This article devises a Bayesian multivariate formulation for analysis of ordinal data that records teacher classroom performance along multiple dimensions to assess aspects characterizing good instruction. Study designs for scoring teachers seek to measure instructional performance over multiple classroom measurement event sessions at varied occasions using disjoint intervals within each session and employment of multiple ratings on intervals scored by different raters; a design which instantiates a nesting structure with each level contributing a source of variation in recorded scores. We generally possess little a priori knowledge of the existence or form of a sparse generating structure for the multivariate dimensions at any level in the nesting that would permit collapsing over dimensions as is done under univariate modeling. Our approach composes a Bayesian data augmentation scheme that introduces a latent continuous multivariate response linked to the observed ordinal scores with the latent response mean constructed as an additive multivariate decomposition of nested level means that permits the extraction of de-noised continuous teacher-level scores and the associated correlation matrix. A semi-parametric extension facilitates inference for teacher-level dependence among the dimensions of classroom performance under multi-modality induced by sub-groupings of rater perspectives. We next replace an inverse Wishart prior specified for the teacher covariance matrix over dimensions of instruction with a factor analytic structure to allow the simultaneous assessment of an underlying sparse generating structure. Our formulation for Bayesian factor analysis employs parameter expansion with an accompanying post-processing sign re-labeling step of factor loadings that together reduce posterior correlations among sampled parameters to improve parameter mixing in our Markov chain Monte Carlo (MCMC) scheme. We evaluate the performance of our formulation on simulated data and make an application for the assessment of the teacher covariance structure with a dataset derived from a study of middle and high school algebra teachers.

Human abilities in perceptual domains have conventionally been described with reference to a threshold that may be defined as the maximum amount of stimulation which leads to baseline performance. Traditional psychometric links, such as the probit, logit, and t, are incompatible with a threshold as there are no true scores corresponding to baseline performance. We introduce a truncated probit link for modeling thresholds and develop a two-parameter IRT model based on this link. The model is Bayesian and analysis is performed with MCMC sampling. Through simulation, we show that the model provides for accurate measurement of performance with thresholds. The model is applied to a digit-classification experiment in which digits are briefly flashed and then subsequently masked. Using parameter estimates from the model, individuals’ thresholds for flashed-digit discrimination is estimated.

Helicobacter pylori (H. pylori) is present in the stomach of half of the world's population. The force of infection describes the rate at which susceptibles acquire infection. In this article, we estimated the age-specific force of infection of H. pylori in Mexico. Data came from a national H. pylori seroepidemiology survey collected in Mexico in 1987–88. We modelled the number of individuals with H. pylori at a given age as a binomial random variable. We assumed that the cumulative risk of infection by a given age follows a modified exponential catalytic model, allowing some fraction of the population to remain uninfected. The cumulative risk of infection was modelled for each state in Mexico and were shrunk towards the overall national cumulative risk curve using Bayesian hierarchical models. The proportion of the population that can be infected (i.e. susceptible population) is 85.9% (95% credible interval (CR) 84.3%–87.5%). The constant rate of infection per year of age among the susceptible population is 0.092 (95% CR 0.084–0.100). The estimated force of infection was highest at birth 0.079 (95% CR 0.071–0.087) decreasing to zero as age increases. This Bayesian hierarchical model allows stable estimation of state-specific force of infection by pooling information between the states, resulting in more realistic estimates.