British Journal of Mathematical & Statistical Psychology最新文献

Recent years have seen a growing interest in the development of person-fit statistics for tests with polytomous items. Some of the most popular person-fit statistics for such tests belong to the class of standardized person-fit statistics, $��T�$, that is assumed to have a standard normal null distribution. However, this distribution only holds when (a) the true ability parameter is known and (b) an infinite number of items are available. In practice, both conditions are violated, and the quality of person-fit results is expected to deteriorate. In this paper, we propose three new corrections for $��T�$ that simultaneously account for the use of an estimated ability parameter and the use of a finite number of items. The three new corrections are direct extensions of those that were developed by Gorney et al. (Psychometrika, 2024, https://doi.org/10.1007/s11336-024-09960-x) for tests with only dichotomous items. Our simulation study reveals that the three new corrections tend to outperform not only the original statistic $��T�$ but also an existing correction for $��T�$ proposed by Sinharay (Psychometrika, 2016, 81, 992). Therefore, the new corrections appear to be promising tools for assessing person fit in tests with polytomous items.

In this study we introduce an innovative mathematical and statistical framework for the analysis of motion energy dynamics in psychotherapy sessions. Our method combines motion energy dynamics with coupled linear ordinary differential equations and a measurement error model, contributing new clinical parameters to enhance psychotherapy research. Our approach transforms raw motion energy data into an interpretable account of therapist–patient interactions, providing novel insights into the dynamics of these interactions. A key aspect of our framework is the development of a new measure of synchrony between the motion energies of therapists and patients, which holds significant clinical and theoretical value in psychotherapy. The practical applicability and effectiveness of our modelling and estimation framework are demonstrated through the analysis of real session data. This work advances the quantitative analysis of motion dynamics in psychotherapy, offering important implications for future research and therapeutic practice.

Inter-rater reliability (IRR) is one of the commonly used tools for assessing the quality of ratings from multiple raters. However, applicant selection procedures based on ratings from multiple raters usually result in a binary outcome; the applicant is either selected or not. This final outcome is not considered in IRR, which instead focuses on the ratings of the individual subjects or objects. We outline the connection between the ratings' measurement model (used for IRR) and a binary classification framework. We develop a simple way of approximating the probability of correctly selecting the best applicants which allows us to compute error probabilities of the selection procedure (i.e., false positive and false negative rate) or their lower bounds. We draw connections between the IRR and the binary classification metrics, showing that binary classification metrics depend solely on the IRR coefficient and proportion of selected applicants. We assess the performance of the approximation in a simulation study and apply it in an example comparing the reliability of multiple grant peer review selection procedures. We also discuss other possible uses of the explored connections in other contexts, such as educational testing, psychological assessment, and health-related measurement, and implement the computations in the R package IRR2FPR.

Computerized adaptive testing (CAT) is a widely embraced approach for delivering personalized educational assessments, tailoring each test to the real-time performance of individual examinees. Despite its potential advantages, CAT�s application in small-scale assessments has been limited due to the complexities associated with calibrating the item bank using sparse response data and small sample sizes. This study addresses these challenges by developing a two-step item bank calibration strategy that leverages the 1-bit matrix completion method in conjunction with two distinct incomplete pretesting designs. We introduce two novel 1-bit matrix completion-based imputation methods specifically designed to tackle the issues associated with item calibration in the presence of sparse response data and limited sample sizes. To demonstrate the effectiveness of these approaches, we conduct a comparative assessment against several established item parameter estimation methods capable of handling missing data. This evaluation is carried out through two sets of simulation studies, each featuring different pretesting designs, item bank structures, and sample sizes. Furthermore, we illustrate the practical application of the methods investigated, using empirical data collected from small-scale assessments.

A sufficient number of participants should be included to adequately address the research interest in the surveys with sensitive questions. In this paper, sample size formulas/iterative algorithms are developed from the perspective of controlling the confidence interval width of the prevalence of a sensitive attribute under four non-randomized response models: the crosswise model, parallel model, Poisson item count technique model and negative binomial item count technique model. In contrast to the conventional approach for sample size determination, our sample size formulas/algorithms explicitly incorporate an assurance probability of controlling the width of a confidence interval within the pre-specified range. The performance of the proposed methods is evaluated with respect to the empirical coverage probability, empirical assurance probability and confidence width. Simulation results show that all formulas/algorithms are effective and hence are recommended for practical applications. A real example is used to illustrate the proposed methods.

Several new models based on item response theory have recently been suggested to analyse intensive longitudinal data. One of these new models is the time-varying dynamic partial credit model (TV-DPCM; Castro-Alvarez et al., Multivariate Behavioral Research, 2023, 1), which is a combination of the partial credit model and the time-varying autoregressive model. The model allows the study of the psychometric properties of the items and the modelling of nonlinear trends at the latent state level. However, there is a severe lack of tools to assess the fit of the TV-DPCM. In this paper, we propose and develop several test statistics and discrepancy measures based on the posterior predictive model checking (PPMC) method (PPMC; Rubin, The Annals of Statistics, 1984, 12, 1151) to assess the fit of the TV-DPCM. Simulated and empirical data are used to study the performance of and illustrate the effectiveness of the PPMC method.

Exploratory structural equation modelling (ESEM) is an alternative to the well-known method of confirmatory factor analysis (CFA). ESEM is mainly used to assess the quality of measurement models of common factors but can be efficiently extended to test structural models. However, ESEM may not be the best option in some model specifications, especially when structural models are involved, because the full flexibility of ESEM could result in technical difficulties in model estimation. Thus, set-ESEM was developed to accommodate the balance between full-ESEM and CFA. In the present paper, we show examples where set-ESEM should be used rather than full-ESEM. Rather than relying on a simulation study, we provide two applied examples using real data that are included in the OSF repository. Additionally, we provide the code needed to run set-ESEM in the free R package lavaan to make the paper practical. Set-ESEM structural models outperform their CFA-based counterparts in terms of goodness of fit and realistic factor correlation, and hence path coefficients in the two empirical examples. In several instances, effects that were non-significant (i.e., attenuated) in the CFA-based structural model become larger and significant in the set-ESEM structural model, suggesting that set-ESEM models may generate more accurate model parameters and, hence, lower Type II error rate.

Different data types often occur in psychological and educational measurement such as computer-based assessments that record performance and process data (e.g., response times and the number of actions). Modelling such data requires specific models for each data type and accommodating complex dependencies between multiple variables. Generalized linear latent variable models are suitable for modelling mixed data simultaneously, but estimation can be computationally demanding. A fast solution is to use Laplace approximations, but existing implementations of joint modelling of mixed data types are limited to ordinal and continuous data. To address this limitation, we derive an efficient estimation method that uses first- or second-order Laplace approximations to simultaneously model ordinal data, continuous data, and count data. We illustrate the approach with an example and conduct simulations to evaluate the performance of the method in terms of estimation efficiency, convergence, and parameter recovery. The results suggest that the second-order Laplace approximation achieves a higher convergence rate and produces accurate yet fast parameter estimates compared to the first-order Laplace approximation, while the time cost increases with higher model complexity. Additionally, models that consider the dependence of variables from the same stimulus fit the empirical data substantially better than models that disregarded the dependence.

Competence-based test development is a recent and innovative method for the construction of tests that are as informative as possible about the competence state (the set of skills an individual has available) underlying the observed item responses. It finds application in different contexts, including the development of tests from scratch, and the improvement or shortening of existing tests. Given a fixed collection of competence states existing in a population of individuals and a fixed collection of competencies (each of which being the subset of skills that allow for solving an item), the competency deletion procedure results in tests that differ from each other in the competencies but are all equally informative about individuals' competence states. This work introduces a streamlined version of the competency deletion procedure that considers information necessary for test construction only, illustrates a straightforward way to incorporate test developer preferences about competencies into the test construction process, and evaluates the performance of the resulting tests in uncovering the competence states from the observed item responses.