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Teacher interactions around instructional practices have been a topic of study for a long time. Previous studies concerning such interactions have focused on questions pertaining to cross-sectional networks. In fact, very few studies have considered longitudinal networks and still fewer have employed longitudinal network models to study changes in such interactions. We analyse teachers’ advice-seeking networks, observed annually between 2010 and 2013, in schools within a district where several initiatives were implemented starting in 2011. We assess whether formal structures, teaching assignment and leadership position, and teacher characteristics, gender and experience, are associated with advice-seeking ties, and the extent to which these associations change over time. To analyse the advice-seeking networks, we implement a Bayesian longitudinal latent space network model with covariates and random sender-receiver effects. Within the Bayesian framework, we address practical aspects of a principled network analysis such as missing ties and yearly immigration and emigration of teachers. Goodness of model fit assessment is conducted using posterior predictive checks. Our results demonstrate that while some of the associations between observed covariates and teachers’ interactions varied in 2011, most were otherwise stable. In 2011, we found decreases in the associations with same grade assignment, leadership position, and teaching in the same school.

Forensic science often involves the comparison of crime-scene evidence to a known-source sample to determine if the evidence and the reference sample came from the same source. Even as forensic analysis tools become increasingly objective and automated, final source identifications are often left to individual examiners’ interpretation of the evidence. Each source identification relies on judgements about the features and quality of the crime-scene evidence that may vary from one examiner to the next. The current approach to characterizing uncertainty in examiners’ decision-making has largely centered around the calculation of error rates aggregated across examiners and identification tasks, without taking into account these variations in behavior. We propose a new approach using IRT and IRT-like models to account for differences among examiners and additionally account for the varying difficulty among source identification tasks. In particular, we survey some recent advances (Luby 2019a) in the application of Bayesian psychometric models, including simple Rasch models as well as more elaborate decision tree models, to fingerprint examiner behavior.

Forensic science often involves the evaluation of crime-scene evidence to determine whether it matches a known-source sample, such as whether a fingerprint or DNA was left by a suspect or if a bullet was fired from a specific firearm. Even as forensic measurement and analysis tools become increasingly automated and objective, final source decisions are often left to individual examiners’ interpretation of the evidence. Furthermore, forensic analyses often consist of a series of steps. While some of these steps may be straightforward and relatively objective, substantial variation may exist in more subjective decisions. The current approach to characterizing uncertainty in forensic decision-making has largely centered around conducting error rate studies (in which examiners evaluate a set of items consisting of known-source comparisons) and calculating error rates aggregated across examiners and identification tasks. We propose a new approach using Item Response Theory (IRT) and IRT-like models to account for differences in examiner behavior and for varying difficulty among identification tasks. There are, however, substantial differences between forensic decision-making and traditional IRT applications such as educational testing. For example, the structure of the response process must be considered, “answer keys” for comparison tasks do not exist, and information about participants and items is not available due to privacy constraints. In this paper, we provide an overview of forensic decision-making, outline challenges in applying IRT in practice, and survey some recent advances in the application of Bayesian psychometric models to fingerprint examiner behavior.

Latent position network models are a versatile tool in network science; applications include clustering entities, controlling for causal confounders, and defining priors over unobserved graphs. Estimating each node's latent position is typically framed as a Bayesian inference problem, with Metropolis within Gibbs being the most popular tool for approximating the posterior distribution. However, it is well-known that Metropolis within Gibbs is inefficient for large networks; the acceptance ratios are expensive to compute, and the resultant posterior draws are highly correlated. In this article, we propose an alternative Markov chain Monte Carlo strategy -- defined using a combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo -- that leverages the posterior distribution's functional form for more efficient posterior computation. We demonstrate that these strategies outperform Metropolis within Gibbs and other algorithms on synthetic networks, as well as on real information-sharing networks of teachers and staff in a school district., Comment: 41 pages, 8 figures

Through the development and field testing of an instrument designed to measure youth social capital in the context of postsecondary transitions, this research addresses the need for theory-driven measures of social capital among youth. The results offer preliminary evidence that dimensions of youth social capital, including network structure and network content, can be reliably measured and that these dimensions of social capital are interrelated in a manner consistent with theory. The results also offer initial support for the validity of the social capital construct within the domain of youth postsecondary transitions. Taken together, the findings provide a foundation for continued research that might surmount inadequate measures and theoretical disputes to encompass more careful and rigorous empirical scrutiny when it comes to the measurement of social capital among children and adolescents.

BACKGROUND: There are distinct trajectories to cognitive impairment among participants in the Multicenter AIDS Cohort Study (MACS). Here we analyzed the relationship between regional brain volumes and the individual trajectories to impairment in a subsample (n = 302) of the cohort. METHODS: 302 (167 HIV-infected; mean age = 55.7 yrs.; mean education: 16.2 yrs.) of the men enrolled in the MACS MRI study contributed data to this analysis. We used voxel-based morphometry (VBM) to segment the brain images to analyze gray and white matter volume at the voxel-level. A Mixed Membership Trajectory Model had previously identified three distinct profiles, and each study participant had a membership weight for each of these three trajectories. We estimated VBM model parameters for 100 imputations, manually performed the post-hoc contrasts, and pooled the results. RESULTS: We examined the associations between brain volume at the voxel level and the MMTM membership weights for two profiles: one considered “unhealthy” and the other considered “Premature aging.” The unhealthy profile was linked to the volume of the posterior cingulate gyrus/precuneus, the inferior frontal cortex, and the insula, whereas the premature aging profile was independently associated with the integrity of a portion of the precuneus. CONCLUSIONS: Trajectories to cognitive impairment are the result, in part, of atrophy in cortical regions linked to normal and pathological aging. These data suggest the possibility of predicting cognitive morbidity based on patterns of CNS atrophy.

The hierarchical network model (HNM) is a framework introduced by Sweet, Thomas, and Junker for modeling interventions and other covariate effects on ensembles of social networks, such as what would be found in randomized controlled trials in education research. In this article, we develop calculations for the power to detect an intervention effect using the hierarchical latent space model, an important subfamily of HNMs. We derive basic convergence results and asymptotic bounds on power, showing that standard error for the treatment effect is inversely proportional to the product of the number of ties and the number of networks; a result rather different from the usual effect of cluster size in hierarchical linear models, for example. We explore these results with a simulation study and suggest a tentative approach to power for practical applications.

We investigated the alignment between a teacher survey self-report measure and classroom observation measure of ambitious mathematics instructional practice among teachers in two urban school districts using two different standards-based mathematics curricula. Survey reports suggested mild differences in teachers’ instructional practices between the two districts, whereas observation ratings indicated starker differences. That said, teachers’ survey and observer ratings were significantly correlated in both districts. Factors significantly predicting the extent of survey-observation alignment included teachers’ grade level, Mathematical Knowledge for Teaching, cognitive demand, and—for one district—teachers’ adherence to the surface-level aspects of their curriculum. Qualitative analyses suggested that teachers’ survey-observation alignment could be a function of their interaction with colleagues who provided instructional models against which they could gauge the extent of their standards-based i...

Assessing the model fit quality of statistical models for network data is an ongoing and under-examined topic in statistical network analysis. Traditional metrics for evaluating model fit on tabular data such as the Bayesian Information Criterion are not suitable for models specialized for network data. We propose a novel self-developed goodness of fit (GOF) measure, the `stratified-sampling cross-validation' (SCV) metric, that uses a procedure similar to traditional cross-validation via stratified-sampling to select dyads in the network's adjacency matrix to be removed. SCV is capable of intuitively expressing different models' ability to predict on missing dyads. Using SCV on real-world social networks, we identify the appropriate statistical models for different network structures and generalize such patterns. In particular, we focus on conditionally independent dyad (CID) models such as the Erdos Renyi model, the stochastic block model, the sender-receiver model, and the latent space model.

We study regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the longitudinal problem, with adaptively selected change points (break points). We present an efficient algorithm for computing such estimates, based on proximal gradient descent. We apply our proposed technique to a longitudinal data set on Alzheimer's disease from the Cardiovascular Health Study Cognition Study. Using data analysis and a simulation study, we motivate and demonstrate several practical considerations such as the selection of tuning parameters and the assessment of model stability. While race, gender, vascular and heart disease, lack of caregivers, and deterioration of learning and memory are all important predictors of dementia, we also find that these risk factors become more relevant in the later stages of life.

The longitudinal trajectories that individuals may take from a state of normal cognition to HIV-associated dementia are unknown. We applied a novel statistical methodology to identify trajectories to cognitive impairment, and factors that affected the 'closeness' of an individual to one of the canonical trajectories.The Multicenter AIDS Cohort Study (MACS) is a four-site longitudinal study of the natural and treated history of HIV disease among gay and bisexual men.Using data from 3892 men (both HIV-infected and HIV-uninfected) enrolled in the neuropsychology substudy of the MACS, a Mixed Membership Trajectory Model (MMTM) was applied to capture the pathways from normal cognitive function to mild impairment to severe impairment. MMTMs allow the data to identify canonical pathways and to model the effects of risk factors on an individual's 'closeness' to these trajectories.First, we identified three distinct trajectories to cognitive impairment: 'normal aging' (low probability of mild impairment until age 60); 'premature aging' (mild impairment starting at age 45-50); and 'unhealthy' (mild impairment in 20s and 30s) profiles. Second, clinically defined AIDS, and not simply HIV disease, was associated with closeness to the premature aging trajectory, and, third, hepatitis-C infection, depression, race, recruitment cohort and confounding conditions all affected individual's closeness to these trajectories.These results provide new insight into the natural history of cognitive dysfunction in HIV disease and provide evidence for a potential difference in the pathophysiology of the development of cognitive impairment based on trajectories to impairment.

Research studies in psychology and education often seek to detect changes or growth in an outcome over a duration of time. This research provides a solution to those interested in estimating latent traits from psychological measures that rely on human raters. Rater effects potentially degrade the quality of scores in constructed response and performance assessments. We develop an extension of the hierarchical rater model (HRM), which yields estimates of latent traits that have been corrected for individual rater bias and variability, for ratings that come from longitudinal designs. The parameterization, called the longitudinal HRM (L-HRM), includes an autoregressive time series process to permit serial dependence between latent traits at adjacent timepoints, as well as a parameter for overall growth. We evaluate and demonstrate the feasibility and performance of the L-HRM using simulation studies. Parameter recovery results reveal predictable amounts and patterns of bias and error for most parameters across conditions. An application to ratings from a study of character strength demonstrates the model. We discuss limitations and future research directions to improve the L-HRM.

Intervention studies in school systems are sometimes aimed not at changing curriculum or classroom technique, but rather at changing the way that teachers, teaching coaches, and administrators in schools work with one another—in short, changing the professional social networks of educators. Current methods of social network analysis are ill-suited to modeling the multiple partially exchangeable networks that arise in randomized field trials and observational studies in which multiple classrooms, schools, or districts are involved, and to detecting the effect of an intervention on the social network itself. To address these needs, we introduce a new modeling framework, the Hierarchical Network Models (HNM) framework. The HNM framework can be used to extend single-network statistical network models to multiple networks, using a hierarchical modeling approach. We show how to generalize the latent space model for a single network to the HNM/multiple-network setting, and illustrate our approach with real and simulated social network data among education professionals.

Proper characterizations of background soil CO2 respiration rates are critical for interpreting CO2 leakage monitoring results at geologic sequestration sites. In this paper, a method is developed for determining temperature-dependent critical values of soil CO2 flux for preliminary leak detection inference. The method is illustrated using surface CO2 flux measurements obtained from the AmeriFlux network fit with alternative models for the soil CO2 flux versus soil temperature relationship. The models are fit first to determine pooled parameter estimates across the sites, then using a Bayesian hierarchical method to obtain both global and site-specific parameter estimates. Model comparisons are made using the deviance information criterion (DIC), which considers both goodness of fit and model complexity. The hierarchical models consistently outperform the corresponding pooled models, demonstrating the need for site-specific data and estimates when determining relationships for background soil respiration. A hierarchical model that relates the square root of the CO2 flux to a quadratic function of soil temperature is found to provide the best fit for the AmeriFlux sites among the models tested. This model also yields effective prediction intervals, consistent with the upper envelope of the flux data across the modeled sites and temperature ranges. Calculation of upper prediction intervals using the proposed method can provide a basis for setting critical values in CO2 leak detection monitoring at sequestration sites.

Teacher mobility is a factor that impacts schoolwide implementation of professional development programs. In this article, we present interim results of a longitudinal randomized field trial of a comprehensive literacy coaching program (Content-Focused Coaching, CFC) for improving instruction and learning in schools with high teacher mobility. We investigate program effects on 73 new treatment and comparison teachers recruited to replace the large proportion of teachers who left their schools during the first year of the program. HLM analyses indicated that the CFC program predicted significantly higher school-level gains on the state standardized test for English language learners (N = 496, ES = .51). By spring, the quality of teachers' self-reported and observed instruction in the CFC schools exceeded that of comparison teachers. Implications for accommodating new teachers into an ongoing and established coaching program to improve instruction and student learning, and conducting randomized tri...

When constructed response test items are scored by more than one rater, the repeated ratings allow for the consideration of individual rater bias and variability in estimating student proficiency. Several hierarchical models based on item response theory have been introduced to model such effects. In this article, the authors demonstrate how these models may be extended to include covariates of the rating process. For example, how do features of an essay grader’s training affect his or her performance? The authors show how to include covariates by embedding a linear model at appropriate levels of the model hierarchy. Depending on the level, such covariates may be thought of as determining fixed effects or random effects on the rating process. The authors also discuss the appropriate design matrix for such covariates, discuss how to incorporate needed identifiability constraints, and illustrate the methods using data from a rating study of a student assessment.

Educational assessments, psychological scales, and social surveys often generate data in the form of a two-way array of discrete response data for N subjects (examinees, respondents, etc.) and J probes (test, scale, or survey items). Subjects' responses to the probes may be viewed as fallible measures of one or more underlying constructs, represented generically by a scalar or vector-valued index {latent variable} for each subject. When the response variables are discrete-valued, item response theory (IRT) and its variants provide a set of modeling and estimation tools for making inferences about the relationships between the Xij and the latent variable(s) θi and about subjects' location in the latent structure represented by θ. This article reviews standard parametric IRT models and estimation methods, extensions to compelx data analysis setting by way of a hierarchical Bayes formulation, nonparametric approaches to IRT, and selected applications in education, psychology, the social sciences, and biostatistics. Extensions of IRT to handle cognitively diagnostic assessment are briefly sketched, and similarities between IRT and Bayesian inference networks are pointed out.

We give a historical introduction to item response theory, which places the work of Thurstone, Lord, Guttman and Coombs in a present-day perspective. The general assumptions of modern item response theory, local independence and monotonicity of response functions, are discussed, followed by a general framework for estimating item response models. Six classes of well-known item response models and recent developments are discussed: (1) models for dichotomous item scores; (2) models for polytomous item scores; (3) nonparametric models; (4) unfolding models; (5) multidimensional models; and (6) models with restrictions on the parameters. Finally, it is noted that item response theory has evolved from unidimensional scaling of items and measurement of persons to data analysis tools for complicated research designs.

Alzheimer disease is the most common form of dementia in the elderly, and the complex relationships among risk factors produce highly variable natural histories from normal cognition through the prodromal stage of mild cognitive impairment (MCI) to clinical dementia. We used a novel statistical approach, mixed membership trajectory models, to capture the variety of such pathways in 652 participants in the Cardiovascular Health Study Cognition Study over 22 years of follow-up (1992–2014). We identified 3 trajectories: a “healthy” profile with a peak probability of MCI between 95 and 100 years of age and only a 50% probability of dementia by age 100; an “intermediate” profile with a peak probability of MCI between 85 and 90 years of age and progression to dementia between 90 and 95 years; and an “unhealthy” profile with a peak probability of progressing to MCI between ages 75 and 80 years and to dementia between the ages of 80 and 85 years. Hypertension, education, race, and the ϵ4 allele of the apolipoprotein E gene all affected the closeness of an individual to 1 or more of the canonical trajectories. These results provide new insights into the natural history of Alzheimer disease and evidence for a potential difference in the pathophysiology of the development of dementia.

Unfolding response models, a class of item response theory (IRT) models that assume a unimodal item response function (IRF), are often used for the measurement of attitudes. Verhelst and Verstralen (1993) and Andrich and Luo (1993) independently developed unfolding response models by relating the observed responses to a more common monotone IRT model using a latent response model (LRM; Maris, 1995 ). This article generalizes their approach, and suggests a data augmentation scheme for the estimation of any unfolding response model. The article introduces two Markov chain Monte Carlo (MCMC) estimation procedures for the Bayesian estimation of unfolding model parameters; one is a direct implementation of MCMC, and the second utilizes the data augmentation method. We use the estimation procedure to analyze three data sets, one simulated, and two from real attitudinal surveys.

A year-long study of 131 second and third graders in 12 classrooms compared three daily 20-minute treatments. a) Fifty-eight students in six classrooms used the 1999–2000 version of Project LISTEN's Reading Tutor, a computer program that uses automated speech recognition to listen to a child read aloud, and gives spoken and graphical assistance. Students took daily turns using one shared Reading Tutor in their classroom while the rest of their class received regular instruction. b) Thirty-four students in the other six classrooms were pulled out daily for one-on-one tutoring by certified teachers. To control for materials, the human tutors used the same set of stories as the Reading Tutor. c) Thirty-nine students served as in-classroom controls, receiving regular instruction without tutoring. We compared students' pre-to post-test gains on the Word Identification, Word Attack, Word Comprehension, and Passage Comprehension subtests of the Woodcock Reading Mastery Test, and in oral reading fluency. Surprisingly, the human-tutored group significantly outgained the Reading Tutor group only in Word Attack (main effects p > .02, effect size .55). Third graders in both the computer- and human-tutored conditions outgained the control group significantly in Word Comprehension ( p > .02, respective effect sizes .56 and .72) and suggestively in Passage Comprehension ( p = .14, respective effect sizes .48 and .34). No differences between groups on gains in Word Identification or fluency were significant. These results are consistent with an earlier study in which students who used the 1998 version of the Reading Tutor outgained their matched classmates in Passage Comprehension ( p = .11, effect size .60), but not in Word Attack, Word Identification, or fluency. To shed light on outcome differences between tutoring conditions and between individual human tutors, we compared process variables. Analysis of logs from all 6,080 human and computer tutoring sessions showed that human tutors included less rereading and more frequent writing than the Reading Tutor. Micro-analysis of 40 videotaped sessions showed that students who used the Reading Tutor spent considerable time waiting for it to respond, requested help more frequently, and picked easier stories when it was their turn. Human tutors corrected more errors, focused more on individual letters, and provided assistance more interactively, for example getting students to sound out words rather than sounding out words for students as the Reading Tutor did.

E. — Une variete de strategies permet d'approcher l'analyse de larges tableaux creuxl'aide de modeles presentant un nombre modeste de parametres. Cet article presente quelques unes de ces strategies, insis- tant sur le role des modeles log-lineaires et le concept d'´ echangeabilite: des generalisations multidimensionnelles du modele de quasi-symetrie du ` Henri Caussinus, des versions bayesiennes du modele de Rasch en theorie des questionnaires et ses generalisations, et le modele de degre d'apparte- nance. ABSTRACT. — A variety of strategies allow one to approach the analy- sis of large sparse contingency tables using models with a modest num- ber of parameters. This paper gives an overview of some of these strate- gies, emphasizing the role of log-linear models and exchangeability: multi- dimensional generalizations of the model of quasi-symmetry due to Henri Caussinus, Bayesian versions of the Rasch model from item response the- ory and its generalizations, and the Grade of Membership model.

Some usability and interpretability issues for single-strategy cognitive assessment models are considered. These models posit a stochastic conjunctive relationship between a set of cognitive attributes to be assessed and performance on particular items/tasks in the assessment. The models considered make few assumptions about the relationship between latent attributes and task performance beyond a simple conjunctive structure. An example shows that these models can be sensitive to cognitive attributes, even in data designed to well fit the Rasch model. Several stochastic ordering and monotonicity properties are considered that enhance the interpretability of the models. Simple data summaries are identified that inform about the presence or absence of cognitive attributes when the full computational power needed to estimate the models is not available.

The monotonicity of item response functions(IRF) is a central feature of most parametric andnonparametric item response models. Monotonicityallows items to be interpreted as measuring a trait,and it allows for a general theory of nonparametricinference for traits. This theory is based on monotonelikelihood ratio and stochastic ordering properties.Thus, confirming the monotonicity assumption isessential to applications of nonparametric itemresponse models. The results of two methods ofevaluating monotonicity are presented: regressingindividual item scores on the total test score andon the ‘rest’ score, which is obtained by omittingthe selected item from the total test score. It wasfound that the item-total regressions of some familiardichotomous item response models with monotoneIRFs exhibited nonmonotonicities that persist as thetest length increased. However, item-rest regressionsnever exhibited nonmonotonicities under the nonparametricmonotone unidimensional item responsemodel. The implications of these results for exploratoryanalysis of dichotomous item response dataand the application of these results to polytomousitem response data are discussed.

Patz and Junker (1999) describe a general Markov chain Monte Carlo (MCMC) strategy, based on Metropolis-Hastings sampling, for Bayesian inference in complex item response theory (IRT) settings. They demonstrate the basic methodology using the two-parameter logistic (2PL) model. In this paper we extend their basic MCMC methodology to address issues such as non-response, designed missingness, multiple raters, guessing behavior and partial credit (polytomous) test items. We apply the basic MCMC methodology to two examples from the National Assessment of Educational Progress 1992 Trial State Assessment in Reading: (a) a multiple item format (2PL, 3PL, and generalized partial credit) subtest with missing response data; and (b) a sequence of rated, dichotomous short-response items, using a new IRT model called the generalized linear logistic test model (GLLTM).

This paper demonstrates Markov chain Monte Carlo (MCMC) techniques that are particularly well-suited to complex models with item response theory (IRT) assumptions. MCMC may be thought of as a successor to the standard practice of first calibrating the items using E-M methods and then taking the item parameters to be known and fixed at their calibrated values when proceeding with inference regarding the latent trait. In contrast to this two-stage E-M approach, MCMC methods treat item and subject parameters at the same time; this allows us to incorporate standard errors of item estimates into trait inferences, and vice versa. We develop a MCMC methodology, based on Metropolis-Hastings sampling, that can be routinely implemented to fit novel IRT models, and we compare the algorithmic features of the MetropolisHastings approach to other approaches based on Gibbs sampling. For concreteness we illustrate the methodology using the familiar two-parameter logistic (2PL) IRT model; more complex models are treated in a subsequent paper (Patz & Junker, in press). Item response theory (IRT; Lord, 1980) models have greatly extended the data analytic reach of psychometricians, social scientists, and educational measurement specialists. The scaling and measurement applications of parametric IRT models in educational measurement are well known in areas ranging from basic questions about item quality and ability estimation (e.g., Linn, 1989) to equating (Holland & Rubin, 1982), differential item functioning (Holland & Wainer

Summary One of the major objections to the standard multiple-recapture approach to population estimation is the assumption of homogeneity of individual ‘capture’ probabilities. Modelling individual capture heterogeneity is complicated by the fact that it shows up as a restricted form of interaction among lists in the contingency table cross-classifying list memberships for all individuals. Traditional log-linear modelling approaches to capture–recapture problems are well suited to modelling interactions among lists but ignore the special dependence structure that individual heterogeneity induces. A random-effects approach, based on the Rasch model from educational testing and introduced in this context by Darroch and co-workers and Agresti, provides one way to introduce the dependence resulting from heterogeneity into the log-linear model; however, previous efforts to combine the Rasch-like heterogeneity terms additively with the usual log-linear interaction terms suggest that a more flexible approach is required. In this paper we consider both classical multilevel approaches and fully Bayesian hierarchical approaches to modelling individual heterogeneity and list interactions. Our framework encompasses both the traditional log-linear approach and various elements from the full Rasch model. We compare these approaches on two examples, the first arising from an epidemiological study of a population of diabetics in Italy, and the second a study intended to assess the ‘size’ of the World Wide Web. We also explore extensions allowing for interactions between the Rasch and log-linear portions of the models in both the classical and the Bayesian contexts.

Scheiblechner (1995) proposes a probabilistic axiomatization of measurement called ISOP (isotonic ordinal probabilistic models) that replaces Rasch's (1980) specific objectivity assumptions with two interesting ordinal assumptions. Special cases of Scheiblechner's model include standard unidimensional factor analysis models in which the loadings are held constant, and the Rasch model for binary item responses. Closely related are the doubly-monotone item response models of Mokken (1971; see also Mokken & Lewis, 1982; Sijtsma, 1988; Molenaar, 1991; Sijtsma & Junker, 1996; and Sijtsma & Hemker, in press). More generally, strictly unidimensional latent variable models have been considered in some detail by Holland and Rosenbaum (1986), Ellis and van den Wollenberg (1993), and Junker (1990, 1993). The purpose of this note is to provide connections with current research in foundations and nonparametric latent variable and item response modeling that are missing from Scheiblechner's (1995) paper, and to point out important related work by Hemker, Sijtsma, Molenaar, & Junker (1996, 1997), Ellis and Junker (in press) and Junker and Ellis (1997). We also discuss counterexamples to three major theorems in the paper. By carrying out these three tasks, we hope to provide researchers interested in the foundations of measurement and item response modeling the opportunity to give the ISOP approach the careful attention it deserves.

We consider latent variable models for an infinite sequence (or universe) of manifest (observable) variables that may be discrete, continuous or some combination of these. The main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable models that satisfy unidimensionality, monotonicity, conditional independence, andtail-measurability. Tail-measurability means that the latent variable can be estimated consistently from the sequence of manifest variables even though an arbitrary finite subsequence has been removed. The characterizing,necessary and sufficient, conditions that the manifest variables must satisfy for these models are conditional association and vanishing conditional dependence (as one conditions upon successively more other manifest variables). Our main theorem considerably generalizes and sharpens earlier results of Ellis and van den Wollenberg (1993), Holland and Rosenbaum (1986), and Junker (1993). It is also related to the work of Stout (1990). The main theorem is preceded by many results for latent variable modelsin general—not necessarily unidimensional and monotone. They pertain to the uniqueness of latent variables and are connected with the conditional independence theorem of Suppes and Zanotti (1981). We discuss new definitions of the concepts of “true-score” and “subpopulation,” which generalize these notions from the “stochastic subject,” “random sampling,” and “domain sampling” formulations of latent variable models (e.g., Holland, 1990; Lord & Novick, 1968). These definitions do not require the a priori specification of a latent variable model.

This article investigates working-memory (WM) failure in phone-based interaction (PBI). We used a computational model of phone-based interaction (PBI USER) to generate predictions about the impact of three factors on WM failure:PBI features (i.e. menu structure), individual differences (i.e., WM capacity), and task characteristics (i.e., number of tasks). Our computational model stipulates that both the storage and the processing of information contribute to WM failure. In practical terms the model and the empirical results indicate that, contrary to guidelines for the design of phone-based interfaces, deep menu hierarchies (no more than three options per menu) do not reduce WM error rates in PBI. At a more theoretical level, the study shows that the use of a computational model in HCI research provides a systematic approach for explaining complex empirical results.

This research provides a framework for specifying the latent trait distribution using the family of loglinear smoothing models. Connections between loglinear smoothing models and the standard normal, normal, and direct estimation of the distribution are the beginning of this framework. The framework is important because it gives the connection between the standard approaches and loglinear smoothing models so that parsimonious (smoothing) models providing adequate representation of the distribution can be identified. Future extensions will include additional complex models for estimating the latent trait distribution.

In a broad class of item response theory (IRT) models for dichotomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait theta. In this study, it is shown that for polytomous items MLR holds for the partial credit model and a trivial generalization of this model. MLR does not necessarily hold if the slopes of the item step response functions vary over items, item steps. or both. MLR holds neither for Samejima's graded response model, nor for nonparametric versions of these three polytomous models. These results are surprising in the context of Grayson's and Huynh's results on MLR for nonparametric dichotomous IRT models, and suggest that establishing stochastic ordering properties for nonparametric polytomous IRT models will be much harder.

Interest in end-of-year accountability exams has increased dramatically since the passing of the No Child Left Behind Act in 2001. With this increased interest comes a desire to use student data collected throughout the year to estimate student proficiency and predict how well they will perform on end-of-year exams. This article uses student performance on the Assistment System, an online mathematics tutor, to show that replacing percentage correct with an Item Response Theory estimate of student proficiency leads to better fitting prediction models. In addition, it uses other tutor performance metrics to further increase prediction accuracy. Prediction error bounds are also calculated to attain an absolute measure to which the models can be compared.

Item response theory (IRT) is a family of statistical psychometric models for discretely scored responses of subjects (students, survey respondents, etc.) to items (questions) on exams, surveys, and so on, using a continuous latent variable to represent the general propensity of each subject to respond positively to each item or question.

A central assumption in the standard capture-recapture approach to the estimation of the size of a closed population is the homogeneity of the “capture” probabilities. In this article we develop an approach that allows for varying susceptibility to capture through individual parameters using a variant of the Rasch model from psychological measurement situations. Our approach requires an additional recapture. In the context of census undercount estimation, this requirement amounts to the use of a second independent sample or alternative data source to be matched with census and Post-Enumeration Survey (PES) data. The models we develop provide a mechanism for separating out the dependence between census and PES induced by individual heterogeneity. The resulting data take the form of an incomplete 23 contingency table, and we describe how to estimate the expected values of the observable cells of this table using log-linear quasi-symmetry models. The projection of these estimates onto the unobserved...

This article introduces statistical methods for describing and summarizing the results of studies and introduces statistical principles that will guide the psychiatric researcher in the evaluation and interpretation of clinical research. We discuss relatively easy-to-use and informal methods for describing and comparing data. Our aim is to develop methods for investigating relationships among variables, to learn about the effect of one variable upon another. Once we have observed an apparent relationship between variables, an important question to be addressed is whether or not this observed relationship is causal in the sense that a change in one variable causes a changes in the other. We discuss and illustrate principles related to the evaluation of the nature of the association among variables. Throughout the article, principles and methods will be illustrated by examples and case studies based on data sets primarily from the psychiatric research literature.

A definition ofessential independence is proposed for sequences of polytomous items. For items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability, we develop a theory ofessential unidimensionality which closely parallels that of Stout. Essentially unidimensional item sequences can be shown to have a unique (up to change-of-scale) dominant underlying trait, which can be consistently estimated by a monotone transformation of the sum of the item scores. In more general polytomous-response latent trait models (with or without ordered responses), anM-estimator based upon maximum likelihood may be shown to be consistent for θ under essentially unidimensional violations of local independence and a variety of monotonicity/identifiability conditions. A rigorous proof of this fact is given, and the standard error of the estimator is explored. These results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence, but standard errors may vary greatly from what is usually expected, depending on the degree of departure from local independence. An index of departure from local independence is also proposed.