Alternative Lens Model Equations for Dichotomous Judgments about Dichotomous Criteria

The Brunswik lens model typically represents a judge's accuracy using parameters derived from linear regression. This is not optimal if the judgment or the ecological criterion is dichotomous. Alternative approaches, modeling dichotomies using logistic regression, or linearizing judgments with confidence ratings, have not been compared with the same data.

Four techniques for deriving lens model equation parameters were compared: 1) linear and 2) logistic regression applied to dichotomous patient outcomes and judgments; 3) linear regression with confidence-adjusted judgments but dichotomous patient outcomes; and 4) a hybrid with a linear model of the confidence-adjusted judgments and a logistic model of the patient outcomes.

Judgment accuracy (r_a) was slightly higher with confidence adjustment of the categorical judgments. The logistic lens model accounted for a higher proportion of r_a than the linear lens model; the confident-linear and hybrid lens models were intermediate. For up to a quarter of participants, different methods identified different cues as most important. Display condition differences in achievement r_a and in lens model components are similar with all lens model methods.

Each of the three alternative lens model equation methods improves on the linear lens model equation's decomposition of the accuracy of dichotomous judgments. Confidence adjustment improves achievement although it requires additional work from the subjects. The logistic lens model equation explains the highest proportion of achievement, but with a small stimulus set it is more vulnerable to cue intercorrelations than either the linear or the confident linear lens model equation.