Evaluating Manifest Monotonicity Using Bayes Factors
نویسندگان
چکیده
The assumption of latent monotonicity in item response theory models for dichotomous data cannot be evaluated directly, but observable consequences such as manifest monotonicity facilitate the assessment of latent monotonicity in real data. Standard methods for evaluating manifest monotonicity typically produce a test statistic that is geared toward falsification, which can only provide indirect support in favor of manifest monotonicity. We propose the use of Bayes factors to quantify the degree of support available in the data in favor of manifest monotonicity or against manifest monotonicity. Through the use of informative hypotheses, this procedure can also be used to determine the support for manifest monotonicity over substantively or statistically relevant alternatives to manifest monotonicity, rendering the procedure highly flexible. The performance of the procedure is evaluated using a simulation study, and the application of the procedure is illustrated using empirical data.
منابع مشابه
Weak monotonicity and Bayes-Nash incentive compatibility
An allocation rule is called Bayes-Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents’ types form a Bayes-Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes-Nash incentive compatible allocation rules in social choice settings where agents have mul...
متن کاملOptimal monotone relabelling of partially non-monotone ordinal data
Noise in multi-criteria data sets can manifest itself as non-monotonicity. Work on the remediation of such non-monotonicity is rather scarce. Nevertheless, errors are often present in real-life data sets, and several monotone classification algorithms are unable to use such partially non-monotone data sets. Fortunately, as we will show here, it is possible to restore monotonicity in an optimal ...
متن کاملBayes Factors 1
In a 1935 paper, and in his book Theory of Probability, Je reys developed a methodology for quantifying the evidence in favor of a scienti c theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. Although there has been much discussion of Bayesian hypothesis testing in the context ...
متن کاملBayes Factors and Model Uncertainty
In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. Although there has been much discussion of Bayesian hypothesis testing in the contex...
متن کاملA Bayesian approach to the verification problem: applications to speaker verification
In this paper, we study the general verification problem from a Bayesian viewpoint. In the Bayesian approach, the verification decision is made by evaluating Bayes factors against a critical threshold. The calculation of the Bayes factors in turn requires the computation of several Bayesian predictive densities. As a case study, we apply the method to speaker verification based on the Gaussian ...
متن کامل