In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in…

In Ramsay curve item response theory (RC-IRT) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's EM algorithm, which yields maximum marginal likelihood estimates. This method, however, does not produce the…

It is a well-known problem in testing the fit of models to multinomial data that the full underlying contingency table will inevitably be sparse for tests of reasonable length and for realistic sample sizes. Under such conditions, full-information test statistics such as Pearson's X[superscript 2] and the likelihood ratio statistic G[superscript…

Despite the growing popularity of diagnostic classification models (e.g., Rupp, Templin, & Henson, 2010) in educational and psychological measurement, methods for testing their absolute goodness-of-fit to real data remain relatively underdeveloped. For tests of reasonable length and for realistic sample size, full-information test statistics…

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…