Axiomatic conjoint measurement methodology offers
a useful approach for evaluating different composition
rules as potential models for fitting the components
of multidimensional stimuli. The usefulness of
this methodology has been somewhat hindered in applied
settings because of a lack of an adequate error
theory for testing the fit of data to the axioms. This
paper presents the results of an attempt to provide a
basis for an examination of errors of the conjoint measurement
axioms. Specifically, this paper describes a
means of evaluating the fit of an additive conjoint
measurement model to a three-factor design. For each
of the critical axioms of axiomatic conjoint measurement,
the proportions of errors that would be expected
by chance for different levels of satisfaction of the
simple independence property are examined. The results
indicate that violations of these axioms occur
much less often than intuitively might be expected.
Error proportion tables based on monte carlo analyses
are presented to aid in comparisons with empirically
obtained results. It is shown that two types of violations
of the axioms can be defined and used to differentiate
between systematic and unsystematic errors in
Nygren, Thomas E. (1985). An examination of conditional violations of axioms for additive conjoint measurement. Applied Psychological Measurement, 9, 249-264. doi:10.1177/014662168500900303
Nygren, Thomas E..
An examination of conditional violations of axioms for additive conjoint measurement.
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