Classification rule for generalised growth curve model

Abstract

This thesis concerns with the developing of linear discriminant analysis for repeatedly measurements with mean following Generalized Growth Curve Model (GGCM). Firstly, we recall the Fisher linear discriminant analysis and the classification rule of Growth Curve model for repeatedly multivariate data and then extended it to the one with mean following GGCM. We develop a linear classification function to classify an individual into one out of two pre-defined groups (and so called populations). Repeatedmeasuresdataarecommoninmanyapplicationsforexampleinpharmacy, medical research studies, agricultural studies, business studies and environmental research. Hence in this thesis Fisher’s linear discriminant function for multivariate distribution is modified and applied to repeatedly measurements with mean following the Generalized Growth Curve model. Actually we are checking the performance and validation of the classification rule proposed in this thesis. Through the simulations we first examine the impact of increasing the number of characteristics for repeatedly measurements. Secondly we investigate the impact of increasing number of repeatedly measurement time points with considering the uncorrelation or correlation between characteristics. The results indicate that classification accuracy increase with the number characteristics, i.e., as number of characteristics increased the classification becomes more efficient. Moreover we have found that classifications with one and two uncorrelated or two correlated characteristics the misclassification error is reduced with increasing the number of independent or AR(1) time point measurements.