Abstract:
In the absence of replication, conventional analyses
do not provide ways to examine three-way interaction in threeway
experiments. Tucker3 analysis based on alternating least
squares algorithm is a general approach that can be used in
such cases. However, Tucker3 options are not available with
standard statistical packages. A few methods for estimating σ2
and testing for three-way interaction using a “single component”
Tucker3 model are available in literature. A method based on
a convenient approximation to a likelihood ratio test is also
available in limited cases for testing three-way interaction in
sub-areas once interaction is present. In this paper the null
distribution of the above likelihood ratio statistic is simulated
using Monte Carlo methods based on exact values obtained
from Tucker3 analysis. Critical points are also obtained for the
test for selected cases. Though the package 3-WAY PACK®
handles Tucker3 analysis it does not conveniently support
WINDOWS® based simulations and therefore MATLAB® is
used for the simulation. The method is illustrated using two
examples involving real data.
