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203.
In categorical data analysis, two-sample cross-validation is used not only for model selection but also to obtain a realistic
impression of the overall predictive effectiveness of the model. The latter is of particular importance in the case of highly
parametrized models capable of capturing every idiosyncracy of the calibrating sample. We show that for maximum likelihood
estimators or other asymptotically efficient estimators Pearson's X
2 is not asymptotically chi-square in the two-sample cross-validation framework due to extra variability induced by using different
samples for estimation and goodness-of-fit testing. We propose an alternative test statistic, X
xval
2, obtained as a modification of X
2 which is asymptotically chi-square with C−1 degrees of freedom in cross-validation samples. Stochastically, X
xval
2 ≤ X
2. Furthermore, the use of X
2 instead of X
xval
2 with a χ
C
−12 reference distribution may provide an unduly poor impression of fit of the model in the cross-validation sample.
This paper is dedicated to the memory of Michael V. Levine.
Requests for reprints should be sent to Albert Maydeu-Olivares, Faculty of Psychology, University of Barcelona, P. Valle de
Hebrón, 171, 0835 Barcelona, Spain. 相似文献
204.
We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency
tables. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when parameters are estimated using any asymptotically normal
consistent estimator. For a widely used item response model, when r is small and multidimensional tables are sparse, the proposed statistics have accurate empirical Type I errors, unlike Pearson's
X
2. For this model in nonsparse situations, the proposed statistics are also more powerful than X
2. In addition, the proposed statistics are asymptotically chi-square when applied to subtables, and can be used for a piecewise
goodness-of-fit assessment to determine the source of misfit in poorly fitting models.
This research has been supported by the Department of Universities, Research, and Information Society (DURSI) of the Catalan
Government, by grant BSO2003-08507 of the Spanish Ministry of Science and Technology, and an NSERC Canada grant. We are grateful
to the referees for comments leading to improvements. 相似文献
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210.
Joe Campbell 《Canadian journal of philosophy》2015,45(1):127-137
In The Riddle of Hume's Treatise: Skepticism, Naturalism, and Irreligion (2008), Paul Russell makes a strong case for the claim that “The primary aim of Hume's series of skeptical arguments, as developed and distributed throughout the Treatise, is to discredit the doctrines and dogmas of Christian philosophy and theology with a view toward redirecting our philosophical investigations to areas of ‘common life,’ with the particular aim of advancing ‘the science of man’” (2008, 290). Understanding Hume in this way, according to Russell, sheds light on the “ultimate riddle” of the Treatise: “is it possible to reconcile Hume's (extreme) skeptical principles and conclusions with his aim to advance the ‘science of man’” (2008, 3)? Or does Hume's skepticism undermine his “secular, scientific account of the foundations of moral life in human nature” (290)? Russell's controversial thesis is that “the irreligious nature of Hume's fundamental intentions in the Treatise” is essential to solving the riddle (11). Russell makes a compelling case for Hume's irreligion as well as his atheism. Contrary to this interpretation I argue that Hume is an irreligious theist and not an atheist. 相似文献