British Journal of Mathematical & Statistical Psychology最新文献

Liu, C. W., & Chalmers, R. P. (2021). A note on computing Louis' observed information matrix identity for IRT and cognitive diagnostic models. British Journal of Mathematical and Statistical Psychology, 74(1), 118–138. https://doi.org/10.1111/bmsp.12207

The acknowledgement of funding was included in error: the paper was received on 30 April 2020, while the mentioned grant commenced on 1 August 2020. Consequently, there is no overlap between the grant period and the received date, rendering the acknowledgment inaccurate.

We apologize for this error.

We didactically derive a correlated traits correlated (methods – 1) [CTC(M – 1)] multitrait-multimethod (MTMM) model for dyadic round-robin data augmented by self-reports. The model is an extension of the CTC(M – 1) model for cross-classified data and can handle dependencies between raters and targets by including reciprocity covariance parameters that are inherent in augmented round-robin designs. It can be specified as a traditional structural equation model. We present the variance decomposition as well as consistency and reliability coefficients. Moreover, we explain how to evaluate fit of a CTC(M – 1) model for augmented round-robin data. In a simulation study, we explore the properties of the full information maximum likelihood estimation of the model. Model (mis)fit can be quite accurately detected with the test of not close fit and dynamic root mean square errors of approximation. Even with few small round-robin groups, relative parameter estimation bias and coverage rates are satisfactory, but several larger round-robin groups are needed to minimize relative parameter estimation inaccuracy. Further, neglecting the reciprocity covariance-structure of the augmented round-robin data does not severely bias the remaining parameter estimates. All analyses (including data, R scripts, and results) and the simulation study are provided in the Supporting Information. Implications and limitations are discussed.

In this paper, we propose a novel Gibbs-INLA algorithm for the Bayesian inference of graded response models with ordinal response based on multidimensional item response theory. With the combination of the Gibbs sampling and the integrated nested Laplace approximation (INLA), the new framework avoids the cumbersome tuning which is inevitable in classical Markov chain Monte Carlo (MCMC) algorithm, and has low computing memory, high computational efficiency with much fewer iterations, and still achieve higher estimation accuracy. Therefore, it has the ability to handle large amount of multidimensional response data with different item responses. Simulation studies are conducted to compare with the Metroplis-Hastings Robbins-Monro (MH-RM) algorithm and an application to the study of the IPIP-NEO personality inventory data is given to assess the performance of the new algorithm. Extensions of the proposed algorithm for application on more complicated models and different data types are also discussed.

We propose a novel nonparametric Bayesian item response theory model that estimates clusters at the question level, while simultaneously allowing for heterogeneity at the examinee level under each question cluster, characterized by a mixture of binomial distributions. The main contribution of this work is threefold. First, we present our new model and demonstrate that it is identifiable under a set of conditions. Second, we show that our model can correctly identify question-level clusters asymptotically, and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a $��\sqrt{��n��}�$ rate (up to a log term). Third, we present a tractable sampling algorithm to obtain valid posterior samples from our proposed model. Compared to the existing methods, our model manages to reveal the multi-dimensionality of the examinees' proficiency level in handling different types of questions parsimoniously by imposing a nested clustering structure. The proposed model is evaluated via a series of simulations as well as apply it to an English proficiency assessment data set. This data analysis example nicely illustrates how our model can be used by test makers to distinguish different types of students and aid in the design of future tests.

Textual data are increasingly common in test data as many assessments include constructed response (CR) items as indicators of participants' understanding. The development of techniques based on natural language processing has made it possible for researchers to rapidly analyse large sets of textual data. One family of statistical techniques for this purpose are probabilistic topic models. Topic modelling is a technique for detecting the latent topic structure in a collection of documents and has been widely used to analyse texts in a variety of areas. The detected topics can reveal primary themes in the documents, and the relative use of topics can be useful in investigating the variability of the documents. Supervised latent Dirichlet allocation (SLDA) is a popular topic model in that family that jointly models textual data and paired responses such as could occur with participants' textual answers to CR items and their rubric-based scores. SLDA has an assumption of a homogeneous relationship between textual data and paired responses across all documents. This approach, while useful for some purposes, may not be satisfied for situations in which a population has subgroups that have different relationships. In this study, we introduce a new supervised topic model that incorporates finite-mixture modelling into the SLDA. This new model can detect latent groups of participants that have different relationships between their textual responses and associated scores. The model is illustrated with an example from an analysis of a set of textual responses and paired scores from a middle grades assessment of science inquiry knowledge. A simulation study is presented to investigate the performance of the proposed model under practical testing conditions.

Many intensive longitudinal measurements are collected at irregularly spaced time intervals, and involve complex, possibly nonlinear and heterogeneous patterns of change. Effective modelling of such change processes requires continuous-time differential equation models that may be nonlinear and include mixed effects in the parameters. One approach of fitting such models is to define random effect variables as additional latent variables in a stochastic differential equation (SDE) model of choice, and use estimation algorithms designed for fitting SDE models, such as the continuous-discrete extended Kalman filter (CDEKF) approach implemented in the dynr R package, to estimate the random effect variables as latent variables. However, this approach's efficacy and identification constraints in handling mixed-effects SDE models have not been investigated. In the current study, we analytically inspect the identification constraints of using the CDEKF approach to fit nonlinear mixed-effects SDE models; extend a published model of emotions to a nonlinear mixed-effects SDE model as an example, and fit it to a set of irregularly spaced ecological momentary assessment data; and evaluate the feasibility of the proposed approach to fit the model through a Monte Carlo simulation study. Results show that the proposed approach produces reasonable parameter and standard error estimates when some identification constraint is met. We address the effects of sample size, process noise variance, and data spacing conditions on estimation results.

The use of joint models for item scores and response times is becoming increasingly popular in educational and psychological testing. In this paper, we propose two new person-fit statistics for such models in order to detect aberrant behaviour. The first statistic is computed by combining two existing person-fit statistics: one for the item scores, and one for the item response times. The second statistic is computed directly using the likelihood function of the joint model. Using detailed simulations, we show that the empirical null distributions of the new statistics are very close to the theoretical null distributions, and that the new statistics tend to be more powerful than several existing statistics for item scores and/or response times. A real data example is also provided using data from a licensure examination.

It has been suggested that equivalence testing (otherwise known as negligible effect testing) should be used to evaluate model fit within structural equation modelling (SEM). In this study, we propose novel variations of equivalence tests based on the popular root mean squared error of approximation and comparative fit index fit indices. Using Monte Carlo simulations, we compare the performance of these novel tests to other existing equivalence testing-based fit indices in SEM, as well as to other methods commonly used to evaluate model fit. Results indicate that equivalence tests in SEM have good Type I error control and display considerable power for detecting well-fitting models in medium to large sample sizes. At small sample sizes, relative to traditional fit indices, equivalence tests limit the chance of supporting a poorly fitting model. We also present an illustrative example to demonstrate how equivalence tests may be incorporated in model fit reporting. Equivalence tests in SEM also have unique interpretational advantages compared to other methods of model fit evaluation. We recommend that equivalence tests be utilized in conjunction with descriptive fit indices to provide more evidence when evaluating model fit.

Anticlustering refers to the process of partitioning elements into disjoint groups with the goal of obtaining high between-group similarity and high within-group heterogeneity. Anticlustering thereby reverses the logic of its better known twin—cluster analysis—and is usually approached by maximizing instead of minimizing a clustering objective function. This paper presents k-plus, an extension of the classical k-means objective of maximizing between-group similarity in anticlustering applications. K-plus represents between-group similarity as discrepancy in distribution moments (means, variance, and higher-order moments), whereas the k-means criterion only reflects group differences with regard to means. While constituting a new criterion for anticlustering, it is shown that k-plus anticlustering can be implemented by optimizing the original k-means criterion after the input data have been augmented with additional variables. A computer simulation and practical examples show that k-plus anticlustering achieves high between-group similarity with regard to multiple objectives. In particular, optimizing between-group similarity with regard to variances usually does not compromise similarity with regard to means; the k-plus extension is therefore generally preferred over classical k-means anticlustering. Examples are given on how k-plus anticlustering can be applied to real norming data using the open source R package anticlust, which is freely available via CRAN.