Psychometrika最新文献

This paper presents a model specification for group comparisons regarding a functional trend over time within a trial and learning across a series of trials in intensive binary longitudinal eye-tracking data. The functional trend and learning effects are modeled using by-variable smooth functions. This model specification is formulated as a generalized additive mixed model, which allowed for the use of the freely available mgcv package (Wood in Package 'mgcv.' https://cran.r-project.org/web/packages/mgcv/mgcv.pdf, 2023) in R. The model specification was applied to intensive binary longitudinal eye-tracking data, where the questions of interest concern differences between individuals with and without brain injury in their real-time language comprehension and how this affects their learning over time. The results of the simulation study show that the model parameters are recovered well and the by-variable smooth functions are adequately predicted in the same condition as those found in the application.

Joint correspondence analysis (JCA) is a statistical method for obtaining a low-dimensional representation of multivariate categorical data. It was developed as an alternative to multiple correspondence analysis (MCA). Typically, the solution is visualized through a map that projects the data onto a reduced space. A joint map, which shows both object and category scores in the same space, helps users explore inter- and intra-relationships in objects and categories. However, unlike MCA, current JCA estimation methods do not allow the joint representation of objects and categories on the map, which limits the interpretability of JCA results. To overcome this limitation, we propose a simultaneous object and category score estimation method for JCA while addressing the underestimated variance problem that is inherent in MCA. In the proposed method, JCA parameters are estimated by minimizing the discrepancy between the observed categorical data and the JCA data model, rather than relying on the JCA covariance model used in existing estimation methods. Previous research has shown that JCA is comparable to exploratory factor analysis. We also address the factor-analytic interpretation of JCA solutions in addition to geometric interpretation. Two real data analysis examples are also presented to demonstrate the geometric and factor-analytic interpretations of the JCA solutions.

Two potential obstacles stand between the observation of a statistical correlation and the design (and deployment) of an effective intervention, omitted variable bias and reverse causality. Whereas the former has received ample attention, comparably scant focus has been devoted to the latter in the methodological literature. Many existing methods for reverse causality testing commence by postulating a structural model that may suffer from widely recognized issues such as the difficulty of properly setting temporal lags, which are critical to model validity. In this article, we draw upon advances in machine learning, specifically the recently established link between causal direction and the effectiveness of semi-supervised learning algorithms, to develop a novel method for reverse causality testing that circumvents many of the assumptions required by traditional methods. Mathematical analysis and simulation studies were carried out to demonstrate the effectiveness of our method. We also performed tests over a real-world dataset to show how our method may be used to identify causal relationships in practice.

We present a multidimensional data analysis framework for the analysis of ordinal response variables. Underlying the ordinal variables, we assume a continuous latent variable, leading to cumulative logit models. The framework includes unsupervised methods, when no predictor variables are available, and supervised methods, when predictor variables are available. We distinguish between dominance variables and proximity variables, where dominance variables are analyzed using inner product models, whereas the proximity variables are analyzed using distance models. An expectation-majorization-minimization algorithm is derived for estimation of the parameters of the models. We illustrate our methodology with three empirical data sets highlighting the advantages of the proposed framework. A simulation study is conducted to evaluate the performance of the algorithm.

Structured latent curve models (SLCMs) for continuous repeated measures data have been the subject of considerable recent research activity. In this article, we develop a first-order SLCM for repeated measures count data where the underlying change process is theorized to develop in distinct phases. Parameters of the multiphase or piecewise growth model, including changepoints, are allowed to vary across individuals. Exposure is allowed to vary across both individuals and time. We demonstrate our modeling approach on empirical expressive language data (grammatical morpheme counts) drawn from multiple distinct corpora available in the Child Language Data Exchange System (CHILDES), where the acquisition of grammatical morphology is understood to occur in distinct phases in typically developing children. A multiphase SLCM is fit to summarize individuals' data as well as the average developmental pattern. Change in time-varying dispersion (unexplained variability in morpheme counts) over the course of early childhood is modeled concurrently to provide additional insights into acquisition. Unique characteristics of count data create modeling, identification, estimation, and diagnostic challenges that are exacerbated by incorporating growth models with nonlinear random effects. These are discussed at length. We provide annotated software code for each of models used in the empirical example.

Cognitive diagnosis models (CDMs) have been popularly used in fields such as education, psychology, and social sciences. While parametric likelihood estimation is a prevailing method for fitting CDMs, nonparametric methodologies are attracting increasing attention due to their ease of implementation and robustness, particularly when sample sizes are relatively small. However, existing consistency results of the nonparametric estimation methods often rely on certain restrictive conditions, which may not be easily satisfied in practice. In this article, the consistency theory for the general nonparametric classification method is reestablished under weaker and more practical conditions.

To assess country-level progress toward these educational goals it is important to monitor trends in educational outcomes over time. The purpose of this article is to demonstrate how optimally predictive growth models can be constructed to monitor the pace of progress at which countries are moving toward (or way from) the education sustainable development goals as specified by the United Nations. A number of growth curve models can be specified to estimate the pace of progress, however, choosing one model and using it for predictive purposes assumes that the chosen model is the one that generated the data, and this choice runs the risk of "over-confident inferences and decisions that are more risky than one thinks they are" (Hoeting et al., 1999). To mitigate this problem, we adapt and apply Bayesian stacking to form mixtures of predictive distributions from an ensemble of individual models specified to predict country-level pace of progress. We demonstrate Bayesian stacking using country-level data from the Program on International Student Assessment. Our results show that Bayesian stacking yields better predictive accuracy than any single model as measured by the Kullback-Leibler divergence. Issues of Bayesian model identification and estimation for growth models are also discussed.

Factor rotation is a crucial step in interpreting the results of exploratory factor analysis. Several rotation methods have been developed for simple structure solutions, but their extensions to bi-factor analysis are often not well established. In this article, we propose a mathematical framework that incorporates customized factor structure as a regularization to produce the optimal orthogonal or oblique rotation. We demonstrate the utility of the framework using examples of simple structure rotation and bi-factor rotation. Through detailed simulations, we show that the new method is accurate and robust in recovering the factor structures and latent correlations when bi-factor analysis is applied. The new method is applied to a test data and a Quality of Life survey data. Results show that our method can reveal bi-factor structures that are consistent with the theories.

With the growing attention on large-scale educational testing and assessment, the ability to process substantial volumes of response data becomes crucial. Current estimation methods within item response theory (IRT), despite their high precision, often pose considerable computational burdens with large-scale data, leading to reduced computational speed. This study introduces a novel "divide- and-conquer" parallel algorithm built on the Wasserstein posterior approximation concept, aiming to enhance computational speed while maintaining accurate parameter estimation. This algorithm enables drawing parameters from segmented data subsets in parallel, followed by an amalgamation of these parameters via Wasserstein posterior approximation. Theoretical support for the algorithm is established through asymptotic optimality under certain regularity assumptions. Practical validation is demonstrated using real-world data from the Programme for International Student Assessment. Ultimately, this research proposes a transformative approach to managing educational big data, offering a scalable, efficient, and precise alternative that promises to redefine traditional practices in educational assessments.