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Abstract 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. 

Abstract Factor analysis is a widely used statistical tool in many scientific disciplines, such as psychology, economics, and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor analysis remains an open problem. In this paper, we focus on high-dimensional factor analysis involving network-connected observations, and propose a generalized factor model with latent factors that account for both the network structure and the dependence structure among high-dimensional variables. These latent factors can be shared by the high-dimensional variables and the network, or exclusively applied to either of them. We develop a computationally efficient estimation procedure and establish asymptotic inferential theories. Notably, we show that by borrowing information from the network, the proposed estimator of the factor loading matrix achieves optimal asymptotic variance under much milder identifiability constraints than existing literature. Furthermore, we develop a hypothesis testing procedure to tackle the challenge of discerning the shared and individual latent factors’ structure. The finite sample performance of the proposed method is demonstrated through simulation studies and a real-world dataset involving a statistician co-authorship network. 

Abstract Data harmonization is an emerging approach to strategically combining data from multiple independent studies, enabling addressing new research questions that are not answerable by a single contributing study. A fundamental psychometric challenge for data harmonization is to create commensurate measures for the constructs of interest across studies. In this study, we focus on a regularized explanatory multidimensional item response theory model (re-MIRT) for establishing measurement equivalence across instruments and studies, where regularization enables the detection of items that violate measurement invariance, also known as differential item functioning (DIF). Because the MIRT model is computationally demanding, we leverage the recently developed Gaussian Variational Expectation–Maximization (GVEM) algorithm to speed up the computation. In particular, the GVEM algorithm is extended to a more complicated and improved multi-group version with categorical covariates and Lasso penalty for re-MIRT, namely, the importance weighted GVEM with one additional maximization step (IW-GVEMM). This study aims to provide empirical evidence to support feasible uses of IW-GVEMM for re-MIRT DIF detection, providing a useful tool for integrative data analysis. Our results show that IW-GVEMM accurately estimates the model, detects DIF items, and finds a more reasonable number of DIF items in a real world dataset. The proposed method has been integrated intoRpackageVEMIRT(https://map-lab-uw.github.io/VEMIRT). 

Abstract Normal ogive (NO) models have contributed substantially to the advancement of item response theory (IRT) and have become popular educational and psychological measurement models. However, estimating NO models remains computationally challenging. The purpose of this paper is to propose an efficient and reliable computational method for fitting NO models. Specifically, we introduce a novel and unified expectation‐maximization (EM) algorithm for estimating NO models, including two‐parameter, three‐parameter, and four‐parameter NO models. A key improvement in our EM algorithm lies in augmenting the NO model to be a complete data model within the exponential family, thereby substantially streamlining the implementation of the EM iteration and avoiding the numerical optimization computation in the M‐step. Additionally, we propose a two‐step expectation procedure for implementing the E‐step, which reduces the dimensionality of the integration and effectively enables numerical integration. Moreover, we develop a computing procedure for estimating the standard errors (SEs) of the estimated parameters. Simulation results demonstrate the superior performance of our algorithm in terms of its recovery accuracy, robustness, and computational efficiency. To further validate our methods, we apply them to real data from the Programme for International Student Assessment (PISA). The results affirm the reliability of the parameter estimates obtained using our method.