Abstract Details
Activity Number:
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108
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Type:
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Invited
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Date/Time:
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Monday, August 4, 2014 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistics in Defense and National Security
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Abstract #313806
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View Presentation
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Title:
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The Sign of the Logistic Regression Coefficient
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Author(s):
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Paul Roediger*+ and Art Owen
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Companies:
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UTRS and Stanford University
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Keywords:
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Abstract:
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The conjecture posed in our 3pod commentary (Ray, et. al.) has been settled in the affirmative. Specifically, let Y be a binary random variable and X a scalar. Let B be the maximum likelihood estimate of the slope in a logistic regression of Y on X with intercept. Further let m0 and m1 be the average of sample X values for cases with Y=0 and Y=1, respectively. Then under a condition that rules out separable predictors, we show that sign(B)=sign (m1-m0). More generally, if X are vector valued then we show that B=0 if and only if m1=m0. This holds for logistic regression and also for more general binary regressions with inverse link functions satisfying a log-concavity condition. Finally, when m1-m0 is not zero then the angle between B and m1-m0 is less than ninety degrees in binary regressions satisfying the log-concavity condition and the separation condition, when the matrix has full rank. For more information see http://arxiv.org/pdf/1402.0845.pdf.
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