Psychometrika

Understanding how the adult human brain learns novel categories is an important problem in neuroscience. Drift-diffusion models are popular in such contexts for their ability to mimic the underlying neural mechanisms. One such model for gradual longitudinal learning was recently developed in Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021). In practice, category response accuracies are often the only reliable measure recorded by behavioral scientists to describe human learning. Category response accuracies are, however, often the only reliable measure recorded by behavioral scientists to describe human learning...

Generalized structured component analysis (GSCA) is a multivariate method for examining theory-driven relationships between variables including components. GSCA can provide the deterministic component score for each individual once model parameters are estimated. As the traditional GSCA always standardizes all indicators and components, however, it could not utilize information on the indicators' scale in parameter estimation. Consequently, its component scores could just show the relative standing of each individual for a component, rather than the individual's absolute standing in terms of the original indicators' measurement scales...

Grade of membership (GoM) models are popular individual-level mixture models for multivariate categorical data. GoM allows each subject to have mixed memberships in multiple extreme latent profiles. Therefore, GoM models have a richer modeling capacity than latent class models that restrict each subject to belong to a single profile. The flexibility of GoM comes at the cost of more challenging identifiability and estimation problems. In this work, we propose a singular value decomposition (SVD)-based spectral approach to GoM analysis with multivariate binary responses...

The present work aims at showing that the identification problems (here meant as both issues of empirical indistinguishability and unidentifiability) of some item response theory models are related to the notion of identifiability in knowledge space theory. Specifically, that the identification problems of the 3- and 4-parameter models are related to the more general issues of forward- and backward-gradedness in all items of the power set, which is the knowledge structure associated with IRT models under the assumption of local independence...

In psychological research and practice, a person's scores on two different traits or abilities are often compared. Such within-person comparisons require that measurements have equal units (EU) and/or equal origins: an assumption rarely validated. We describe a multidimensional SEM/IRT model from the literature and, using principles of conjoint measurement, show that its expected response variables satisfy the axioms of additive conjoint measurement for measurement on a common scale. In an application to Quality of Life data, the EU analysis is used as a pre-processing step to derive a simple structure Quality of Life model with three dimensions expressed in equal units...

Most measures of agreement are chance-corrected. They differ in three dimensions: their definition of chance agreement, their choice of disagreement function, and how they handle multiple raters. Chance agreement is usually defined in a pairwise manner, following either Cohen's kappa or Fleiss's kappa. The disagreement function is usually a nominal, quadratic, or absolute value function. But how to handle multiple raters is contentious, with the main contenders being Fleiss's kappa, Conger's kappa, and Hubert's kappa, the variant of Fleiss's kappa where agreement is said to occur only if every rater agrees...

Restricted latent class models (RLCMs) provide an important framework for diagnosing and classifying respondents on a collection of multivariate binary responses. Recent research made significant advances in theory for establishing identifiability conditions for RLCMs with binary and polytomous response data. Multiclass data, which are unordered nominal response data, are also widely collected in the social sciences and psychometrics via forced-choice inventories and multiple choice tests. We establish new identifiability conditions for parameters of RLCMs for multiclass data and discuss the implications for substantive applications...

Generalized structured component analysis (GSCA) is a structural equation modeling (SEM) procedure that constructs components by weighted sums of observed variables and confirmatorily examines their regressional relationship. The research proposes an exploratory version of GSCA, called exploratory GSCA (EGSCA). EGSCA is analogous to exploratory SEM (ESEM) developed as an exploratory factor-based SEM procedure, which seeks the relationships between the observed variables and the components by orthogonal rotation of the parameter matrices...

Cognitive diagnostic models (CDMs) are discrete latent variable models popular in educational and psychological measurement. In this work, motivated by the advantages of deep generative modeling and by identifiability considerations, we propose a new family of DeepCDMs, to hunt for deep discrete diagnostic information. The new class of models enjoys nice properties of identifiability, parsimony, and interpretability. Mathematically, DeepCDMs are entirely identifiable, including even fully exploratory settings and allowing to uniquely identify the parameters and discrete loading structures (the "[Formula: see text]-matrices") at all different depths in the generative model...

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational challenge of estimating MIRT models prohibits its wide use because many of the extant methods can hardly provide results in a realistic time frame when the number of dimensions, sample size, and test length are large...

It is widely believed that a joint factor analysis of item responses and response time (RT) may yield more precise ability scores that are conventionally predicted from responses only. For this purpose, a simple-structure factor model is often preferred as it only requires specifying an additional measurement model for item-level RT while leaving the original item response theory (IRT) model for responses intact. The added speed factor indicated by item-level RT correlates with the ability factor in the IRT model, allowing RT data to carry additional information about respondents' ability...

Response process data from computer-based problem-solving items describe respondents' problem-solving processes as sequences of actions. Such data provide a valuable source for understanding respondents' problem-solving behaviors. Recently, data-driven feature extraction methods have been developed to compress the information in unstructured process data into relatively low-dimensional features. Although the extracted features can be used as covariates in regression or other models to understand respondents' response behaviors, the results are often not easy to interpret since the relationship between the extracted features, and the original response process is often not explicitly defined...

The key assumption of conditional independence of item responses given latent ability in item response theory (IRT) models is addressed for multistage adaptive testing (MST) designs. Routing decisions in MST designs can cause patterns in the data that are not accounted for by the IRT model. This phenomenon relates to quasi-independence in log-linear models for incomplete contingency tables and impacts certain types of statistical inference based on assumptions on observed and missing data. We demonstrate that generalized residuals for item pair frequencies under IRT models as discussed by Haberman and Sinharay (J Am Stat Assoc 108:1435-1444, 2013...

Optimal treatment regimes (OTRs) have been widely employed in computer science and personalized medicine to provide data-driven, optimal recommendations to individuals. However, previous research on OTRs has primarily focused on settings that are independent and identically distributed, with little attention given to the unique characteristics of educational settings, where students are nested within schools and there are hierarchical dependencies. The goal of this study is to propose a framework for designing OTRs from multisite randomized trials, a commonly used experimental design in education and psychology to evaluate educational programs...

Categorical marginal models (CMMs) are flexible tools for modelling dependent or clustered categorical data, when the dependencies themselves are not of interest. A major limitation of maximum likelihood (ML) estimation of CMMs is that the size of the contingency table increases exponentially with the number of variables, so even for a moderate number of variables, say between 10 and 20, ML estimation can become computationally infeasible. An alternative method, which retains the optimal asymptotic efficiency of ML, is maximum empirical likelihood (MEL) estimation...

How social networks influence human behavior has been an interesting topic in applied research. Existing methods often utilized scale-level behavioral data (e.g., total number of positive responses) to estimate the influence of a social network on human behavior. This study proposes a novel approach to studying social influence that utilizes item-level behavioral measures. Under the latent space modeling framework, we integrate the two latent spaces for respondents' social network data and item-level behavior measures into a single space we call 'interaction map'...

In this article, we present a general theorem and proof for the global identification of composed CFA models. They consist of identified submodels that are related only through covariances between their respective latent factors. Composed CFA models are frequently used in the analysis of multimethod data, longitudinal data, or multidimensional psychometric data. Firstly, our theorem enables researchers to reduce the problem of identifying the composed model to the problem of identifying the submodels and verifying the conditions given by our theorem...

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Multidimensional forced-choice (MFC) tests are increasing in popularity but their construction is complex. The Thurstonian item response model (Thurstonian IRT model) is most often used to score MFC tests that contain dominance items. Currently, in a frequentist framework, information about the latent traits in the Thurstonian IRT model is computed for binary outcomes of pairwise comparisons, but this approach neglects stochastic dependencies. In this manuscript, it is shown how to estimate Fisher information on the block level...

In social, behavioral and economic sciences, researchers are interested in modeling a social network among a group of individuals, along with their attributes. The attributes can be responses to survey questionnaires and are often high dimensional. We propose a joint latent space model (JLSM) that summarizes information from the social network and the multivariate attributes in a person-attribute joint latent space. We develop a variational Bayesian expectation-maximization estimation algorithm to estimate the attribute and person locations in the joint latent space...