Quantal Response Analysis in the Absence of a Zone of Mixed Results Using Data Augmentation

Report No. ARL-TR-4604
Authors: David W. Webb
Date/Pages: September 2008; 20 pages
Abstract: Quantal response analysis is used to estimate the probability of a dichotomous response, e.g., complete penetration, as a function of a stimulus variable. Using maximum likelihood and the DiDonato-Jarnagin algorithm, estimates of the normal distribution parameters that underlie threshold stimulus levels are obtainable if a zone of mixed results is observed in the test data and if the average success-producing stimulus exceeds the average failure-producing stimulus. In the absence of a zone of mixed results, a method is proposed that utilizes data augmentation to estimate some parameter of interest, e.g., the probability of success at a specific stimulus level. This method generates artificial copies of the original data set of stimuli and responses and then adds a random noise component to each of the stimuli. The perturbed and original data are combined into an augmented data set until a zone of mixed results is obtained and the usual analysis can proceed. Confidence statements are attainable by repeating this process to yield an empirical distribution of the parameter of interest.
Distribution: Approved for public release
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Last Update / Reviewed: September 1, 2008