A sparse latent class model incorporating response times.

Diagnostic models (DM) have been widely used to classify respondents' latent attributes in cognitive and non-cognitive assessments. The integration of response times (RTs) with DM presents additional evidence to understand respondents' problem-solving behaviours. While recent research has explored using sparse latent class models (SLCM) to infer the latent structure of items based on item responses, the incorporation of RT data within these models remains underexplored.

Restricted Latent Class Models for Nominal Response Data: Identifiability and Estimation.

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.

A sequential exploratory diagnostic model using a Pólya-gamma data augmentation strategy.

Cognitive diagnostic models provide a framework for classifying individuals into latent proficiency classes, also known as attribute profiles. Recent research has examined the implementation of a Pólya-gamma data augmentation strategy binary response model using logistic item response functions within a Bayesian Gibbs sampling procedure. In this paper, we propose a sequential exploratory diagnostic model for ordinal response data using a logit-link parameterization at the category level and extend the Pólya-gamma data augmentation strategy to ordinal response processes.

Identifiability of Hidden Markov Models for Learning Trajectories in Cognitive Diagnosis.

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.

Bayesian Inference for an Unknown Number of Attributes in Restricted Latent Class Models.

The specification of the [Formula: see text] matrix in cognitive diagnosis models is important for correct classification of attribute profiles. Researchers have proposed many methods for estimation and validation of the data-driven [Formula: see text] matrices. However, inference of the number of attributes in the general restricted latent class model remains an open question.

Extending exploratory diagnostic classification models: Inferring the effect of covariates.

Diagnostic models provide a statistical framework for designing formative assessments by classifying student knowledge profiles according to a collection of fine-grained attributes. The context and ecosystem in which students learn may play an important role in skill mastery, and it is therefore important to develop methods for incorporating student covariates into diagnostic models. Including covariates may provide researchers and practitioners with the ability to evaluate novel interventions or understand the role of background knowledge in attribute mastery.

A Note on Weaker Conditions for Identifying Restricted Latent Class Models for Binary Responses.

Restricted latent class models (RLCMs) are an important class of methods that provide researchers and practitioners in the educational, psychological, and behavioral sciences with fine-grained diagnostic information to guide interventions. Recent research established sufficient conditions for identifying RLCM parameters. A current challenge that limits widespread application of RLCMs is that existing identifiability conditions may be too restrictive for some practical settings.

Exploratory Restricted Latent Class Models with Monotonicity Requirements under PÒLYA-GAMMA Data Augmentation.

Restricted latent class models (RLCMs) provide an important framework for supporting diagnostic research in education and psychology. Recent research proposed fully exploratory methods for inferring the latent structure. However, prior research is limited by the use of restrictive monotonicity condition or prior formulations that are unable to incorporate prior information about the latent structure to validate expert knowledge.

Inferring Latent Structure in Polytomous Data with a Higher-Order Diagnostic Model.

Researchers continue to develop and advance models for diagnostic research in the social and behavioral sciences. These diagnostic models (DMs) provide researchers with a framework for providing a fine-grained classification of respondents into substantively meaningful latent classes as defined by a multivariate collection of binary attributes. A central concern for DMs is advancing exploratory methods for uncovering the latent structure, which corresponds with the relationship between unobserved binary attributes and observed polytomous items with two or more response options.

A Multivariate Probit Model for Learning Trajectories: A Fine-Grained Evaluation of an Educational Intervention.

Advances in educational technology provide teachers and schools with a wealth of information about student performance. A critical direction for educational research is to harvest the available longitudinal data to provide teachers with real-time diagnoses about students' skill mastery. Cognitive diagnosis models (CDMs) offer educational researchers, policy makers, and practitioners a psychometric framework for designing instructionally relevant assessments and diagnoses about students' skill profiles.

Inferring the Number of Attributes for the Exploratory DINA Model.

Diagnostic classification models (DCMs) are widely used for providing fine-grained classification of a multidimensional collection of discrete attributes. The application of DCMs requires the specification of the latent structure in what is known as the [Formula: see text] matrix. Expert-specified [Formula: see text] matrices might be biased and result in incorrect diagnostic classifications, so a critical issue is developing methods to estimate [Formula: see text] in order to infer the relationship between latent attributes and items.

A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model.

Recently, there has been a renewed interest in the four-parameter item response theory model as a way to capture guessing and slipping behaviors in responses. Research has shown, however, that the nested three-parameter model suffers from issues of unidentifiability (San Martín et al. in Psychometrika 80:450-467, 2015), which places concern on the identifiability of the four-parameter model.

An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation.

Diagnostic models (DMs) provide researchers and practitioners with tools to classify respondents into substantively relevant classes. DMs are widely applied to binary response data; however, binary response models are not applicable to the wealth of ordinal data collected by educational, psychological, and behavioral researchers. Prior research developed confirmatory ordinal DMs that require expert knowledge to specify the underlying structure.

High-Stakes Testing Case Study: A Latent Variable Approach for Assessing Measurement and Prediction Invariance.

The existence of differences in prediction systems involving test scores across demographic groups continues to be a thorny and unresolved scientific, professional, and societal concern. Our case study uses a two-stage least squares (2SLS) estimator to jointly assess measurement invariance and prediction invariance in high-stakes testing. So, we examined differences across groups based on latent as opposed to observed scores with data for 176 colleges and universities from The College Board.

Estimating the Cognitive Diagnosis [Formula: see text] Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset.

Cognitive diagnosis models (CDMs) are an important psychometric framework for classifying students in terms of attribute and/or skill mastery. The [Formula: see text] matrix, which specifies the required attributes for each item, is central to implementing CDMs. The general unavailability of [Formula: see text] for most content areas and datasets poses a barrier to widespread applications of CDMs, and recent research accordingly developed fully exploratory methods to estimate Q.

An Improved Strategy for Bayesian Estimation of the Reduced Reparameterized Unified Model.

A Bayesian formulation for a popular conjunctive cognitive diagnosis model, the reduced reparameterized unified model (rRUM), is developed. The new Bayesian formulation of the rRUM employs a latent response data augmentation strategy that yields tractable full conditional distributions. A Gibbs sampling algorithm is described to approximate the posterior distribution of the rRUM parameters.

A Hidden Markov Model for Learning Trajectories in Cognitive Diagnosis With Application to Spatial Rotation Skills.

The increasing presence of electronic and online learning resources presents challenges and opportunities for psychometric techniques that can assist in the measurement of abilities and even hasten their mastery. Cognitive diagnosis models (CDMs) are ideal for tracking many fine-grained skills that comprise a domain, and can assist in carefully navigating through the training and assessment of these skills in e-learning applications. A class of CDMs for modeling changes in attributes is proposed, which is referred to as learning trajectories.

Bayesian Estimation of the DINA Q matrix.

Cognitive diagnosis models are partially ordered latent class models and are used to classify students into skill mastery profiles. The deterministic inputs, noisy "and" gate model (DINA) is a popular psychometric model for cognitive diagnosis. Application of the DINA model requires content expert knowledge of a Q matrix, which maps the attributes or skills needed to master a collection of items.

A Hierarchical Model for Accuracy and Choice on Standardized Tests.

This paper assesses the psychometric value of allowing test-takers choice in standardized testing. New theoretical results examine the conditions where allowing choice improves score precision. A hierarchical framework is presented for jointly modeling the accuracy of cognitive responses and item choices.

Revisiting the 4-Parameter Item Response Model: Bayesian Estimation and Application.

There has been renewed interest in Barton and Lord's (An upper asymptote for the three-parameter logistic item response model (Tech. Rep. No.

An Improved Correction for Range Restricted Correlations Under Extreme, Monotonic Quadratic Nonlinearity and Heteroscedasticity.

Standardized tests are frequently used for selection decisions, and the validation of test scores remains an important area of research. This paper builds upon prior literature about the effect of nonlinearity and heteroscedasticity on the accuracy of standard formulas for correcting correlations in restricted samples. Existing formulas for direct range restriction require three assumptions: (1) the criterion variable is missing at random; (2) a linear relationship between independent and dependent variables; and (3) constant error variance or homoscedasticity.

Using the Criterion-Predictor Factor Model to Compute the Probability of Detecting Prediction Bias with Ordinary Least Squares Regression.

The study of prediction bias is important and the last five decades include research studies that examined whether test scores differentially predict academic or employment performance. Previous studies used ordinary least squares (OLS) to assess whether groups differ in intercepts and slopes. This study shows that OLS yields inaccurate inferences for prediction bias hypotheses.

Using analysis of covariance (ANCOVA) with fallible covariates.

Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e.

Studying Individual Differences in Predictability With Gamma Regression and Nonlinear Multilevel Models.

Statistical prediction remains an important tool for decisions in a variety of disciplines. An equally important issue is identifying factors that contribute to more or less accurate predictions. The time series literature includes well developed methods for studying predictability and volatility over time.