Partition Model

Partition Model

At the time of the Lichtenstein et al. (1982) review, the only existing model precise enough to be fit to empirical data was the decision variable partition model (herein the partition model) of Ferrell and McGoey (1980). In the tradition of signal detection theory, this model describes confidence judgment as a process of partitioning an internal decision variable (which might be thought of as a feeling of confidence) into confidence categories, which are used in making the overt judgment or response. The decision variable itself is not scaled in terms of probability; instead, the judgment is assumed to arise from a partition of some underlying variable. The model successfully fits calibration curves found in general knowledge tasks, though it should be noted that in such applications the number of free parameters is relatively high when compared to the number of data points being fit. Perhaps more impressive is the partition model’s performance when supplemented by the assumption that the judge’s set of partition cutoffs is insensitive to changes in task difficulty in the absence of performance feedback (Ferrell & McGoey, 1980; Smith & Ferrell, 1983; Suantak, Bolger, & Ferrell, 1996). Although there exists, for any given level of proportion correct, a set of cutoffs that would ensure perfect calibration, Ferrell and colleagues have found that the miscalibration observed in experimental contexts is often well accounted for by a single set of cutoffs that is not changed over large variations in task difficulty. In this sense, the partition model with fixed cutoffs can be seen as a close relative of RST with fixed extremity and focal bias parameters.

Perhaps the single greatest weakness of the partition model is its agnosticism regarding the underlying determinants of the unobservable decision variable, that is, the feeling of confidence upon which the partition is constructed. The model makes no attempt to specify how evidence is evaluated to arrive at the feeling of confidence, or how the judge goes about partitioning the resulting decision variable. In this sense, the partition model might be construed rather narrowly as a model of the response stage of the confidence assessment process, as Ferrell has acknowledged (e.g., Ferrell, 1994, p. 433). Although the partition model typically produces a good fit to empirical calibration curves (and response proportions), achieving such a fit requires estimation of a fairly large number of parameters. For example, to fit a full-range calibration dataset with 11 probability categories (0%, 10%, . . ., 100%), the partition model requires discriminability and base-rate parameters comparable to those of RST, but in addition requires estimation of a set of 10 cutoff values, for which RST substitutes only two additional parameters (extremity and focal bias). Arguably, RST’s parameter values are also more readily interpreted (e.g., in terms of case- vs. class-based reasoning) than those of the partition model.