Multiple discriminant analysis: A BASIC program for microcomputers

Abstract

The author's mailing address is: School of Psychology, University of Ottawa, 275 Nicholas, Ottawa, Ontario, Canada KIN 6N5. Multiple discriminant analysis (MDA) is a multivariate data-analysis technique that can be used to examine the possibility that a linear combination (discriminant function) of P correlated variables can be used to discriminate K groups of subjects, to test the significance ofdifference between groups centroids, and/or to classify subjects into various groups along the discriminant function. The foundations, as well as the mechanics involved, are described in most textbooks on multivariate analysis (Lindeman, Merenda, & Gold, 1980; Marascuilo & Levin, 1983; Pedhazur, 1982; Tabachnick & Fidell, 1983). The purpose of the program presented here is to perform multiple discriminant analysis, including tests of significance and generation of the classification functions. All critical computations are performed in double precision to minimize rounding errors. The routine to obtain the eigenstructure of the asymmetrical matrix, using the deflation power method, was derived from Douglass's (1983) algorithm. The computational procedure used in the program development was described in Marascuilo and Levin (1983) and in Pedhazur (1982). Input. The program requests the number of variables (NV), the number of groups (K), and the number of subjects within each group (nj). Unequal numbers of subjects per cell are allowed. The raw data can then be entered either sequentially from the keyboard or from a disk file. In the latter case, the data file editor (described earlier, in Coulombe, 1983) can be used to generate a data file suitable as input to this program. The file should contain, first, the total number of scores (NV x Enj) and then the scores themselves, from A1SIV1 to AkSn(k)Vnv, the last index moving fastest (A = group, S = subject, and V = variable). Output. All outputs are directed to the line printer. If screen output is desired, the LPRINT statements should be replaced with PRINT statements. This can be performed easily with the line editor function (EDLIN) provided with MS-DOS. Table 1 is a sample printout obtained using data presented in Lindeman et al. (1980, p. 188). It includes a listing of: (1) the mean and standard deviation vectors observed for each group and variables; (2) the characteristic roots (eigenvalues), index ofdiscriminatory power, Wilks' lambda, R squared, and test of significance (Bartlett's test); (3) the discriminant functions, expressed in both standardized and unstan-