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A Simulation Study of the Performance of Five Discriminant Analysis Methods for Mixtures of Continuous and Binary Variables
Abstract:The present study investigates the performance of fice discrimination methods for data consisting of a mixture of continuous and binary variables. The methods are Fisher’s linear discrimination, logistic discrimination, quadratic discrimination, a kernal model and an independence model. Six-dimensional data, consisting of three binary and three continuous variables, are simulated according to a location model. The results show an almost identical performance for Fisher’s linear discrimination and logistic discrimination. Only in situations with independently distributed variables the independence model does have a reasonable discriminatory ability for the dimensionality considered. If the log likelihood ratio is non-linear ratio is non-linear with respect to its continuous and binary part, the quadratic discrimination method is substantial better than linear and logistic discrimination, followed by the kernel method. A very good performance is obtained when in every situation the better one of linear and quardratic discrimination is used.
Keywords:Discriminant analysis  mixtures of variables  linear discrimination  logistic discrimination  quadratic discrimination  kernel model  independence model  discriminatory ability  simulation
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