It is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations: The negative logarithm of the correlations satisfies the triangle inequality. This inequality is not implied by the condition that the correlations are nonnegative, the criterion that coefficient H exceeds 0.30, or manifest monotonicity. The inequality implies both a lower bound and an upper bound for each correlation between two items, based on the correlations of those two items with every possible third item. It is discussed how this can be used in Mokken’s (A theory and procedure of scale-analysis, Mouton, The Hague, 1971) scale analysis.

Exploratory process factor analysis (EPFA) is a data-driven latent variable model for multivariate time series. This article presents analytic standard errors for EPFA. Unlike standard errors for exploratory factor analysis with independent data, the analytic standard errors for EPFA take into account the time dependency in time series data. In addition, factor rotation is treated as the imposition of equality constraints on model parameters. Properties of the analytic standard errors are demonstrated using empirical and simulated data.

An unfolding model for continuous bounded responses is proposed, derived both from a hypothetical interpolation response mechanism and from the hypothesis of two opposite sources of item refusal being collapsed. These two sources of refusal are made explicit in a three-component Dirichlet response model and then collapsed to obtain a (two-component) beta response model. The two natural parameters of the beta are interpreted as acceptance and refusal parameters and expressed as functions of person-item distances on a latent continuum. The potentially bimodal shape of the beta is exploited to model chaotic response choices among ambivalent subjects.

We consider spectral decompositions of multiple time series that arise in studies where the interest lies in assessing the influence of two or more factors. We write the spectral density of each time series as a sum of the spectral densities associated to the different levels of the factors. We then use Whittle’s approximation to the likelihood function and follow a Bayesian non-parametric approach to obtain posterior inference on the spectral densities based on Bernstein–Dirichlet prior distributions. The prior is strategically important as it carries identifiability conditions for the models and allows us to quantify our degree of confidence in such conditions. A Markov chain Monte Carlo (MCMC) algorithm for posterior inference within this class of frequency-domain models is presented.

We illustrate the approach by analyzing simulated and real data via spectral one-way and two-way models. In particular, we present an analysis of functional magnetic resonance imaging (fMRI) brain responses measured in individuals who participated in a designed experiment to study pain perception in humans.

Value added is a common tool in educational research on effectiveness. It is often modeled as a (prediction of a) random effect in a specific hierarchical linear model. This paper shows that this modeling strategy is not valid when endogeneity is present. Endogeneity stems, for instance, from a correlation between the random effect in the hierarchical model and some of its covariates. This paper shows that this phenomenon is far from exceptional and can even be a generic problem when the covariates contain the prior score attainments, a typical situation in value added modeling. Starting from a general, model-free definition of value added, the paper derives an explicit expression of the value added in an endogeneous hierarchical linear Gaussian model. Inference on value added is proposed using an instrumental variable approach. The impact of endogeneity on the value added and the estimated value added is calculated accurately. This is also illustrated on a large data set of individual scores of about 200,000 students in Chile.

Although latent attributes that follow a hierarchical structure are anticipated in many areas of educational and psychological assessment, current psychometric models are limited in their capacity to objectively evaluate the presence of such attribute hierarchies. This paper introduces the Hierarchical Diagnostic Classification Model (HDCM), which adapts the Log-linear Cognitive Diagnosis Model to cases where attribute hierarchies are present. The utility of the HDCM is demonstrated through simulation and by an empirical example. Simulation study results show the HDCM is efficiently estimated and can accurately test for the presence of an attribute hierarchy statistically, a feature not possible when using more commonly used DCMs. Empirically, the HDCM is used to test for the presence of a suspected attribute hierarchy in a test of English grammar, confirming the data is more adequately represented by hierarchical attribute structure when compared to a crossed, or nonhierarchical structure.

We present an idiographic approach to modeling dyadic interactions using differential equations. Using data representing daily affect ratings from romantic relationships, we examined several models conceptualizing different types of dyadic interactions. We fitted each model to each of the dyads and the resulting AICc values were used to classify the most likely configuration of interaction for each dyad. Additionally, the AICc from the different models were used in parameter averaging across models. Averaged parameters were used in models involving predictors of relationship dynamics, as indexed by these parameters, as well as models wherein the parameters predicted distal outcomes of the dyads such as relationship satisfaction and status. Results indicated that, within our sample, the most likely interaction style was that of independence, without evidence of emotional interrelations between the two individuals in the couple. Attachment-related avoidance and anxiety showed significant relations with model parameters, such that ideal levels of affect for males were negatively influenced by higher levels of avoidance from their partner while their own levels of anxiety had positive effects on their levels of dyadic coregulation. For females coregulation was negatively influenced by both time in the relationship and their partner’s level of avoidance. Analysis involving distal outcomes showed modest influences from the individual’s level of ideal affect.

Developmental studies of mental disorders based on epidemiological data are often based on cross-sectional retrospective surveys. Under such designs, observations are right-censored, causing underestimation of lifetime prevalences and correlations, and inducing bias in latent trait models on the observations. In this paper we propose a Partial Likelihood (PL) method to estimate unbiased IRT models of lifetime predisposition to develop a certain outcome. A two-step estimation procedure corrects the IRT likelihood of outcome appearance with a function depending on (a) projected outcome frequencies at the end of the risk period, and (b) outcome censoring status at the time of the observation. Simulation results showed that the PL method yielded good recovery of true frequencies and intercepts. Slopes were best estimated when events were sufficiently correlated. When PL is applied to lifetime mental health disorders (assessed in the ESEMeD project surveys), estimated univariate prevalences were, on average, 1.4 times above raw estimates, and 2.06 higher in the case of bivariate prevalences.

Moderation analysis is widely used in social and behavioral research. The most commonly used model for moderation analysis is moderated multiple regression (MMR) in which the explanatory variables of the regression model include product terms, and the model is typically estimated by least squares (LS). This paper argues for a two-level regression model in which the regression coefficients of a criterion variable on predictors are further regressed on moderator variables. An algorithm for estimating the parameters of the two-level model by normal-distribution-based maximum likelihood (NML) is developed. Formulas for the standard errors (SEs) of the parameter estimates are provided and studied. Results indicate that, when heteroscedasticity exists, NML with the two-level model gives more efficient and more accurate parameter estimates than the LS analysis of the MMR model. When error variances are homoscedastic, NML with the two-level model leads to essentially the same results as LS with the MMR model. Most importantly, the two-level regression model permits estimating the percentage of variance of each regression coefficient that is due to moderator variables. When applied to data from General Social Surveys 1991, NML with the two-level model identified a significant moderation effect of race on the regression of job prestige on years of education while LS with the MMR model did not. An R package is also developed and documented to facilitate the application of the two-level model.

Decision making usually involves uncertainty and risk. Understanding which parts of the human brain are activated during decisions under risk and which neural processes underly (risky) investment decisions are important goals in neuroeconomics. Here, we analyze functional magnetic resonance imaging (fMRI) data on 17 subjects who were exposed to an investment decision task from Mohr, Biele, Krugel, Li, and Heekeren (in NeuroImage 49, 2556–2563, 2010b). We obtain a time series of three-dimensional images of the blood-oxygen-level dependent (BOLD) fMRI signals. We apply a panel version of the dynamic semiparametric factor model (DSFM) presented in Park, Mammen, Wolfgang, and Borak (in Journal of the American Statistical Association 104(485), 284–298, 2009) and identify task-related activations in space and dynamics in time. With the panel DSFM (PDSFM) we can capture the dynamic behavior of the specific brain regions common for all subjects and represent the high-dimensional time-series data in easily interpretable low-dimensional dynamic factors without large loss of variability. Further, we classify the risk attitudes of all subjects based on the estimated low-dimensional time series. Our classification analysis successfully confirms the estimated risk attitudes derived directly from subjects’ decision behavior.

This commentary addresses the modeling and final analytical path taken, as well as the terminology used, in the paper “Hierarchical diagnostic classification models: a family of models for estimating and testing attribute hierarchies” by Templin and Bradshaw (Psychometrika, doi:10.1007/s11336-013-9362-0, 2013). It raises several issues concerning use of cognitive diagnostic models that either assume attribute hierarchies or assume a certain form of attribute interactions. The issues raised are illustrated with examples, and references are provided for further examination.

With the advent of web-based technology, online testing is becoming a mainstream mode in large-scale educational assessments. Most online tests are administered continuously in a testing window, which may post test security problems because examinees who take the test earlier may share information with those who take the test later. Researchers have proposed various statistical indices to assess the test security, and one most often used index is the average test-overlap rate, which was further generalized to the item pooling index (Chang & Zhang, 2002, 2003). These indices, however, are all defined as the means (that is, the expected proportion of common items among examinees) and they were originally proposed for computerized adaptive testing (CAT). Recently, multistage testing (MST) has become a popular alternative to CAT. The unique features of MST make it important to report not only the mean, but also the standard deviation (SD) of test overlap rate, as we advocate in this paper. The standard deviation of test overlap rate adds important information to the test security profile, because for the same mean, a large SD reflects that certain groups of examinees share more common items than other groups. In this study, we analytically derived the lower bounds of the SD under MST, with the results under CAT as a benchmark. It is shown that when the mean overlap rate is the same between MST and CAT, the SD of test overlap tends to be larger in MST. A simulation study was conducted to provide empirical evidence. We also compared the security of MST under the single-pool versus the multiple-pool designs; both analytical and simulation studies show that the non-overlapping multiple-pool design will slightly increase the security risk.

Asking sensitive or personal questions in surveys or experimental studies can both lower response rates and increase item non-response and misreports. Although non-response is easily diagnosed, misreports are not. However, misreports cannot be ignored because they give rise to systematic bias. The purpose of this paper is to present a modeling approach that identifies misreports and corrects for them. Misreports are conceptualized as a motivated process under which respondents edit their answers before they report them. For example, systematic bias introduced by overreports of socially desirable behaviors or underreports of less socially desirable ones can be modeled, leading to more-valid inferences. The proposed approach is applied to a large-scale experimental study and shows that respondents who feel powerful tend to overclaim their knowledge.