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On the limitations of fixed‐step‐size adaptive methods with response confidence
Author(s) -
Hsu YungFong,
Chin ChingLan
Publication year - 2014
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12018
Subject(s) - quantile , extension (predicate logic) , consistency (knowledge bases) , parametric statistics , algorithm , binary number , mathematics , computer science , confidence interval , statistics , artificial intelligence , arithmetic , programming language
The family of (non‐parametric, fixed‐step‐size) adaptive methods, also known as ‘up–down’ or ‘staircase’ methods, has been used extensively in psychophysical studies for threshold estimation. Extensions of adaptive methods to non‐binary responses have also been proposed. An example is the three‐category weighted up–down (WUD) method (Kaernbach, 2001) and its four‐category extension (Klein, 2001). Such an extension, however, is somewhat restricted, and in this paper we discuss its limitations. To facilitate the discussion, we characterize the extension of WUD by an algorithm that incorporates response confidence into a family of adaptive methods. This algorithm can also be applied to two other adaptive methods, namely Derman's up–down method and the biased‐coin design, which are suitable for estimating any threshold quantiles. We then discuss via simulations of the above three methods the limitations of the algorithm. To illustrate, we conduct a small scale of experiment using the extended WUD under different response confidence formats to evaluate the consistency of threshold estimation.