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Abstract Differential item functioning (DIF) screening has long been suggested to ensure assessment fairness. Traditional DIF methods typically focus on the main effects of demographic variables on item parameters, overlooking the interactions among multiple identities. Drawing on the intersectionality framework, we define intersectional DIF as deviations in item parameters that arise from the interactions among demographic variables beyond their main effects and propose a novel item response theory (IRT) approach for detecting intersectional DIF. Under our framework, fixed effects are used to account for traditional DIF, while random item effects are introduced to capture intersectional DIF. We further introduce the concept of intersectional impact, which refers to interaction effects on group-level mean ability. Depending on which item parameters are affected and whether intersectional impact is considered, we propose four models, which aim to detect intersectional uniform DIF (UDIF), intersectional UDIF with intersectional impact, intersectional non-uniform DIF (NUDIF), and intersectional NUDIF with intersectional impact, respectively. For efficient model estimation, a regularized Gaussian variational expectation-maximization algorithm is developed. Simulation studies demonstrate that our methods can effectively detect intersectional UDIF, although their detection of intersectional NUDIF is more limited. 

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. 

Abstract Mediation analysis aims to assess if, and how, a certain exposure influences an outcome of interest through intermediate variables. This problem has recently gained a surge of attention due to the tremendous need for such analyses in scientific fields. Testing for the mediation effect (ME) is greatly challenged by the fact that the underlying null hypothesis (i.e. the absence of MEs) is composite. Most existing mediation tests are overly conservative and thus underpowered. To overcome this significant methodological hurdle, we develop an adaptive bootstrap testing framework that can accommodate different types of composite null hypotheses in the mediation pathway analysis. Applied to the product of coefficients test and the joint significance test, our adaptive testing procedures provide type I error control under the composite null, resulting in much improved statistical power compared to existing tests. Both theoretical properties and numerical examples of the proposed methodology are discussed. 

Abstract In this paper, we develop a mixed stochastic approximation expectation‐maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four‐parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of the stochastic approximation expectation‐maximization (SAEM) algorithm for multidimensional data, but it also alleviates the potential instability caused by label‐switching, and then improved the estimation accuracy. Simulation studies are conducted to illustrate the good performance of the proposed MSAEM method, where MSAEM consistently performs better than SAEM and some other existing methods in multidimensional item response theory. Moreover, the proposed method is applied to a real data set from the 2018 Programme for International Student Assessment (PISA) to demonstrate the usefulness of the 4PNO model as well as MSAEM in practice. 

Abstract Establishing the invariance property of an instrument (e.g., a questionnaire or test) is a key step for establishing its measurement validity. Measurement invariance is typically assessed by differential item functioning (DIF) analysis, i.e., detecting DIF items whose response distribution depends not only on the latent trait measured by the instrument but also on the group membership. DIF analysis is confounded by the group difference in the latent trait distributions. Many DIF analyses require knowing several anchor items that are DIF-free in order to draw inferences on whether each of the rest is a DIF item, where the anchor items are used to identify the latent trait distributions. When no prior information on anchor items is available, or some anchor items are misspecified, item purification methods and regularized estimation methods can be used. The former iteratively purifies the anchor set by a stepwise model selection procedure, and the latter selects the DIF-free items by a LASSO-type regularization approach. Unfortunately, unlike the methods based on a correctly specified anchor set, these methods are not guaranteed to provide valid statistical inference (e.g., confidence intervals andp-values). In this paper, we propose a new method for DIF analysis under a multiple indicators and multiple causes (MIMIC) model for DIF. This method adopts a minimal$$L_1$$ $L_1$norm condition for identifying the latent trait distributions. Without requiring prior knowledge about an anchor set, it can accurately estimate the DIF effects of individual items and further draw valid statistical inferences for quantifying the uncertainty. Specifically, the inference results allow us to control the type-I error for DIF detection, which may not be possible with item purification and regularized estimation methods. We conduct simulation studies to evaluate the performance of the proposed method and compare it with the anchor-set-based likelihood ratio test approach and the LASSO approach. The proposed method is applied to analysing the three personality scales of the Eysenck personality questionnaire-revised (EPQ-R). 

Abstract After graphene was first exfoliated in 2004, research worldwide has focused on discovering and exploiting its distinctive electronic, mechanical, and structural properties. Application of the efficacious methodology used to fabricate graphene, mechanical exfoliation followed by optical microscopy inspection, to other analogous bulk materials has resulted in many more two-dimensional (2D) atomic crystals. Despite their fascinating physical properties, manual identification of 2D atomic crystals has the clear drawback of low-throughput and hence is impractical for any scale-up applications of 2D samples. To combat this, recent integration of high-performance machine-learning techniques, usually deep learning algorithms because of their impressive object recognition abilities, with optical microscopy have been used to accelerate and automate this traditional flake identification process. However, deep learning methods require immense datasets and rely on uninterpretable and complicated algorithms for predictions. Conversely, tree-based machine-learning algorithms represent highly transparent and accessible models. We investigate these tree-based algorithms, with features that mimic color contrast, for automating the manual inspection process of exfoliated 2D materials (e.g., MoSe₂). We examine their performance in comparison to ResNet, a famous Convolutional Neural Network (CNN), in terms of accuracy and the physical nature of their decision-making process. We find that the decision trees, gradient boosted decision trees, and random forests utilize physical aspects of the images to successfully identify 2D atomic crystals without suffering from extreme overfitting and high training dataset demands. We also employ a post-hoc study that identifies the sub-regions CNNs rely on for classification and find that they regularly utilize physically insignificant image attributes when correctly identifying thin materials. 

Abstract A central but challenging problem in genetic studies is to test for (usually weak) associations between a complex trait (e.g., a disease status) and sets of multiple genetic variants. Due to the lack of a uniformly most powerful test, data‐adaptive tests, such as the adaptive sum of powered score (aSPU) test, are advantageous in maintaining high power against a wide range of alternatives. However, there is often no closed‐form to accurately and analytically calculate thep‐values of many adaptive tests like aSPU, thus Monte Carlo (MC) simulations are often used, which can be time consuming to achieve a stringent significance level (e.g., 5e‐8) used in genome‐wide association studies (GWAS). To estimate such a smallp‐value, we need a huge number of MC simulations (e.g., 1e+10). As an alternative, we propose using importance sampling to speed up such calculations. We develop some theory to motivate a proposed algorithm for the aSPU test, and show that the proposed method is computationally more efficient than the standard MC simulations. Using both simulated and real data, we demonstrate the superior performance of the new method over the standard MC simulations.