Abstract
The performance of four discriminant analysis procedures for the classification of observations from unknown populations was examined by Monte Carlo methods. The procedures examined were the Fisher Linear discriminant function, the quadratic discriminant function, a polynomial discriminant function and A-B linear procedure designed for use in situations where covariance matrices are equal. Each procedure was observed under conditions of equal sample sizes, equal covariance matrices, and in conditions where the sample was drawn from populations that have a multivariate normal distribution. When the population covariance matrices were equal, or not greatly different, the quadratic discriminant function performed similarly or marginally the same like Linear procedures. In all cases the polynomial discriminate function demonstrated the poorest, linear discriminant function performed much better than the other procedures. All of the procedures were greatly affected by non-normality and tended to make many more errors in the classification of one group than the other, suggesting that data be standardized when non-normality is suspected.
Highlights
Many practical problems can be reduced to the assignment of various objects to different classes
While a good deal is known in the two group situation, the robustness of these procedures under non-optimal conditions for binary variable is essentially unknown
The results in table 3.1b indicate that, in general, with samples drawn from MVN populations with equal covariance matrices, the fisher LDF, the A-B procedure, the Quadratic Discriminant function (QDF) and Polynomial discriminant function (PDF) performed but as the degree of heterogeneity increases, the QDF outperformed the other procedures
Summary
Many practical problems can be reduced to the assignment of various objects to different classes. In assignment problems in biomedical research, one or more of these techniques is often used. The assumptions underlying these techniques are not always evident to the user, nor are the consequences of their violation. The assumptions include multivariate normality, common covariance matrices and correct assignment of the initial groups [17], [18] and [19]. While a good deal is known in the two group situation, the robustness of these procedures under non-optimal conditions for binary variable is essentially unknown. The purpose of this paper is to compare and delineate these problems systematically and to suggest useful areas of research
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: American Journal of Theoretical and Applied Statistics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
