ArticleApplied psychological measurement2016
A Note on the Poisson's Binomial Distribution in Item Response Theory.
Article in Applied psychological measurement, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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4 citing papers in PubMed.
- Genetic control of mRNA splicing as a potential mechanism for incomplete penetrance of rare coding variants.Genetics · 2023Article
- Evaluating Equating Transformations in IRT Observed-Score and Kernel Equating Methods.Applied psychological measurement · 2023Article
- Genetic control of mRNA splicing as a potential mechanism for incomplete penetrance of rare coding variants.bioRxiv : the preprint server for biology · 2023Article
- Significance evaluation in factor graphs.BMC bioinformatics · 2017Article
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3 authors.
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Abstract
The Poisson's binomial (PB) is the probability distribution of the number of successes in independent but not necessarily identically distributed binary trials. The independent non-identically distributed case emerges naturally in the field of item response theory, where answers to a set of binary items are conditionally independent given the level of ability, but with different probabilities of success. In many applications, the number of successes represents the score obtained by individuals, and the compound binomial (CB) distribution has been used to obtain score probabilities. It is shown here that the PB and the CB distributions lead to equivalent probabilities. Furthermore, one of the proposed algorithms to calculate the PB probabilities coincides exactly with the well-known Lord and Wingersky (LW) algorithm for CBs. Surprisingly, we could not find any reference in the psychometric literature pointing to this equivalence. In a simulation study, different methods to calculate the PB distribution are compared with the LW algorithm. Providing an exact alternative to the traditional LW approximation for obtaining score distributions is a contribution to the field.
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