Psychometrika最新文献

Multivariate bounded discrete data arises in many fields. In the setting of dementia studies, such data are collected when individuals complete neuropsychological tests. We outline a modeling and inference procedure that can model the joint distribution conditional on baseline covariates, leveraging previous work on mixtures of experts and latent class models. Furthermore, we illustrate how the work can be extended when the outcome data are missing at random using a nested EM algorithm. The proposed model can incorporate covariate information and perform imputation and clustering. We apply our model to simulated data and an Alzheimer's disease data set.

Reliability analysis is one of the most conducted analyses in applied psychometrics. It entails the assessment of reliability of both item scores and scale scores using coefficients that estimate the reliability (e.g., Cronbach's alpha), measurement precision (e.g., estimated standard error of measurement), or the contribution of individual items to the reliability (e.g., corrected item-total correlations). Most statistical software packages used in social and behavioral sciences offer these reliability coefficients, whereas standard errors are generally unavailable, which is a bit ironic for coefficients about measurement precision. This article provides analytic nonparametric standard errors for coefficients used in reliability analysis. As most scores used in behavioral sciences are discrete, standard errors are derived under the relatively unrestrictive multinomial sampling scheme. Tedious derivations are presented in appendices, and R functions for computing standard errors are available from the Open Science Framework. Bias and variance of standard errors, and coverage of the corresponding Wald-based confidence intervals are studied using simulated item scores. Bias and variance, and coverage are generally satisfactory for larger sample sizes, and parameter values are not close to the boundary of the parameter space.

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.

In maximum likelihood factor analysis, we need to solve a complicated system of algebraic equations, known as the normal equation, to get maximum likelihood estimates (MLEs). Since this equation is difficult to solve analytically, its solutions are typically computed with continuous optimization methods, such as the Newton-Raphson method. With this procedure, however, the MLEs are dependent on initial values since the log-likelihood function is highly non-concave. Particularly, the estimates of unique variances can result in zero or negative, referred to as improper solutions; in this case, the MLE can be severely unstable. To delve into the issue of the instability, we algebraically compute all candidates for the MLE. We provide an algorithm based on algebraic computations that is carefully designed for maximum likelihood factor analysis. To be specific, Gröbner bases are employed, powerful tools to get simplified sub-problems for given systems of algebraic equations. Our algebraic algorithm provides the MLE independent of the initial values. While computationally demanding, our algebraic approach is applicable to small-scale problems and provides valuable insights into the characterization of improper solutions. For larger-scale problems, we provide numerical methods as practical alternatives to the algebraic approach. We perform numerical experiments to investigate the characteristics of the MLE with our two approaches.

The article proposes a novel item response theory model to handle continuous responses and sparse polytomous responses in psychological and educational measurement. The model extends the traditional two-parameter logistic model by incorporating a precision parameter, which, along with a beta distribution, forms an error component that accounts for the response continuity. Furthermore, transforming ordinal responses to a continuous scale enables the fitting of polytomous item responses while consistently applying three parameters per item for model parsimony. The model's accuracy, stability, and computational efficiency in parameter estimation were examined. An empirical application demonstrated the model's effectiveness in representing the characteristics of continuous item responses. Additionally, the model's applicability to sparse polytomous data was supported by cross-validation results from another empirical dataset, which indicates that the model's parsimony can enhance model-data fit compared to existing polytomous models.

Bifactor Item Response Theory (IRT) models are the usual option for modeling composite constructs. However, in application, researchers typically must assume that all dimensions of person parameter space are orthogonal. This can result in absurd model interpretations. We propose a new bifactor model-the Completely Oblique Rasch Bifactor (CORB) model-which allows for estimation of correlations between all dimensions. We discuss relations of this model to other oblique bifactor models and study the conditions for its identification in the dichotomous case. We analytically prove that this model is identified in the case that (a) at least one item loads solely on the general factor and no items are shared between any pair of specific factors (we call this the G-structure), or (b) if no items load solely on the general factor, but at least one item is shared between every pair of the specific factors (the S-structure). Using simulated and real data, we show that this model outperforms the other partially oblique bifactor models in terms of model fit because it corresponds to the more realistic assumptions about construct structure. We also discuss possible difficulties in the interpretation of the CORB model's parameters using, by analogy, the "explaining away" phenomenon from Bayesian reasoning.

The latent Markov model (LMM) has been increasingly used to analyze log data from computer-interactive assessments. An important consideration in applying the LMM to assessment data is measurement effects of items. In educational and psychological assessment, items exhibit distinct psychometric qualities and induce systematic variance to assessment outcome data. The current development in LMM, however, assumes that items have uniform effects and do not contribute to the variance of measurement outcomes. In this study, we propose a refinement of LMM that relaxes the measurement invariance constraint and examine empirical performance of the new framework through numerical experimentation. We modify the LMM for noninvariant measurements and refine the inferential scheme to accommodate the event-specific measurement effects. Numerical experiments are conducted to validate the proposed inference methods and evaluate the performance of the new framework. Results suggest that the proposed inferential scheme performs adequately well in retrieving the model parameters and state profiles. The new LMM framework demonstrated reliable and stable performance in modeling latent processes while appropriately accounting for items' measurement effects. Compared with the traditional scheme, the refined framework demonstrated greater relevance to real assessment data and yielded more robust inference results when the model was ill-specified. The findings from the empirical evaluations suggest that the new framework has potential for serving large-scale assessment data that exhibit distinct measurement effects.