British Journal of Mathematical & Statistical Psychology最新文献

Careless and insufficient effort responding (C/IER) on self-report measures results in responses that do not reflect the trait to be measured, thereby posing a major threat to the quality of survey data. Reliable approaches for detecting C/IER aid in increasing the validity of inferences being made from survey data. First, once detected, C/IER can be taken into account in data analysis. Second, approaches for detecting C/IER support a better understanding of its occurrence, which facilitates designing surveys that curb the prevalence of C/IER. Previous approaches for detecting C/IER are limited in that they identify C/IER at the aggregate respondent or scale level, thereby hindering investigations of item characteristics evoking C/IER. We propose an explanatory mixture item response theory model that supports identifying and modelling C/IER at the respondent-by-item level, can detect a wide array of C/IER patterns, and facilitates a deeper understanding of item characteristics associated with its occurrence. As the approach only requires raw response data, it is applicable to data from paper-and-pencil and online surveys. The model shows good parameter recovery and can well handle the simultaneous occurrence of multiple types of C/IER patterns in simulated data. The approach is illustrated on a publicly available Big Five inventory data set, where we found later item positions to be associated with higher C/IER probabilities. We gathered initial supporting validity evidence for the proposed approach by investigating agreement with multiple commonly employed indicators of C/IER.

Several psychometric tests and self-reports generate count data (e.g., divergent thinking tasks). The most prominent count data item response theory model, the Rasch Poisson Counts Model (RPCM), is limited in applicability by two restrictive assumptions: equal item discriminations and equidispersion (conditional mean equal to conditional variance). Violations of these assumptions lead to impaired reliability and standard error estimates. Previous work generalized the RPCM but maintained some limitations. The two-parameter Poisson counts model allows for varying discriminations but retains the equidispersion assumption. The Conway–Maxwell–Poisson Counts Model allows for modelling over- and underdispersion (conditional mean less than and greater than conditional variance, respectively) but still assumes constant discriminations. The present work introduces the Two-Parameter Conway–Maxwell–Poisson (2PCMP) model which generalizes these three models to allow for varying discriminations and dispersions within one model, helping to better accommodate data from count data tests and self-reports. A marginal maximum likelihood method based on the EM algorithm is derived. An implementation of the 2PCMP model in R and C++ is provided. Two simulation studies examine the model's statistical properties and compare the 2PCMP model to established models. Data from divergent thinking tasks are reanalysed with the 2PCMP model to illustrate the model's flexibility and ability to test assumptions of special cases.

A family of score-based tests has been proposed in recent years for assessing the invariance of model parameters in several models of item response theory (IRT). These tests were originally developed in a maximum likelihood framework. This study discusses analogous tests for Bayesian maximum-a-posteriori estimates and multiple-group IRT models. We propose two families of statistical tests, which are based on an approximation using a pooled variance method, or on a simulation approach based on asymptotic results. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a categorical or continuous person covariate in the two- and three-parametric logistic models. Whereas the method based on pooled variance was found to be useful in practice with maximum likelihood as well as maximum-a-posteriori estimates, the simulation-based approach was found to require large sample sizes to lead to satisfactory results.

Recently, the Urnings algorithm (Bolsinova et al.,  2022, J. R. Stat. Soc. Ser. C Appl. Statistics, 71, 91) has been proposed that allows for tracking the development of abilities of the learners and the difficulties of the items in adaptive learning systems. It is a simple and scalable algorithm which is suited for large-scale applications in which large streams of data are coming into the system and on-the-fly updating is needed. Compared to alternatives like the Elo rating system and its extensions, the Urnings rating system allows the uncertainty of the ratings to be evaluated and accounts for adaptive item selection which, if not corrected for, may distort the ratings. In this paper we extend the Urnings algorithm to allow for both between-item and within-item multidimensionality. This allows for tracking the development of interrelated abilities both at the individual and the population level. We present formal derivations of the multidimensional Urnings algorithm, illustrate its properties in simulations, and present an application to data from an adaptive learning system for primary school mathematics called Math Garden.

The g-and-h family of distributions is a computationally efficient, flexible option to model and simulate non-normal data. In spite of its popularity, there are several theoretical aspects of these distributions that need special consideration when they are used. In this paper some of these aspects are explored. In particular, through mathematical analysis it is shown that a popular multivariate generalization of the g-and-h distribution may result in marginal distributions which are no longer g-and-h distributed, that more than one set of (g,h) parameters can correspond to the same values of population skewness and excess kurtosis, and that multivariate generalizations of g-and-h distributions available in the literature are special cases of Gaussian copula distributions. A small-scale simulation is also used to demonstrate how simulation conclusions can change when different (g,h) parameters are used to simulate data, even if they imply the same population values of skewness and excess kurtosis.

Attributes and the Q-matrix are the central components for cognitive diagnostic assessment, and are usually defined by domain experts. However, it is challenging and time consuming for experts to specify the attributes and Q-matrix manually. Thus, there is an urgent need for an automatic and intelligent means to address this concern. This paper presents a new data-driven approach for learning the Q-matrix from response data. By constructing a statistical index and a heuristic algorithm based on Boolean matrix factorization, the response matrix is decomposed into the Boolean product of the Q-matrix and the attribute mastery patterns. The feasibility of the proposed approach is evaluated using simulated data generated under various conditions. A real data example is also presented to demonstrate the usefulness of the proposed approach.

Cognitive diagnosis models have become popular in educational assessment and are used to provide more individualized feedback about a student's specific strengths and weaknesses than traditional total scores. However, if the testing data are contaminated by certain biases or aberrant response patterns, such predictions may not be accurate. The current research objective is to develop a new person-fit method that is based on machine learning and improves the functionality of existing person-fit methods. Various simulations were designed under three aberrant conditions: cheating, sleeping and random guessing. Simulation results showed that the new method was more powerful and effective than previous methods, especially for short-length tests.

A cluster randomized controlled trial (C-RCT) is common in educational intervention studies. Multilevel modelling (MLM) is a dominant analytic method to evaluate treatment effects in a C-RCT. In most MLM applications intended to detect an interaction effect, a single interaction effect (called a conflated effect) is considered instead of level-specific interaction effects in a multilevel design (called unconflated multilevel interaction effects), and the linear interaction effect is modelled. In this paper we present a generalized additive mixed model (GAMM) that allows an unconflated multilevel interaction to be estimated without assuming a prespecified form of the interaction. R code is provided to estimate the model parameters using maximum likelihood estimation and to visualize the nonlinear treatment-by-covariate interaction. The usefulness of the model is illustrated using instructional intervention data from a C-RCT. Results of simulation studies showed that the GAMM outperformed an alternative approach to recover an unconflated logistic multilevel interaction. In addition, the parameter recovery of the GAMM was relatively satisfactory in multilevel designs found in educational intervention studies, except when the number of clusters, cluster sizes, and intraclass correlations were small. When modelling a linear multilevel treatment-by-covariate interaction in the presence of a nonlinear effect, biased estimates (such as overestimated standard errors and overestimated random effect variances) and incorrect predictions of the unconflated multilevel interaction were found.

In cognitive diagnostic assessment a property of the Q-matrix, usually referred to as completeness, warrants that the cognitive attributes underlying the observed behaviour can be uniquely assessed. Characterizations of completeness were first derived under the assumption of independent attributes, and are currently under investigation for interdependent attributes. The dominant approach considers so-called attribute hierarchies, which are conceptualized through a partial order on the set of attributes. The present paper extends previously published results on this issue obtained for conjunctive attribute hierarchy models. Drawing upon results from knowledge structure theory, it provides novel sufficient and necessary conditions for completeness of the Q-matrix, not only for conjunctive models on attribute hierarchies, but also on more general attribute structures.

We propose a new metric for evaluating the informativeness of a set of ratings from a single rater on a given scale. Such evaluations are of interest when raters rate numerous comparable items on the same scale, as occurs in hiring, college admissions, and peer review. Our exposition takes the context of peer review, which involves univariate and multivariate cardinal ratings. We draw on this context to motivate an information-theoretic measure of the refinement of a set of ratings – entropic refinement – as well as two secondary measures. A mathematical analysis of the three measures reveals that only the first, which captures the information content of the ratings, possesses properties appropriate to a refinement metric. Finally, we analyse refinement in real-world grant-review data, finding evidence that overall merit scores are more refined than criterion scores.