Discriminant analysis and some alternative regression analysis

It is a frequent occurrence that the response variable studied has a qualitative scale structure. In cases where the response variable structure has two or more categories, the classification methods are used instead of the linear regression methods to obtain an estimate of the response variable. Discriminant analysis is one of the most basic classification methods used to separate the observations into categories they belong to by minimizing the probability of incorrect classification. In this thesis, in addition to the discriminant analysis, logistic and probit regression analyzes which are proposed as alternatives to the discriminant analysis, are examined separately for response variables with two and more than two categories. For this purpose, firstly some preliminary information about the classification methods are given and it is described that why the linear regression can not be applied. Linear discriminant analysis which requires the assumption that the variables have multivariate normal distribution with common variance-covariance matrix and quadratic discriminant analysis that does not require common variance covariance matrix, are examined. The logistic and probit regression analyzes, which are proposed in the conditions where these assumptions do not take place, are given respectively. The findings obtained by the application are summarized and the classification accuracy of these methods are compared.