The psychometric function: II. Bootstrap-based confidence intervals and sampling
The psychometric function: II. Bootstrap-based confidence intervals and sampling
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DOI：
10.3758/bf03194545
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发表时间：
2001-11-01
期刊：
影响因子：
--
通讯作者：
Hill, NJ
中科院分区：
文献类型：
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作者：
Wichmann, FA;Hill, NJ
心理测量函数将观察者的表现与一个独立变量联系起来，通常是实验刺激的物理量。即使一个模型成功地拟合了数据，并且它的拟合优度是可以接受的，实验者也需要对参数的可变性进行估计，以评估不同条件下的差异是否显著。然而，由于心理物理数据集通常规模较小，很难获得对变异性的准确估计：传统的统计技术仅是渐近正确的，并且在某些常见情况下可能被证明是不可靠的。在这里和我们的同伴论文（Wichmann & Hill, 2001）中，我们建议基于蒙特卡罗重采样方法的替代统计技术。本文的主要主题是拟合参数和衍生量（如阈值和斜率）的可变性估计。首先，我们概述了基本的自举过程，并论证了参数自举与非参数自举的不同之处。其次，我们描述了如何测试程序有效性所依赖的自举桥接假设。第三，我们展示了抽样方案的选择（样本点在刺激轴上的位置）如何强烈影响自举置信区间的可靠性，并就如何有效地对心理测量函数进行抽样提出了建议。第四，我们表明，在某些情况下，分布函数的（任意）选择会对所获得的自举置信区间的大小产生不必要的影响，并且我们就如何避免这种影响提出了建议。最后，我们引入了改进的置信区间（偏差校正和加速），改进了先前使用的参数化和基于百分位数的自举置信区间。实现我们方法的软件是可用的。
The psychometric function relates an observer's performance to an independent variable, usually a physical quantity of an experimental stimulus. Even if a model is successfully fit to the data and its goodness of fit is acceptable, experimenters require an estimate of the variability of the parameters to assess whether differences across conditions are significant. Accurate estimates of variability are difficult to obtain, however, given the typically small size of psychophysical data sets: Traditional statistical techniques are only asymptotically correct and can be shown to be unreliable in some common situations. Here and in our companion paper (Wichmann & Hill, 2001), we suggest alternative statistical techniques based on Monte Carlo resampling methods. The present paper's principal topic is the estimation of the variability of fitted parameters and derived quantities, such as thresholds and slopes. First, we outline the basic bootstrap procedure and argue in favor of the parametric, as opposed to the nonparametric, bootstrap. Second, we describe how the bootstrap bridging assumption, on which the validity of the procedure depends, can be tested. Third, we show how one's choice of sampling scheme (the placement of sample points on the stimulus axis) strongly affects the reliability of bootstrap confidence intervals, and we make recommendations on how to sample the psychometric function efficiently. Fourth, we show that, under certain circumstances, the (arbitrary) choice of the distribution function can exert an unwanted influence on the size of the bootstrap confidence intervals obtained, and we make recommendations on how to avoid this influence. Finally, we introduce improved confidence intervals (bias corrected and accelerated) that improve on the parametric and percentile-based bootstrap confidence intervals previously used. Software implementing our methods is available.