Subjective probabilities play an important role in marketing research, for example where individuals rate the likelihood that they will purchase a new to develop product. The tau-equivalent model can describe the joint behaviour of multiple test items measuring the same subjective probability. It improves the reliability of the subjective probability estimate by using a weighted sum as the outcome of the test rather than an unweighted sum. One can choose the weights to obtain maximal reliability. In this paper we stress the use of confidence intervals to assess maximal reliability, as this allows for a more critical assessment of the items as measurement instruments. Furthermore, two new confidence intervals for the maximal reliability are derived and compared to intervals derived earlier in \\citet{YuanBentler2002, RaykovPenev2006}. The comparison involves coverage curves, a methodology that is new in the field of reliability. The existing Yuan-Bentler and Raykov-Penev intervals are shown to overestimate the maximal reliability, whereas one of our proposed intervals, the stable interval, performs very well. This stable interval hardly shows any bias, and has a coverage for the true value which is approximately equal to the confidence level.

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Econometric Institute Research Papers
Report / Econometric Institute, Erasmus University Rotterdam
Erasmus School of Economics

Lam, K. Y., Koning, A., & Franses, P. H. (2007). Confidence intervals for maximal reliability of probability judgments (No. EI 2007-09). Report / Econometric Institute, Erasmus University Rotterdam. Retrieved from