both meaning sets. It was alsodetermined that the original variable contributing the explanatory capacity of U and V the most waschest depth.Key Words: Canonical correlation coefficient, partial canonical correlation coefficient, canonicalvariate.