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Bayesian Identification of Outliers in Computerized Adaptive Tests

计算机化自适应测试中异常作答者的贝叶斯识别

We consider the problem of identifying examinees with aberrant response patterns in a computerized adaptive test (CAT). The vector Y of responses of an examinee from a CAT is a multivariate response vector. Multivariate observations may be outlying in many different directions, and we characterize specific directions as corresponding to outliers with different interpretations. We develop a class of outlier statistics to identify different types of outliers based on a control…

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Bayesian Identification of Outliers in Computerized Adaptive Tests

计算机自适应测试中异常作答者的贝叶斯识别

We consider the problem of identifying examinees with aberrant response patterns in a computerized adaptive test (CAT). The vector Y of responses of an examinee from a CAT is a multivariate response vector. Multivariate observations may be outlying in many different directions, and we characterize specific directions as corresponding to outliers with different interpretations. We develop a class of outlier statistics to identify different types of outliers based on a control…

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The Cost of Adding Parameters to a Model

模型增加参数的代价

SUMMARY For a general regression model with n independent observations we consider the variance of the estimate of a quantity of interest under two scenarios. One scenario is where all the parameters are estimated from the data; the other scenario is where a subset of the parameters is assumed known at their true values and the remaining parameters are estimated. We focus on quantities of interest which are defined on the scale of the response variable. We show that, under…

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The Influence of Variable Selection: A Bayesian Diagnostic Perspective

变量选择的影响:贝叶斯诊断视角

Variable selection is ubiquitous in statistical practice. Forward selection, backwards elimination, or a combination thereof are among the most popular techniques. Statistical texts teach direct interpretation of coefficients after variable selection. For scientific purposes, the desired interpretation is unconditional on the variable selection. In this article an influence analysis of variable selection is performed from a Bayesian viewpoint. Variable selection is shown to…

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A graphical case statistic for assessing posterior influenceo

评估后验影响的图形化个案统计量

A single number summary of the influence of an observation on the posterior of the parameter of interest is useful, but does not convey all aspects of the effect of deleting the observation. We propose a plot that does convey all the effects of an observation on the posterior.

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