Conditional association, essential independence and monotone unidimensional item response models

DOI10.1214/aos/1176349262zbMath0791.62099OpenAlexW2022407215MaRDI QIDQ1314457

Publication date: 20 July 1994

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176349262

zbMATH Keywords

item response theory monotonicity condition IRT conditional association local independence achievement and aptitude tests binary response variables dichotomous scoring empirical response curves essentially unidimensional models negative association condition strictly unidimensional latent variable representation useful latent variable models

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Characterization and structure theory of statistical distributions (62E10) Applications of statistics to psychology (62P15)

Related Items

Multidimensional item response theory models with collateral information as Poisson regression models ⋮ Analysis of Local Dependence and Multidimensionality in Graphical Loglinear Rasch Models ⋮ A multidimensional item response model: Constrained latent class analysis using the Gibbs sampler and posterior predictive checks ⋮ Stochastic ordering using the latent trait and the sum score in polytomous IRT models ⋮ Posterior convergence given the mean ⋮ Some remarks on Scheiblechner's treatment of ISOP models ⋮ Corrections of theorems in Scheiblechner's treatment of ISOP models and comments on Junker's remarks ⋮ Tail-measurability in monotone latent variable models ⋮ A test to distinguish monotone homogeneity from monotone multifactor models ⋮ An isotonic partial credit model for ordering subjects on the basis of their sum scores ⋮ Some exact tests for manifest properties of latent trait models ⋮ Psychometrics: from practice to theory and back. 15 years of nonparametric multidimensional IRT, DIF/test equity, and skills diagnostic assessment ⋮ An inequality for correlations in unidimensional monotone latent variable models for binary variables ⋮ Nonparametric item response theory axioms and properties under nonlinearity and their exemplification with knowledge space theory ⋮ Polytomous IRT models and monotone likelihood ratio of the total score ⋮ Generalized Residuals for General Models for Contingency Tables With Application to Item Response Theory ⋮ Cumulative or adjacent logits: Which choice for an ordinal logistic latent variable model? ⋮ Stochastic order in dichotomous item response models for fixed, adaptive, and multidimensional tests ⋮ Asymptotic normality of the posterior given a statistic ⋮ Adjusting for information inflation due to local dependency in moderately large item clusters ⋮ Conditional covariance structure of generalized compensatory multidimensional items ⋮ Item screening in graphical loglinear Rasch models ⋮ Nonparametric IRT: testing the bi-isotonicity of isotonic probabilistic models (ISOP) ⋮ Measuring the ability of transitive reasoning, using product and strategy information ⋮ Constant latent odds-ratios models and the Mantel-Haenszel null hypothesis ⋮ Loss of information in estimating item parameters in incomplete designs ⋮ Testing for local dependency in dichotomous and polytomous item response models ⋮ The person response function as a tool in person-fit research ⋮ On measurement properties of continuation ratio models ⋮ Log-multiplicative association models as item response models ⋮ Conditional covariance theory and detect for polytomous items ⋮ Manifest characterization and testing for certain latent properties ⋮ Incomplete tests of conditional association for the assessment of model assumptions