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Full Length Research Paper
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The
efficiency of the linear classification rule in
multi-group discriminant
analysis
Romain Lucas Glèlè Kakaï1,
Dieter Pelz2 and Rudy Palm3
1Faculty
of Agronomic Sciences, University of Abomey-Calavi, 04 BP
1525, Cotonou, Benin.
2Department
of Forest Biometry, University of Freiburg, Germany.
3Gembloux
Agricultural University, Belgium.
*Corresponding author.
E-mail:
gleleromain@yahoo.fr. Tel:
(00229) 95 84 08 00.
Fax: (00229) 21 3030 84.
Accepted 1 September, 2009 |
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Abstract |
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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, re of 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.
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