Psychometrika最新文献

Fit indices are highly frequently used for assessing the goodness of fit of latent variable models. Most prominent fit indices, such as the root-mean-square error of approximation (RMSEA) or the comparative fit index (CFI), are based on a noncentrality parameter estimate derived from the model fit statistic. While a noncentrality parameter estimate is well suited for quantifying the amount of systematic error, the complex weighting function involved in its calculation makes indices derived from it challenging to interpret. Moreover, noncentrality-parameter-based fit indices yield systematically different values, depending on the indicators' level of measurement. For instance, RMSEA and CFI yield more favorable fit indices for models with categorical as compared to metric variables under otherwise identical conditions. In the present article, approaches for obtaining an approximation discrepancy estimate that is independent from any specific weighting function are considered. From these unweighted approximation error estimates, fit indices analogous to RMSEA and CFI are calculated and their finite sample properties are investigated using simulation studies. The results illustrate that the new fit indices consistently estimate their true value which, in contrast to other fit indices, is the same value for metric and categorical variables. Advantages with respect to interpretability are discussed and cutoff criteria for the new indices are considered.

Hidden Markov models (HMMs) have been applied in various domains, which makes the identifiability issue of HMMs popular among researchers. Classical identifiability conditions shown in previous studies are too strong for practical analysis. In this paper, we propose generic identifiability conditions for discrete time HMMs with finite state space. Also, recent studies about cognitive diagnosis models (CDMs) applied first-order HMMs to track changes in attributes related to learning. However, the application of CDMs requires a known [Formula: see text] matrix to infer the underlying structure between latent attributes and items, and the identifiability constraints of the model parameters should also be specified. We propose generic identifiability constraints for our restricted HMM and then estimate the model parameters, including the [Formula: see text] matrix, through a Bayesian framework. We present Monte Carlo simulation results to support our conclusion and apply the developed model to a real dataset.

Latent class models are powerful statistical modeling tools widely used in psychological, behavioral, and social sciences. In the modern era of data science, researchers often have access to response data collected from large-scale surveys or assessments, featuring many items (large J) and many subjects (large N). This is in contrary to the traditional regime with fixed J and large N. To analyze such large-scale data, it is important to develop methods that are both computationally efficient and theoretically valid. In terms of computation, the conventional EM algorithm for latent class models tends to have a slow algorithmic convergence rate for large-scale data and may converge to some local optima instead of the maximum likelihood estimator (MLE). Motivated by this, we introduce the tensor decomposition perspective into latent class analysis with binary responses. Methodologically, we propose to use a moment-based tensor power method in the first step and then use the obtained estimates as initialization for the EM algorithm in the second step. Theoretically, we establish the clustering consistency of the MLE in assigning subjects into latent classes when N and J both go to infinity. Simulation studies suggest that the proposed tensor-EM pipeline enjoys both good accuracy and computational efficiency for large-scale data with binary responses. We also apply the proposed method to an educational assessment dataset as an illustration.

Researchers have widely used exploratory factor analysis (EFA) to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that they often use to find interpretable loading matrices. In this paper, we propose a new family of oblique rotations based on component-wise [Formula: see text] loss functions [Formula: see text] that is closely related to an [Formula: see text] regularised estimator. We develop model selection and post-selection inference procedures based on the proposed rotation method. When the true loading matrix is sparse, the proposed method tends to outperform traditional rotation and regularised estimation methods in terms of statistical accuracy and computational cost. Since the proposed loss functions are nonsmooth, we develop an iteratively reweighted gradient projection algorithm for solving the optimisation problem. We also develop theoretical results that establish the statistical consistency of the estimation, model selection, and post-selection inference. We evaluate the proposed method and compare it with regularised estimation and traditional rotation methods via simulation studies. We further illustrate it using an application to the Big Five personality assessment.

We present generalized additive latent and mixed models (GALAMMs) for analysis of clustered data with responses and latent variables depending smoothly on observed variables. A scalable maximum likelihood estimation algorithm is proposed, utilizing the Laplace approximation, sparse matrix computation, and automatic differentiation. Mixed response types, heteroscedasticity, and crossed random effects are naturally incorporated into the framework. The models developed were motivated by applications in cognitive neuroscience, and two case studies are presented. First, we show how GALAMMs can jointly model the complex lifespan trajectories of episodic memory, working memory, and speed/executive function, measured by the California Verbal Learning Test (CVLT), digit span tests, and Stroop tests, respectively. Next, we study the effect of socioeconomic status on brain structure, using data on education and income together with hippocampal volumes estimated by magnetic resonance imaging. By combining semiparametric estimation with latent variable modeling, GALAMMs allow a more realistic representation of how brain and cognition vary across the lifespan, while simultaneously estimating latent traits from measured items. Simulation experiments suggest that model estimates are accurate even with moderate sample sizes.

The study presents statistical procedures that monitor functioning of items over time. We propose generalized likelihood ratio tests that surveil multiple item parameters and implement with various sampling techniques to perform continuous or intermittent monitoring. The procedures examine stability of item parameters across time and inform compromise as soon as they identify significant parameter shift. The performance of the monitoring procedures was validated using simulated and real-assessment data. The empirical evaluation suggests that the proposed procedures perform adequately well in identifying the parameter drift. They showed satisfactory detection power and gave timely signals while regulating error rates reasonably low. The procedures also showed superior performance when compared with the existent methods. The empirical findings suggest that multivariate parametric monitoring can provide an efficient and powerful control tool for maintaining the quality of items. The procedures allow joint monitoring of multiple item parameters and achieve sufficient power using powerful likelihood-ratio tests. Based on the findings from the empirical experimentation, we suggest some practical strategies for performing online item monitoring.

Significant heterogeneity in network structures reflecting individuals' dynamic processes can exist within subgroups of people (e.g., diagnostic category, gender). This makes it difficult to make inferences regarding these predefined subgroups. For this reason, researchers sometimes wish to identify subsets of individuals who have similarities in their dynamic processes regardless of any predefined category. This requires unsupervised classification of individuals based on similarities in their dynamic processes, or equivalently, in this case, similarities in their network structures of edges. The present paper tests a recently developed algorithm, S-GIMME, that takes into account heterogeneity across individuals with the aim of providing subgroup membership and precise information about the specific network structures that differentiate subgroups. The algorithm has previously provided robust and accurate classification when evaluated with large-scale simulation studies but has not yet been validated on empirical data. Here, we investigate S-GIMME's ability to differentiate, in a purely data-driven manner, between brain states explicitly induced through different tasks in a new fMRI dataset. The results provide new evidence that the algorithm was able to resolve, in an unsupervised data-driven manner, the differences between different active brain states in empirical fMRI data to segregate individuals and arrive at subgroup-specific network structures of edges. The ability to arrive at subgroups that correspond to empirically designed fMRI task conditions, with no biasing or priors, suggests this data-driven approach can be a powerful addition to existing methods for unsupervised classification of individuals based on their dynamic processes.

Research questions in the human sciences often seek to answer if and when a process changes across time. In functional MRI studies, for instance, researchers may seek to assess the onset of a shift in brain state. For daily diary studies, the researcher may seek to identify when a person's psychological process shifts following treatment. The timing and presence of such a change may be meaningful in terms of understanding state changes. Currently, dynamic processes are typically quantified as static networks where edges indicate temporal relations among nodes, which may be variables reflecting emotions, behaviors, or brain activity. Here we describe three methods for detecting changes in such correlation networks from a data-driven perspective. Networks here are quantified using the lag-0 pair-wise correlation (or covariance) estimates as the representation of the dynamic relations among variables. We present three methods for change point detection: dynamic connectivity regression, max-type method, and a PCA-based method. The change point detection methods each include different ways to test if two given correlation network patterns from different segments in time are significantly different. These tests can also be used outside of the change point detection approaches to test any two given blocks of data. We compare the three methods for change point detection as well as the complementary significance testing approaches on simulated and empirical functional connectivity fMRI data examples.

The Polytomous Local Independence Model (PoLIM) by Stefanutti, de Chiusole, Anselmi, and Spoto, is an extension of the Basic Local Independence Model (BLIM) to accommodate polytomous items. BLIM, a model for analyzing responses to binary items, is based on Knowledge Space Theory, a framework developed by cognitive scientists and mathematical psychologists for modeling human knowledge acquisition and representation. The purpose of this commentary is to show that PoLIM is simply a paraphrase of a DINA model in cognitive diagnosis for polytomous items. Specifically, BLIM is shown to be equivalent to the DINA model when the BLIM-items are conceived as binary single-attribute items, each with a distinct attribute; thus, PoLIM is equivalent to the DINA for polytomous single-attribute items, each with a distinct attribute.

This article reviews recent advances in the psychometric and econometric modeling of eye-movements during decision making. Eye movements offer a unique window on unobserved perceptual, cognitive, and evaluative processes of people who are engaged in decision making tasks. They provide new insights into these processes, which are not easily available otherwise, allow for explanations of fundamental search and choice phenomena, and enable predictions of future decisions. We propose a theoretical framework of the search and choice tasks that people commonly engage in and of the underlying cognitive processes involved in those tasks. We discuss how these processes drive specific eye-movement patterns. Our framework emphasizes the central role of task and strategy switching for complex goal attainment. We place the extant literature within that framework, highlight recent advances in modeling eye-movement behaviors during search and choice, discuss limitations, challenges, and open problems. An agenda for further psychometric modeling of eye movements during decision making concludes the review.