Abstract

A Monte Carlo study was performed to assess the relative efficiency of the linear classification rule in 2, 3 and 5-group discriminant analysis. The simulation design took into account the number  of variables (4, 6, 10, and 18), the size sample  so that: = 1.5, 2.5 and 5. Three values of the overlap, e of the populations were considered (0.05; 0.1; 0.15) and their common distribution was normal, chi-square with 12, 8, and 4 df; the heteroscedasticity degree,  was measured by the value of the power function of the homoscedasticity test related to  (0.05; 0.4; 0.6; 0.8). For each combination of these factors, the actual empirically computed error rate was used to calculate the relative error, reof the rule. The results showed that for normal or homoscedastic populations, the efficiency of the rule became better for large number of groups. Non-normality or heteroscedasticity negatively impacted the performance of the rule whereas high values of the ratio n/p and high overlap have positive effect on the rule. The mean relative error of the rule became three times more important from homoscedastic to heteroscedasticity.

Key words: Error rate, data samples, linear rule, multi-group, simulation.