Search

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.

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.

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.