Brain activation and connectivity analyses in task-based functional magnetic resonance imaging (fMRI) experiments with multiple subjects are currently at the forefront of data-driven neuroscience. In such experiments, interest often lies in understanding activation of brain voxels due to external stimuli and strong association or connectivity between the measurements on a set of pre-specified groups of brain voxels, also known as regions of interest (ROI). This article proposes a joint Bayesian additive mixed modeling framework that simultaneously assesses brain activation and connectivity patterns from multiple subjects. In particular, fMRI measurements from each individual obtained in the form of a multi-dimensional array/tensor at each time are regressed on functions of the stimuli. We impose a low-rank parallel factorization decomposition on the tensor regression coefficients corresponding to the stimuli to achieve parsimony. Multiway stick-breaking shrinkage priors are employed to infer activation patterns and associated uncertainties in each voxel. Further, the model introduces region-specific random effects which are jointly modeled with a Bayesian Gaussian graphical prior to account for the connectivity among pairs of ROIs. Empirical investigations under various simulation studies demonstrate the effectiveness of the method as a tool to simultaneously assess brain activation and connectivity. The method is then applied to a multi-subject fMRI dataset from a balloon-analog risk-taking experiment, showing the effectiveness of the model in providing interpretable joint inference on voxel-level activations and inter-regional connectivity associated with how the brain processes risk. The proposed method is also validated through simulation studies and comparisons to other methods used within the neuroscience community.

Methods for the analysis of one-factor randomized groups designs with ordered treatments are well established, but they do not apply in the case of more complex experiments. This article describes ordered treatment methods based on maximum-likelihood and robust estimation that apply to designs with clustered data, including those with a vector of covariates. The contrast coefficients proposed for the ordered treatment estimates yield higher power than those advocated by Abelson and Tukey; the proposed robust estimation method is shown (using theory and simulation) to yield both high power and robustness to outliers. Extensions for nonmonotonic alternatives are easily obtained.

Social network data represent interactions and relationships among groups of individuals. One aspect of social interaction is social influence, the idea that beliefs or behaviors change as a result of one’s social network. The purpose of this article is to introduce a new model for social influence, the latent space model for influence, which employs latent space positions so that individuals are affected most by those who are “closest” to them in the latent space. We describe this model along with some of the contexts in which it can be used and explore the operating characteristics using a series of simulation studies. We conclude with an example of teacher advice-seeking networks to show that changes in beliefs about teaching mathematics may be attributed to network influence.

A maximum likelihood estimation routine for two-level structural equation models with random slopes for latent covariates is presented. Because the likelihood function does not typically have a closed-form solution, numerical integration over the random effects is required. The routine relies upon a method proposed by du Toit and Cudeck (Psychometrika 74(1):65–82, 2009) for reformulating the likelihood function so that an often large subset of the random effects can be integrated analytically, reducing the computational burden of high-dimensional numerical integration. The method is demonstrated and assessed using a small-scale simulation study and an empirical example.

The social relations model (SRM) is widely used in psychology to investigate the components that underlie interpersonal perceptions, behaviors, and judgments. SRM researchers are often interested in investigating the multivariate relations between SRM effects. However, at present, it is not possible to investigate such relations without relying on a two-step approach that depends on potentially unreliable estimates of the true SRM effects. Here, we introduce a way to combine the SRM with the structural equation modeling (SEM) framework and show how the parameters of our combination can be estimated with a maximum likelihood (ML) approach. We illustrate the model with an example from personality psychology. We also investigate the statistical properties of the model in a small simulation study showing that our approach performs well in most simulation conditions. An R package (called srm) is available implementing the proposed methods.

Factor analysis is a well-known method for describing the covariance structure among a set of manifest variables through a limited number of unobserved factors. When the observed variables are collected at various occasions on the same statistical units, the data have a three-way structure and standard factor analysis may fail. To overcome these limitations, three-way models, such as the Parafac model, can be adopted. It is often seen as an extension of principal component analysis able to discover unique latent components. The structural version, i.e., as a reparameterization of the covariance matrix, has been also formulated but rarely investigated. In this article, such a formulation is studied by discussing under what conditions factor uniqueness is preserved. It is shown that, under mild conditions, such a property holds even if the specific factors are assumed to be within-variable, or within-occasion, correlated and the model is modified to become scale invariant.

This article develops a class of models called sender/receiver finite mixture exponential random graph models (SRFM-ERGMs). This class of models extends the existing exponential random graph modeling framework to allow analysts to model unobserved heterogeneity in the effects of nodal covariates and network features without a block structure. An empirical example regarding substance use among adolescents is presented. Simulations across a variety of conditions are used to evaluate the performance of this technique. We conclude that unobserved heterogeneity in effects of nodal covariates can be a major cause of misfit in network models, and the SRFM-ERGM approach can alleviate this misfit. Implications for the analysis of social networks in psychological science are discussed.

This paper considers multiple imputation (MI) approaches for handling non-monotone missing longitudinal binary responses when estimating parameters of a marginal model using generalized estimating equations (GEE). GEE has been shown to yield consistent estimates of the regression parameters for a marginal model when data are missing completely at random (MCAR). However, when data are missing at random (MAR), the GEE estimates may not be consistent; the MI approaches proposed in this paper minimize bias under MAR. The first MI approach proposed is based on a multivariate normal distribution, but with the addition of pairwise products among the binary outcomes to the multivariate normal vector. Even though the multivariate normal does not impute 0 or 1 values for the missing binary responses, as discussed by Horton et al. (Am Stat 57:229–232, 2003), we suggest not rounding when filling in the missing binary data because it could increase bias. The second MI approach considered is the fully conditional specification (FCS) approach. In this approach, we specify a logistic regression model for each outcome given the outcomes at other time points and the covariates. Typically, one would only include main effects of the outcome at the other times as predictors in the FCS approach, but we explore if bias can be reduced by also including pairwise interactions of the outcomes at other time point in the FCS. In a study of asymptotic bias with non-monotone missing data, the proposed MI approaches are also compared to GEE without imputation. Finally, the proposed methods are illustrated using data from a longitudinal clinical trial comparing four psychosocial treatments from the National Institute on Drug Abuse Collaborative Cocaine Treatment Study, where patients’ cocaine use is collected monthly for 6 months during treatment.

A shadow-test approach to the calibration of field-test items embedded in adaptive testing is presented. The objective function used in the shadow-test model selects both the operational and field-test items adaptively using a Bayesian version of the criterion of $D_{\mathrm{s}}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$D_{\mathrm{s}}$$\end{document}-optimality. The constraint set for the model can be used to hide the field-test items completely in the content of the test as well as to deal with such practical issues as random control of their exposure rates. The approach runs on efficient implementations of the Gibbs sampler for the real-time updating of the ability and field-test parameters. Optimal settings for the proposed algorithms were found and used to demonstrate item calibration with smaller than traditional sample sizes in runtimes fully comparable with conventional adaptive testing.

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. Borrowing from recent advances in the identification of cognitive diagnostic models, in particular, the DINA model (Gu and Xu in Stat Sin https://doi.org/10.5705/ss.202018.0420, 2019), a new model is proposed with restrictions inspired by this new literature to help with the identification issue. Specifically, we show conditions under which the four-parameter model is strictly and generically identified. These conditions inform the presentation of a new exploratory model, which we call the dyad four-parameter normal ogive (Dyad-4PNO) model. This model is developed by placing a hierarchical structure on the DINA model and imposing equality constraints on a priori unknown dyads of items. We present a Bayesian formulation of this model, and show that model parameters can be accurately recovered. Finally, we apply the model to a real dataset.

We consider a bivariate normal distribution with linear correlation ρ whose random components are discretized according to two assigned sets of thresholds. On the resulting bivariate ordinal random variable, one can compute Goodman and Kruskal’s gamma coefficient,γ which is a common measure of ordinal association. Given the known analytical monotonic relationship between Pearson’s ρ and Kendall’s rank correlation τ for the bivariate normal distribution, and since in the continuous case, Kendall’s τ coincides with Goodman and Kruskal’s γ, the change of this association measure before and after discretization is worth studying. We consider several experimental settings obtained by varying the two sets of thresholds, or, equivalently, the marginal distributions of the final ordinal variables. This study, confirming previous findings, shows how the gamma coefficient is always larger in absolute value than Kendall’s rank correlation; this discrepancy lessens when the number of categories increases or, given the same number of categories, when using equally probable categories. Based on these results, a proposal is suggested to build a bivariate ordinal variable with assigned margins and Goodman and Kruskal’s γ by ordinalizing a bivariate normal distribution. Illustrative examples employing artificial and real data are provided.

In diagnostic classification models (DCMs), the Q matrix encodes in which attributes are required for each item. The Q matrix is usually predetermined by the researcher but may in practice be misspecified which yields incorrect statistical inference. Instead of using a predetermined Q matrix, it is possible to estimate it simultaneously with the item and structural parameters of the DCM. Unfortunately, current methods are computationally intensive when there are many attributes and items. In addition, the identification constraints necessary for DCMs are not always enforced in the estimation algorithms which can lead to non-identified models being considered. We address these problems by simultaneously estimating the item, structural and Q matrix parameters of the Deterministic Input Noisy “And” gate model using a constrained Metropolis–Hastings Robbins–Monro algorithm. Simulations show that the new method is computationally efficient and can outperform previously proposed Bayesian Markov chain Monte-Carlo algorithms in terms of Q matrix recovery, and item and structural parameter estimation. We also illustrate our approach using Tatsuoka’s fraction–subtraction data and Certificate of Proficiency in English data.

The maintenance of item bank is essential for continuously implementing adaptive tests. Calibration of new items online provides an opportunity to efficiently replenish items for the operational item bank. In this study, a new optimal design for online calibration (referred to as D-c) is proposed by incorporating the idea of original D-optimal design into the reformed D-optimal design proposed by van der Linden and Ren (Psychometrika 80:263–288, 2015) (denoted as D-VR design). To deal with the dependence of design criteria on the unknown item parameters of new items, Bayesian versions of the locally optimal designs (e.g., D-c and D-VR) are put forward by adding prior information to the new items. In the simulation implementation of the locally optimal designs, five calibration sample sizes were used to obtain different levels of estimation precision for the initial item parameters, and two approaches were used to obtain the prior distributions in Bayesian optimal designs. Results showed that the D-c design performed well and retired smaller number of new items than the D-VR design at almost all levels of examinee sample size; the Bayesian version of D-c using the prior obtained from the operational items worked better than that using the default priors in BILOG-MG and PARSCALE; and Bayesian optimal designs generally outperformed locally optimal designs when the initial item parameters of the new items were poorly estimated.

The recent “Every Student Succeed Act" encourages schools to use an innovative assessment to provide feedback about students’ mastery level of grade-level content standards. Mastery of a skill requires the ability to complete the task with not only accuracy but also fluency. This paper offers a new sight on using both response times and response accuracy to measure fluency with cognitive diagnosis model framework. Defining fluency as the highest level of a categorical latent attribute, a polytomous response accuracy model and two forms of response time models are proposed to infer fluency jointly. A Bayesian estimation approach is developed to calibrate the newly proposed models. These models were applied to analyze data collected from a spatial rotation test. Results demonstrate that compared with the traditional CDM that using response accuracy only, the proposed joint models were able to reveal more information regarding test takers’ spatial skills. A set of simulation studies were conducted to evaluate the accuracy of model estimation algorithm and illustrate the various degrees of model complexities.

In this study, a new item response theory model is developed to account for situations in which respondents overreport or underreport their actual opinions on a positive or negativeissue. Such behavior is supposed to be a result of deception and transfer mechanisms. In the proposed model, this behavior is simulated by incorporating a deception term into a multidimensional rating scale model, followed by multiplication by a transfer term, with the two operations performed by an indicator function and a transition matrix separately. The proposed model is presented in a Bayesian framework approximated by Markov chain Monte Carlo algorithms. Through a series of simulations, the parameters of the proposed model are recovered accurately. The methodology is also implemented within an online experimental study to demonstrate the methodology’s application.

In many areas of psychology, correlation-based network approaches (i.e., psychometric networks) have become a popular tool. In this paper, we propose an approach that recursively splits the sample based on covariates in order to detect significant differences in the structure of the covariance or correlation matrix. Psychometric networks or other correlation-based models (e.g., factor models) can be subsequently estimated from the resultant splits. We adapt model-based recursive partitioning and conditional inference tree approaches for finding covariate splits in a recursive manner. The empirical power of these approaches is studied in several simulation conditions. Examples are given using real-life data from personality and clinical research.

We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (Psychometrika 84:124–146, 2019b) for exploratory item factor analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for joint maximum likelihood estimation in Chen et al. (2019b). Thanks to the analytic and computational properties of SVD, this algorithm guarantees a unique solution and has computational advantage over other exploratory IFA methods. Its computational advantage becomes significant when the numbers of respondents, items, and factors are all large. This algorithm can be viewed as a generalization of principal component analysis to binary data. In this note, we provide the statistical underpinning of the algorithm. In particular, we show its statistical consistency under the same double asymptotic setting as in Chen et al. (2019b). We also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory. Further extensions of the algorithm are discussed. Finally, simulation studies suggest that the algorithm has good finite sample performance.

Multi-layer networks arise when more than one type of relation is observed on a common set of actors. Modeling such networks within the exponential-family random graph (ERG) framework has been previously limited to special cases and, in particular, to dependence arising from just two layers. Extensions to ERGMs are introduced to address these limitations: Conway–Maxwell–Binomial distribution to model the marginal dependence among multiple layers; a “layer logic” language to translate familiar ERGM effects to substantively meaningful interactions of observed layers; and nondegenerate triadic and degree effects. The developments are demonstrated on two previously published datasets.