Statistical Inference After Model Selection |
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Authors: | Richard Berk Lawrence Brown Linda Zhao |
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Institution: | (1) Department of Statistics, University of Pennsylvania, Philadelphia, PA, USA;(2) Department of Criminology, University of Pennsylvania, Philadelphia, PA, USA |
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Abstract: | Conventional statistical inference requires that a model of how the data were generated be known before the data are analyzed.
Yet in criminology, and in the social sciences more broadly, a variety of model selection procedures are routinely undertaken
followed by statistical tests and confidence intervals computed for a “final” model. In this paper, we examine such practices
and show how they are typically misguided. The parameters being estimated are no longer well defined, and post-model-selection
sampling distributions are mixtures with properties that are very different from what is conventionally assumed. Confidence
intervals and statistical tests do not perform as they should. We examine in some detail the specific mechanisms responsible.
We also offer some suggestions for better practice and show though a criminal justice example using real data how proper statistical
inference in principle may be obtained. |
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Keywords: | |
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