閾值估計探究：引入反應信心量尺於適測方法

Incorporating Response Confidence into Adaptive Methods for Threshold Estimation

心理物理實驗常藉二回答選項的適測方法估計閾值，但從參與者角度而言，有時不易給予二分答案。為解決此問題，學者曾提出增加回答選項個數於其適測方法中（Kaernbach, 2001；Klein, 2001），但如Hsu 與Chin（2014）所論述，該法仍有其局限。本文接續Hsu 與Chin（2014）的研究，針對「是」／「否」作業，提出一結合反應信心量尺與適測方法的架構；其中，我們引入「截點」的概念，將心理計量函數的意涵擴充至心理計量曲面。我們藉電腦模擬探討此架構之可行性，考慮三種無母數適測方法：「德爾曼上下法」（Derman, 1957）、「偏差硬幣投擲法」（Durham & Flournoy, 1995）及「帶權重上下法」（Kaernbach, 1991），系統性地操弄初始值、步距、截點及嘗試次數等變量，探討它們對上述適測方法的影響。模擬結果顯示所提之架構大體可行；此外，「帶權重上下法」與「偏差硬幣投擲法」的表現略優於「德爾曼上下法」。本研究亦將此信心量尺適測方法架構擴展至心理計量函數並非單調遞增之「同」／「異」作業；我們在避免修改上述適測方法的情況下，從這兩種作業的反應信心量尺切入，發展一轉換方法得其相對應之心理計量曲面，如此上述架構便可方便應用於「同」／「異」作業。

In psychophysical studies of discrimination, thresholds are commonly estimated by (nonparametric, fixed-stepsize) adaptive methods using a binary response format. However, it can sometimes be challenging for participants to give a dichotomous response. To resolve the issue, scholars have suggested adding more response categories to the algorithm (Kaernbach, 2001; Klein, 2001). However, Hsu and Chin (2014) argued that their extension has some limitations. Following Hsu and Chin (2014), we proposed an alternative framework to incorporate response confidence into existing adaptive methods for Yes/No tasks. In particular, we introduced the concept of a “cut-off,” thereby expanding the meaning of psychometric functions to psychometric surfaces. We performed simulations to investigate the feasibility of the framework. We considered three adaptive methods, namely Derman’s Up-Down (DUD) method (Derman, 1957), the Biased Coin Design (BCD) (Durham & Flournoy, 1995), and the Weighted Up-Down (WUD) method (Kaernbach, 1991). Setting 0.75 as the target probability for the threshold, we systematically manipulated the initial value, step size, cut-off, and number of trials to examine their impact on the threshold estimation performance of the three adaptive methods. Our simulation results showed that the proposed framework is applicable in general and that WUD and BCD performed slightly better than DUD. We also extended the framework to the Same/Different task, where the psychometric function is not monotonically increasing. We tackled this issue by providing mappings between the response confidence scales of the Same/Different task and the Yes/No task. Doing this enables us to obtain a transformed psychometric function that satisfies the monotonicity property, and thus the aforementioned framework can be readily applied to the Same/Different task.