In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we examine a broader class of problems in psychometrics that can be addressed via conditional likelihoods. Specifically, we consider cluster-level endogeneity where the standard assumption that observed explanatory variables are independent from latent variables is violated. Here, “cluster” refers to the entity characterized by latent variables or random effects, such as individuals in measurement models or schools in multilevel models and “unit” refers to the elementary entity such as an item in measurement. Cluster-level endogeneity problems can arise in a number of settings, including unobserved confounding of causal effects, measurement error, retrospective sampling, informative cluster sizes, missing data, and heteroskedasticity. Severely inconsistent estimation can result if these challenges are ignored.

Despite its frequent consideration in test development, item complexity receives little attention in the psychometric modeling of item response data. In this address, I consider how variability in item complexity can be expected to emerge in the form of item characteristic curve (ICC) asymmetry, and how such effects may significantly influence applications of item response theory, especially those that assume interval-level properties of the latent proficiency metric and groups that vary substantially in mean proficiency. One application is the score gain deceleration phenomenon often observed in vertical scaling contexts, especially in subject areas like math or second language acquisition. It is demonstrated how the application of symmetric IRT models in the presence of complexity-induced positive ICC asymmetry can be a likely cause. A second application concerns the positive correlation between DIF and difficulty commonly seen in verbal proficiency (and other subject area) tests where problem-solving complexity is minimal and proficiency-related guessing effects are likely pronounced. Here we suggest negative ICC asymmetry as a probable cause and apply sensitivity analyses to demonstrate the ease with which such correlations disappear when allowing for negative ICC asymmetry. Unfortunately, the presence of systematic forms of ICC asymmetry is easily missed due to the considerable flexibility afforded by latent trait metrics in IRT. Speculation is provided regarding other applications for which attending to ICC asymmetry may prove useful.

A growing number of publications focus on estimating Gaussian graphical models (GGM, networks of partial correlation coefficients). At the same time, generalizibility and replicability of these highly parameterized models are debated, and sample sizes typically found in datasets may not be sufficient for estimating the underlying network structure. In addition, while recent work emerged that aims to compare networks based on different samples, these studies do not take potential cross-study heterogeneity into account. To this end, this paper introduces methods for estimating GGMs by aggregating over multiple datasets. We first introduce a general maximum likelihood estimation modeling framework in which all discussed models are embedded. This modeling framework is subsequently used to introduce meta-analytic Gaussian network aggregation (MAGNA). We discuss two variants: fixed-effects MAGNA, in which heterogeneity across studies is not taken into account, and random-effects MAGNA, which models sample correlations and takes heterogeneity into account. We assess the performance of MAGNA in large-scale simulation studies. Finally, we exemplify the method using four datasets of post-traumatic stress disorder (PTSD) symptoms, and summarize findings from a larger meta-analysis of PTSD symptom.

In this paper, we present and evaluate a novel Bayesian regime-switching zero-inflated multilevel Poisson (RS-ZIMLP) regression model for forecasting alcohol use dynamics. The model partitions individuals’ data into two phases, known as regimes, with: (1) a zero-inflation regime that is used to accommodate high instances of zeros (non-drinking) and (2) a multilevel Poisson regression regime in which variations in individuals’ log-transformed average rates of alcohol use are captured by means of an autoregressive process with exogenous predictors and a person-specific intercept. The times at which individuals are in each regime are unknown, but may be estimated from the data. We assume that the regime indicator follows a first-order Markov process as related to exogenous predictors of interest. The forecast performance of the proposed model was evaluated using a Monte Carlo simulation study and further demonstrated using substance use and spatial covariate data from the Colorado Online Twin Study (CoTwins). Results showed that the proposed model yielded better forecast performance compared to a baseline model which predicted all cases as non-drinking and a reduced ZIMLP model without the RS structure, as indicated by higher AUC (the area under the receiver operating characteristic (ROC) curve) scores, and lower mean absolute errors (MAEs) and root-mean-square errors (RMSEs). The improvements in forecast performance were even more pronounced when we limited the comparisons to participants who showed at least one instance of transition to drinking.

Many of the models that have been proposed for response data share the assumptions that define the monotone homogeneity (MH) model. Observable properties that are implied by the MH model allow for these assumptions to be tested. For binary response data, the most restrictive of these properties is called conditional association (CA). All the other properties considered can be considered incomplete tests of CA that alleviate the practical limitations encountered when assessing the MH model assumptions using CA. It is found that the assessment of the MH model assumptions with an incomplete test of CA, rather than CA, is generally associated with a substantial loss of information. We also look at the sensitivity of the observable properties to model violation and discuss the implications of the results. It is argued that more research is required about the extent to which the assumptions and the model specifications influence the inferences made from response data.

Time limits are imposed on many computer-based assessments, and it is common to observe examinees who run out of time, resulting in missingness due to not-reached items. The present study proposes an approach to account for the missing mechanisms of not-reached items via response time censoring. The censoring mechanism is directly incorporated into the observed likelihood of item responses and response times. A marginal maximum likelihood estimator is proposed, and its asymptotic properties are established. The proposed method was evaluated and compared to several alternative approaches that ignore the censoring through simulation studies. An empirical study based on the PISA 2018 Science Test was further conducted.

A comprehensive class of models is proposed that can be used for continuous, binary, ordered categorical and count type responses. The difficulty of items is described by difficulty functions, which replace the item difficulty parameters that are typically used in item response models. They crucially determine the response distribution and make the models very flexible with regard to the range of distributions that are covered. The model class contains several widely used models as the binary Rasch model and the graded response model as special cases, allows for simplifications, and offers a distribution free alternative to count type items. A major strength of the models is that they can be used for mixed item formats, when different types of items are combined to measure abilities or attitudes. It is an immediate consequence of the comprehensive modeling approach that allows that difficulty functions automatically adapt to the response distribution. Basic properties of the model class are shown. Several real data sets are used to illustrate the flexibility of the models

The Ising model is one of the most widely analyzed graphical models in network psychometrics. However, popular approaches to parameter estimation and structure selection for the Ising model cannot naturally express uncertainty about the estimated parameters or selected structures. To address this issue, this paper offers an objective Bayesian approach to parameter estimation and structure selection for the Ising model. Our methods build on a continuous spike-and-slab approach. We show that our methods consistently select the correct structure and provide a new objective method to set the spike-and-slab hyperparameters. To circumvent the exploration of the complete structure space, which is too large in practical situations, we propose a novel approach that first screens for promising edges and then only explore the space instantiated by these edges. We apply our proposed methods to estimate the network of depression and alcohol use disorder symptoms from symptom scores of over 26,000 subjects.

Graph-based causal models are a flexible tool for causal inference from observational data. In this paper, we develop a comprehensive framework to define, identify, and estimate a broad class of causal quantities in linearly parametrized graph-based models. The proposed method extends the literature, which mainly focuses on causal effects on the mean level and the variance of an outcome variable. For example, we show how to compute the probability that an outcome variable realizes within a target range of values given an intervention, a causal quantity we refer to as the probability of treatment success. We link graph-based causal quantities defined via the do-operator to parameters of the model implied distribution of the observed variables using so-called causal effect functions. Based on these causal effect functions, we propose estimators for causal quantities and show that these estimators are consistent and converge at a rate of $N^{-1/2}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N^{-1/2}$$\end{document} under standard assumptions. Thus, causal quantities can be estimated based on sample sizes that are typically available in the social and behavioral sciences. In case of maximum likelihood estimation, the estimators are asymptotically efficient. We illustrate the proposed method with an example based on empirical data, placing special emphasis on the difference between the interventional and conditional distribution.

Intensive longitudinal data (ILD) is an increasingly common data type in the social and behavioral sciences. Despite the many benefits these data provide, little work has been dedicated to realize the potential such data hold for forecasting dynamic processes at the individual level. To address this gap in the literature, we present the multi-VAR framework, a novel methodological approach allowing for penalized estimation of ILD collected from multiple individuals. Importantly, our approach estimates models for all individuals simultaneously and is capable of adaptively adjusting to the amount of heterogeneity present across individual dynamic processes. To accomplish this, we propose a novel proximal gradient descent algorithm for solving the multi-VAR problem and prove the consistency of the recovered transition matrices. We evaluate the forecasting performance of our method in comparison with a number of benchmark methods and provide an illustrative example involving the day-to-day emotional experiences of 16 individuals over an 11-week period.

Graphical models have received an increasing amount of attention in network psychometrics as a promising probabilistic approach to study the conditional relations among variables using graph theory. Despite recent advances, existing methods on graphical models usually assume a homogeneous population and focus on binary or continuous variables. However, ordinal variables are very popular in many areas of psychological science, and the population often consists of several different groups based on the heterogeneity in ordinal data. Driven by these needs, we introduce the finite mixture of ordinal graphical models to effectively study the heterogeneous conditional dependence relationships of ordinal data. We develop a penalized likelihood approach for model estimation, and design a generalized expectation-maximization (EM) algorithm to solve the significant computational challenges. We examine the performance of the proposed method and algorithm in simulation studies. Moreover, we demonstrate the potential usefulness of the proposed method in psychological science through a real application concerning the interests and attitudes related to fan avidity for students in a large public university in the United States.

In this paper, the notion of Markov move from algebraic statistics is used to analyze the weighted kappa indices in rater agreement problems. In particular, the problem of the maximum kappa and its dependence on the choice of the weighting schemes are discussed. The Markov moves are also used in a simulated annealing algorithm to actually find the configuration of maximum agreement.

The use of multilevel VAR(1) models to unravel within-individual process dynamics is gaining momentum in psychological research. These models accommodate the structure of intensive longitudinal datasets in which repeated measurements are nested within individuals. They estimate within-individual auto- and cross-regressive relationships while incorporating and using information about the distributions of these effects across individuals. An important quality feature of the obtained estimates pertains to how well they generalize to unseen data. Bulteel and colleagues (Psychol Methods 23(4):740–756, 2018a) showed that this feature can be assessed through a cross-validation approach, yielding a predictive accuracy measure. In this article, we follow up on their results, by performing three simulation studies that allow to systematically study five factors that likely affect the predictive accuracy of multilevel VAR(1) models: (i) the number of measurement occasions per person, (ii) the number of persons, (iii) the number of variables, (iv) the contemporaneous collinearity between the variables, and (v) the distributional shape of the individual differences in the VAR(1) parameters (i.e., normal versus multimodal distributions). Simulation results show that pooling information across individuals and using multilevel techniques prevent overfitting. Also, we show that when variables are expected to show strong contemporaneous correlations, performing multilevel VAR(1) in a reduced variable space can be useful. Furthermore, results reveal that multilevel VAR(1) models with random effects have a better predictive performance than person-specific VAR(1) models when the sample includes groups of individuals that share similar dynamics.

With the advent of new data collection technologies, intensive longitudinal data (ILD) are collected more frequently than ever. Along with the increased prevalence of ILD, more methods are being developed to analyze these data. However, relatively few methods have yet been applied for making long- or even short-term predictions from ILD in behavioral settings. Applications of forecasting methods to behavioral ILD are still scant. We first establish a general framework for modeling ILD and then extend that frame to two previously existing forecasting methods: these methods are Kalman prediction and ensemble prediction. After implementing Kalman and ensemble forecasts in free and open-source software, we apply these methods to daily drug and alcohol use data. In doing so, we create a simple, but nonlinear dynamical system model of daily drug and alcohol use and illustrate important differences between the forecasting methods. We further compare the Kalman and ensemble forecasting methods to several simpler forecasts of daily drug and alcohol use. Ensemble forecasts may be more appropriate than Kalman forecasts for nonlinear dynamical systems models, but further forecasting evaluation methods must be put into practice.

Network analysis is an increasingly popular approach to study mental disorders in all their complexity. Multiple methods have been developed to extract networks from cross-sectional data, with these data being either continuous or binary. However, when it comes to time series data, most efforts have focused on continuous data. We therefore propose ConNEcT, a network approach for binary symptom data across time. ConNEcT allows to visualize and study the prevalence of different symptoms as well as their co-occurrence, measured by means of a contingency measure in one single network picture. ConNEcT can be complemented with a significance test that accounts for the serial dependence in the data. To illustrate the usefulness of ConNEcT, we re-analyze data from a study in which patients diagnosed with major depressive disorder weekly reported the absence or presence of eight depression symptoms. We first extract ConNEcTs for all patients that provided data during at least 104 weeks, revealing strong inter-individual differences in which symptom pairs co-occur significantly. Second, to gain insight into these differences, we apply Hierarchical Classes Analysis on the co-occurrence patterns of all patients, showing that they can be grouped into meaningful clusters. Core depression symptoms (i.e., depressed mood and/or diminished interest), cognitive problems and loss of energy seem to co-occur universally, but preoccupation with death, psychomotor problems or eating problems only co-occur with other symptoms for specific patient subgroups.

Computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time (RT) measures. A key question in modeling this type of data is how to incorporate RT data, for example, in aid of ability estimation in item response theory (IRT) models. To address this, we propose a joint model consisting of a two-parameter IRT model for the dichotomous item response data, a log-normal model for the continuous RT data, and a normal model for corresponding paper-and-pencil scores. Then, we reformulate and reparameterize the model to capture the relationship between the model parameters, to facilitate the prior specification, and to make the Bayesian computation more efficient. Further, we propose several new model assessment criteria based on the decomposition of deviance information criterion (DIC) the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement in the fit of one part of the multidimensional data given the other parts. Finally, we have conducted several simulation studies to examine the empirical performance of the proposed model assessment criteria and have illustrated the application of these criteria using a real dataset from a computerized educational assessment program.

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. We develop new methods that relax existing monotonicity restrictions and provide greater insight about the latent structure. Furthermore, existing Bayesian methods only use a probit link function and we provide a new formulation for using the exploratory RLCM with a logit link function that has an additional advantage of being computationally more efficient for larger sample sizes. We present four new Bayesian formulations that employ different link functions (i.e., the logit using the Pòlya—gamma data augmentation versus the probit) and priors for inducing sparsity in the latent structure. We report Monte Carlo simulation studies to demonstrate accurate parameter recovery. Furthermore, we report results from an application to the Last Series of the Standard Progressive Matrices to illustrate our new methods.