In some popular test designs (including computerized adaptive testing and multistage testing), many item pairs are not administered to any test takers, which may result in some complications during dimensionality analyses. In this paper, a modified DETECT index is proposed in order to perform dimensionality analyses for response data from such designs. It is proven in this paper that under certain conditions, the modified DETECT can successfully find the dimensionality-based partition of items. Furthermore, the modified DETECT index is decomposed into two parts, which can serve as indices of the reliability of results from the DETECT procedure when response data are judged to be multidimensional. A simulation study shows that the modified DETECT can successfully recover the dimensional structure of response data under reasonable specifications. Finally, the modified DETECT procedure is applied to real response data from two-stage tests to demonstrate how to utilize these indices and interpret their values in dimensionality analyses.

In this paper it will be shown that a certain class of constrained latent class models may be interpreted as a special case of nonparametric multidimensional item response models. The parameters of this latent class model will be estimated using an application of the Gibbs sampler. It will be illustrated that the Gibbs sampler is an excellent tool if inequality constraints have to be taken into consideration when making inferences. Model fit will be investigated using posterior predictive checks. Checks for manifest monotonicity, the agreement between the observed and expected conditional association structure, marginal local homogeneity, and the number of latent classes will be presented.

This paper presents a study of the impact of prior structure on paradoxical results in multidimensional item response theory. Paradoxical results refer to the possibility that an incorrect response could be beneficial to an examinee. We demonstrate that when three or more ability dimensions are being used, paradoxical results can be induced by using priors in which all abilities are positively correlated where they would not occur if the abilities were modeled as being independent. In the case of separable tests, we demonstrate the mathematical causes of paradoxical results, develop a computationally feasible means to check whether they can occur in any given test, and demonstrate a class of prior covariance matrices that can be guaranteed to avoid them.

Person fit statistics are frequently used to detect aberrant behavior when assuming an item response model generated the data. A common statistic, $l_z$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$l_z$$\end{document}, has been shown in previous studies to perform well under a myriad of conditions. However, it is well-known that $l_z$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$l_z$$\end{document} does not follow a standard normal distribution when using an estimated latent trait. As a result, corrections of $l_z$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$l_z$$\end{document}, called $l_z^{\ast }$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$l_z^*$$\end{document}, have been proposed in the literature for specific item response models. We propose a more general correction that is applicable to many types of data, namely survey or tests with multiple item types and underlying latent constructs, which subsumes previous work done by others. In addition, we provide corrections for multiple estimators of $\theta$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta $$\end{document}, the latent trait, including MLE, MAP and WLE. We provide analytical derivations that justifies our proposed correction, as well as simulation studies to examine the performance of the proposed correction with finite test lengths. An applied example is also provided to demonstrate proof of concept. We conclude with recommendations for practitioners when the asymptotic correction works well under different conditions and also future directions.

Objectives: Multicomponent interventions (MCIs), consisting of at least two interventions, are common in rehabilitation and other healthcare fields. When the effectiveness of the MCI versus that of its single interventions is comparable or unknown, evidence of their expected incremental cost-effectiveness can be helpful in deciding which intervention to recommend. As such evidence often is unavailable this study proposes an approach to estimate what is more cost-effective; the MCI or the single intervention(s).

Methods: We reviewed the literature for potential methods. Of those identified, headroom analysis was selected as the most suitable basis for developing the approach, based on the criteria of being able to estimate the cost-effectiveness of the single interventions versus that of the MCI (a) within a limited time frame, (b) in the absence of full data, and (c) taking into account carry-over and interaction effects. We illustrated the approach with an MCI for cancer survivors.

Results: The approach starts with analyzing the costs of the MCI. Given a specific willingness-to-pay-value, it is analyzed how much effectiveness the MCI would need to generate to be considered cost-effective, and if this is likely to be attained. Finally, the cost-effectiveness of the single interventions relative to the potential of the MCI for being cost-effective can be compared.

Conclusions: A systematic approach using headroom analysis was developed for estimating whether an MCI is likely to be more cost effective than one (or more) of its single interventions.

We introduce the open degree of a compact space, and we show that for every natural number $n$, the separable Rosenthal compact spaces of degree $n$ have a finite basis.

Poverty analysis is currently undergoing a multidimensional turn, increasingly focusing on the many ways in which human life can be impoverished and not just on material poverty. In this paper, we present an analysis of material poverty and multiple deprivation in Britain, which is inspired by the capability approach. We argue that the additional complexity of multidimensional analysis requires that it provides some insight not achieved by a more straightforward approach focusing on material poverty alone. Our findings indicate that whether a multidimensional assessment identifies different people as being in poverty depends on whether our interest is in identifying vulnerable individuals or in identifying vulnerable groups and whether we focus on dimensions in aggregate or disaggregate forms. We find that, although material poverty and multiple deprivation identify very different individuals, they display greater congruence in terms of identifying vulnerable groups, especially where aggregate measures are used.

We investigate the multidimensional non-isentropic Euler–Poisson (or full hydrodynamic) model for semiconductors, which contain an energy-conserved equation with non-zero thermal conductivity coefficient. We first discuss existence and uniqueness of the non-constant stationary solutions to the corresponding drift–diffusion equations. Then we establish the global existence of smooth solutions to the Cauchy problem with initial data, which are close to the stationary solutions. We find that these smooth solutions tend to the stationary solutions exponentially fast as $t\rightarrow+\infty$.

The 3′ end of replication-dependent histone mRNAs terminate in a conserved sequence containing a stem-loop. This 26-nt sequence is the binding site for a protein, stem-loop binding protein (SLBP), that is involved in multiple aspects of histone mRNA metabolism and regulation. We have determined the structure of the 26-nt sequence by multidimensional NMR spectroscopy. There is a 16-nt stem-loop motif, with a conserved 6-bp stem and a 4-nt loop. The loop is closed by a conserved U[bull ]A base pair that terminates the canonical A-form stem. The pyrimidine-rich 4-nt loop, UUUC, is well organized with the three uridines stacking on the helix, and the fourth base extending across the major groove into the solvent. The flanking nucleotides at the base of the hairpin stem do not assume a unique conformation, despite the fact that the 5′ flanking nucleotides are a critical component of the SLBP binding site.