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- W2044218370 abstract "Multivariate Totally Positive $(MTP_2)$ binary distributions have been studied in many fields, such as statistical mechanics, computer storage and latent variable models. We show that $MTP_2$ is equivalent to the requirement that the parameters of a saturated log-linear model belong to a convex cone, and we provide a Fisher-scoring algorithm for maximum likelihood estimation.We also show that the asymptotic distribution of the log-likelihood ratio is a mixture of chi-squares (a distribution known as chi-bar-squared in the literature on order restricted inference); for this we derive tight bounds which turn out to have very simple forms. A potential application of this method is for Item Response Theory (IRT) models, which are used in educational assessment to analyse the responses of a group of subjects to a collection of questions (items): an important issue within IRT is whether the joint distribution of the manifest variables is compatible with a single latent variable representation satisfying local independence and monotonicity which, in turn, imply that the joint distribution of item responses is $MTP_2$." @default.
- W2044218370 created "2016-06-24" @default.
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- W2044218370 modified "2023-10-13" @default.
- W2044218370 title "A likelihood ratio test for $MTP_2$ within binary variables" @default.
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- W2044218370 doi "https://doi.org/10.1214/aos/1015956713" @default.
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