This paper proposes a novel collapsed Gibbs sampling algorithm that marginalizes model parameters and directly samples latent attribute mastery patterns in diagnostic classification models. This estimation method makes it possible to avoid boundary problems in the estimation of model item parameters by eliminating the need to estimate such parameters. A simulation study showed the collapsed Gibbs sampling algorithm can accurately recover the true attribute mastery status in various conditions. A second simulation showed the collapsed Gibbs sampling algorithm was computationally more efficient than another MCMC sampling algorithm, implemented by JAGS. In an analysis of real data, the collapsed Gibbs sampling algorithm indicated good classification agreement with results from a previous study.

Multilevel factor analysis models are widely used in the social sciences to account for heterogeneity in mean structures. In this paper we extend previous work on multilevel models to account for general forms of heterogeneity in confirmatory factor analysis models. We specify various models of mean and covariance heterogeneity in confirmatory factor analysis and develop Markov Chain Monte Carlo (MCMC) procedures to perform Bayesian inference, model checking, and model comparison.

We test our methodology using synthetic data and data from a consumption emotion study. The results from synthetic data show that our Bayesian model perform well in recovering the true parameters and selecting the appropriate model. More importantly, the results clearly illustrate the consequences of ignoring heterogeneity. Specifically, we find that ignoring heterogeneity can lead to sign reversals of the factor covariances, inflation of factor variances and underappreciation of uncertainty in parameter estimates. The results from the emotion study show that subjects vary both in means and covariances. Thus traditional psychometric methods cannot fully capture the heterogeneity in our data.

The elicitation of an ordinal judgment on multiple alternatives is often required in many psychological and behavioral experiments to investigate preference/choice orientation of a specific population. The Plackett–Luce model is one of the most popular and frequently applied parametric distributions to analyze rankings of a finite set of items. The present work introduces a Bayesian finite mixture of Plackett–Luce models to account for unobserved sample heterogeneity of partially ranked data. We describe an efficient way to incorporate the latent group structure in the data augmentation approach and the derivation of existing maximum likelihood procedures as special instances of the proposed Bayesian method. Inference can be conducted with the combination of the Expectation-Maximization algorithm for maximum a posteriori estimation and the Gibbs sampling iterative procedure. We additionally investigate several Bayesian criteria for selecting the optimal mixture configuration and describe diagnostic tools for assessing the fitness of ranking distributions conditionally and unconditionally on the number of ranked items. The utility of the novel Bayesian parametric Plackett–Luce mixture for characterizing sample heterogeneity is illustrated with several applications to simulated and real preference ranked data. We compare our method with the frequentist approach and a Bayesian nonparametric mixture model both assuming the Plackett–Luce model as a mixture component. Our analysis on real datasets reveals the importance of an accurate diagnostic check for an appropriate in-depth understanding of the heterogenous nature of the partial ranking data.

In this paper, a class of probability models for ranking data, the order-statistics models, is investigated. We extend the usual normal order-statistics model into one where the underlying random variables follow a multivariate normal distribution. Bayesian approach and the Gibbs sampling technique are used for parameter estimation. In addition, methods to assess the adequacy of model fit are introduced. Robustness of the model is studied by considering a multivariate-t distribution. The proposed method is applied to analyze the presidential election data of the American Psychological Association (APA).

There has been renewed interest in Barton and Lord’s (An upper asymptote for the three-parameter logistic item response model (Tech. Rep. No. 80-20). Educational Testing Service, 1981) four-parameter item response model. This paper presents a Bayesian formulation that extends Béguin and Glas (MCMC estimation and some model fit analysis of multidimensional IRT models. Psychometrika, 66 (4):541–561, 2001) and proposes a model for the four-parameter normal ogive (4PNO) model. Monte Carlo evidence is presented concerning the accuracy of parameter recovery. The simulation results support the use of less informative uniform priors for the lower and upper asymptotes, which is an advantage to prior research. Monte Carlo results provide some support for using the deviance information criterion and ${\mathit{\chi }}^2$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\chi ^{2}$$\end{document} index to choose among models with two, three, and four parameters. The 4PNO is applied to 7491 adolescents’ responses to a bullying scale collected under the 2005–2006 Health Behavior in School-Aged Children study. The results support the value of the 4PNO to estimate lower and upper asymptotes in large-scale surveys.

This paper introduces a new technique for estimating the parameters of models with continuous latent data. Using the Rasch model as an example, it is shown that existing Bayesian techniques for parameter estimation, such as the Gibbs sampler, are not always easy to implement. Then, a new sampling-based Bayesian technique, called the DA-T-Gibbs sampler, is introduced. The DA-T-Gibbs sampler relies on the particular latent data structure of latent response models to simplify the computations involved in parameter estimation.

Multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs. We develop practical simulation based procedures for Bayesian inference of multilevel binary factor analysis models. We illustrate how Markov Chain Monte Carlo procedures such as Gibbs sampling and Metropolis-Hastings methods can be used to perform Bayesian inference, model checking and model comparison without the need for multidimensional numerical integration. We illustrate the proposed estimation methods using three simulation studies and an application involving student's achievement results in different areas of mathematics.

A shadow-test approach to the calibration of field-test items embedded in adaptive testing is presented. The objective function used in the shadow-test model selects both the operational and field-test items adaptively using a Bayesian version of the criterion of $D_{\mathrm{s}}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$D_{\mathrm{s}}$$\end{document}-optimality. The constraint set for the model can be used to hide the field-test items completely in the content of the test as well as to deal with such practical issues as random control of their exposure rates. The approach runs on efficient implementations of the Gibbs sampler for the real-time updating of the ability and field-test parameters. Optimal settings for the proposed algorithms were found and used to demonstrate item calibration with smaller than traditional sample sizes in runtimes fully comparable with conventional adaptive testing.

This article proposes an Item Response Theoretical (IRT) forecasting model that incorporates proper scoring rules and provides evaluations of forecasters’ expertise in relation to the features of the specific questions they answer. We illustrate the model using geopolitical forecasts obtained by the Good Judgment Project (GJP) (see Mellers, Ungar, Baron, Ramos, Gurcay, Fincher, Scott, Moore, Atanasov, Swift, Murray, Stone & Tetlock, 2014). The expertise estimates from the IRT model, which take into account variation in the difficulty and discrimination power of the events, capture the underlying construct being measured and are highly correlated with the forecasters’ Brier scores. Furthermore, our expertise estimates based on the first three years of the GJP data are better predictors of both the forecasters’ fourth year Brier scores and their activity level than the overall Brier scores obtained and Merkle’s (2016) predictions, based on the same period. Lastly, we discuss the benefits of using event-characteristic information in forecasting.

An infinite mixture model is applied to model-based speaker clustering with sampling-based optimization to make it possible to estimate the number of speakers. For this purpose, a framework of non-parametric Bayesian modeling is implemented with the Markov chain Monte Carlo and incorporated in the utterance-oriented speaker model. The proposed model is called the utterance-oriented Dirichlet process mixture model (UO-DPMM). The present paper demonstrates that UO-DPMM is successfully applied on large-scale data and outperforms the conventional hierarchical agglomerative clustering, especially for large amounts of utterances.

We construct an integrated probabilistic model to capture interactions between atoms of a nanocomponent. We then use this model to assess reliabilities of nanocomponents with different structures. Several properties of our proposed model are also described under a sparseness condition. The model is an extension of our previous model based on Markovian random field theory. The proposed integrated model is flexible in that pairwise relationship information among atoms as well as features of individual atoms can be easily incorporated. An important feature that distinguishes the integrated probabilistic model from our previous model is that the integrated approach uses all available sources of information with different weights for different types of interaction. In this paper we consider the nanocomponent at a fixed moment of time, say the present moment, and we assume that the present state of the nanocomponent depends only on the present states of its atoms.

During the typical recovery from U.S. postwar period economic downturns, employment recovers to its prerecession level within months of the output trough. However, during the past two recoveries, employment has taken up to three years to achieve its prerecession benchmark. We propose a formal empirical model of business cycles with recovery periods to demonstrate that the past two recoveries have been statistically different from previous experiences. We find that this difference can be attributed to a shift in the speed of transition between business cycle regimes. Moreover, we find this shift results from both durable and nondurable manufacturing sectors losing their cyclical characteristics. We argue that this finding of acyclicality in post-1980 manufacturing sectors is consistent with previous hypotheses (e.g., improved inventory management) regarding the reduction in macroeconomic volatility over the same period. These results suggest a link between the two phenomena, which have heretofore been studied separately.

Simulated data were used to determine the properties of multivariate prediction of breeding values for categorical and continuous traits using phenotypic, molecular genetic and pedigree information by mixed linear–threshold animal models via Gibbs sampling. Simulation parameters were chosen such that the data resembled situations encountered in Warmblood horse populations. Genetic evaluation was performed in the context of the radiographic findings in the equine limbs. The simulated pedigree comprised seven generations and 40 000 animals per generation. The simulated data included additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits. For one of the binary traits, quantitative trait locus (QTL) effects and genetic markers were simulated, with three different scenarios with respect to recombination rate (r) between genetic markers and QTL and polymorphism information content (PIC) of genetic markers being studied: r = 0.00 and PIC = 0.90 (r0p9), r = 0.01 and PIC = 0.90 (r1p9), and r = 0.00 and PIC = 0.70 (r0p7). For each scenario, 10 replicates were sampled from the simulated horse population, and six different data sets were generated per replicate. Data sets differed in number and distribution of animals with trait records and the availability of genetic marker information. Breeding values were predicted via Gibbs sampling using a Bayesian mixed linear–threshold animal model with residual covariances fixed to zero and a proper prior for the genetic covariance matrix. Relative breeding values were used to investigate expected response to multi- and single-trait selection. In the sires with 10 or more offspring with trait information, correlations between true and predicted breeding values ranged between 0.89 and 0.94 for the continuous traits and between 0.39 and 0.77 for the binary traits. Proportions of successful identification of sires of average, favourable and unfavourable genetic value were 81% to 86% for the continuous trait and 57% to 74% for the binary traits in these sires. Expected decrease of prevalence of the QTL trait was 3% to 12% after multi-trait selection for all binary traits and 9% to 17% after single-trait selection for the QTL trait. The combined use of phenotype and genotype data was superior to the use of phenotype data alone. It was concluded that information on phenotypes and highly informative genetic markers should be used for prediction of breeding values in mixed linear–threshold animal models via Gibbs sampling to achieve maximum reduction in prevalences of binary traits.

Parameters of daily milk yield during the first three lactations of Chios ewes were estimated with random regression models. Data consisted of 42 675 test-day records of 7121 ewes from 75 flocks that had lambed between 1998 and 2000. Models fitted fourth order fixed regressions on Legendre polynomials of the number of days post partum and fourth order random regressions on the individual animal. (Co)variance components were estimated with Gibbs sampling. Lactations were analysed separately. The four eigen values accounted for 0·80 to 0·84, 0·11 to 0·15, 0·04 to 0·05 and about 0·01 of the animal variance, respectively, depending on lactation number. Animal variance estimates, including genetic and, partly, permanent environment effects, were high at the beginning of each lactation and decreased as lactation progressed, suggesting that the animal effect is most important to early daily records. Residual variance was highest in the middle of lactation, suggesting that non-systematic environmental factors play a bigger at that time. Animal correlation estimates between daily yield records ranged from 0·26 to 0·99, were highest for adjacent days and decreased for days further apart. The decline had a different shape in the three lactations and was more evident in the first, suggesting that the three lactations may be biologically distinct traits. Animal correlation estimates between daily and total lactation milk yield ranged from 0·61 to 0·98 and were highest in the middle and lowest towards the end of lactation. Early lactation daily yield had an animal correlation of 0·70 to 0·80 with total lactation milk yield, in all three lactations. Results of this study suggest that daily milk yield records in the early stages of lactation may be useful for selection of ewes with high producing ability and accurate prediction of total lactation milk yield.