Quantal Response: Estimation and Inference

Report No. ARL-TR-7088
Authors: Joseph C Collins
Date/Pages: September 2014; 78 pages
Abstract: Quantal response modeling denotes sensitivity testing or analysis of a binary response to a continuous stimulus. Historically, this has been computed from first principles by assuming a single simple parameterization and imposing the form of a specific cumulative distribution function on the response. Application of the Generalized Linear Model approach admits arbitrary response functions and model complexity in a unified framework and subsumes the historical approach as a specific case. The Likelihood Ratio approach to quantal response modeling allows statistical analysis of data with or without a zone of mixed results on equal ground. Confidence interval (estimation) and hypothesis test (inference) computations are documented with particular attention to the 2-parameter model most commonly used for V50 ballistic limit armor acceptance testing. It is the aim of this paper to present the relevant theory and methodology in an open and complete manner and thus encourage discussion, criticism, and implementation by the larger community.
Distribution: Approved for public release
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Last Update / Reviewed: September 1, 2014