Two sets of three-outcome gambles were constructed
to vary factorially along the factors Amount to
Lose, Amount to Win, Probability of Losing, and
Probability of Winning. Single stimulus ratings of
attractiveness and risk were obtained for each of
the constructed gambles from 19 subjects. In addition,
paired comparison strength of preference and
difference in risk judgments were obtained for a
subset of these gambles. Two additive conjoint scaling
procedures, Carroll’s (1972) MDPREF and
Johnson’s (1975) NMRG, were used to generate predicted
paired comparison preference and risk judgments
from the single stimulus ratings for each
subject. These predictions were then compared with
the observed paired comparison judgments. Results
indicated that although the goodness-of-fit measures
associated with each of the scaling models indicated
that the subject’s data were being fit very
well by the additive models, additivity among the
payoff and probability factors was clearly violated.
A procedure for detecting nonadditivity is outlined
and illustrated with the data. The limitations of
using these additive conjoint scaling procedures as
predictive techniques when additivity is violated are
shown and their implications are discussed.
Nygren, Thomas E. (1980). Limitations of additive conjoint scaling procedures: Detecting nonadditivity when additivity is known to be violated. Applied Psychological Measurement, 4, 367-383. doi:10.1177/014662168000400308
Nygren, Thomas E..
Limitations of additive conjoint scaling procedures: Detecting nonadditivity when additivity is known to be violated.
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