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Nonlinear Models in Decision Making

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60 YOAV GANZACH<br />

of judges’ nonl<strong>in</strong>ear accuracy. It also should be noted that these rules are not<br />

the result of a fish<strong>in</strong>g expedition, but are derived from the analysis of cl<strong>in</strong>ical<br />

judgment, and that they cannot be expla<strong>in</strong>ed by criterion contam<strong>in</strong>ation, s<strong>in</strong>ce<br />

contam<strong>in</strong>ation is, if anyth<strong>in</strong>g, detrimental to their validity.<br />

Are these results generalizable? That is, do they <strong>in</strong>dicate that <strong>in</strong>crementally<br />

valid nonl<strong>in</strong>ear rules could be found <strong>in</strong> doma<strong>in</strong>s other than the diagnosis of<br />

psychosis versus neurosis from the MMPI? The current data do not provide<br />

an answer to this question. On the one hand, it is possible that the nonl<strong>in</strong>ear<br />

relationships between the MMPI scales and pathology are a unique example<br />

of nonl<strong>in</strong>ear relationships between predictors and criteria stemm<strong>in</strong>g from the<br />

fact that even one strong psychotic [neurotic] characteristic is sufficient for<br />

the diagnosis of the patient as psychotic [neurotic]. Furthermore, it is also<br />

possible that attempt<strong>in</strong>g to identify nonl<strong>in</strong>ear relationships between predictors<br />

and criteria on the basis of nonl<strong>in</strong>ear relationships between predictions and<br />

judgments is unwarranted because judgments are often characterized by erroneous<br />

configural strategies (Ganzach, 1993; 1997). The third nonl<strong>in</strong>ear rule<br />

which was found <strong>in</strong> the judgments of Meehl’s experiment—the rule associated<br />

with the <strong>in</strong>tegration of the neurotic and psychotic scales (Ganzach, 1995)—is<br />

a relevant example, s<strong>in</strong>ce it characterizes the judgment but not the criterion.<br />

On the other hand, nonl<strong>in</strong>ear relationships between predictors and criteria<br />

<strong>in</strong> which extreme predictors are more <strong>in</strong>dicative of the criterion than moderate<br />

predictors may be possible. For example, success <strong>in</strong> professional football may<br />

be determ<strong>in</strong>ed by the player’s best skill (e.g., kick<strong>in</strong>g, throw<strong>in</strong>g) rather than<br />

by the average of his skills, whereas success <strong>in</strong> obstacle-course runn<strong>in</strong>g may<br />

be determ<strong>in</strong>ed by the runner’s worst skill (jump<strong>in</strong>g, runn<strong>in</strong>g). It is also possible<br />

that nonl<strong>in</strong>ear characteristics are <strong>in</strong>troduced <strong>in</strong>to the relationships between<br />

predictors and criteria because many real-world criteria <strong>in</strong>clude strong judgmental<br />

elements. The op<strong>in</strong>ion of a supervisor is used as a measure of employee<br />

performance, and the impression of a cl<strong>in</strong>ician is an important <strong>in</strong>put <strong>in</strong>to<br />

diagnostic decisions. Therefore, s<strong>in</strong>ce nonl<strong>in</strong>earity is a strong characteristic of<br />

the judgment (e.g., Camerer, 1981; Ganzach, 1994), it may also characterize<br />

the criterion.<br />

Dawes and Corrigan (1974) argued conv<strong>in</strong>c<strong>in</strong>gly that, because of the robustness<br />

of l<strong>in</strong>ear models, when the relationships between predictors and criterion<br />

are conditionally monotone, even if the true model is nonl<strong>in</strong>ear, the <strong>in</strong>cremental<br />

variance of nonl<strong>in</strong>ear elements will be small. However, this does not<br />

mean that the identification of nonl<strong>in</strong>ear relationships between predictors and<br />

criteria is unimportant or futile. First, with the advent of the computer age,<br />

the accumulation of large databases is likely to supply researchers with more<br />

and more power to identify stable nonl<strong>in</strong>ear relationships; second, when the<br />

predictions of the model are important—for example, when they are used to<br />

make decisions about a large population—even a small <strong>in</strong>crease <strong>in</strong> expla<strong>in</strong>ed<br />

variance due to nonl<strong>in</strong>ear relationships may be associated with a large <strong>in</strong>cremental<br />

value; and third, the identification of nonl<strong>in</strong>ear relationships may very<br />

well supply <strong>in</strong>sights <strong>in</strong>to the causal processes that relate predictors to outcome.

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