The Republic of Sakha (Yakutia) faces serious demographic challenges. One of the most important among them is the imbalance of population flows within internal migration. This paper examines the patterns of internal migration in the Republic, based on the distribution of municipal districts (uluses) by economic zones designated by the authorities for administrative purposes. The six most common indices characterising the intensity of migration of the population were used for the analysis. The homogeneity of Yakutia’s districts according to these indices was tested using the van der Waerden test. The article reveals that the intensity of migration in Yakutia has increased since 2011. The financial crisis of 2008–2009 and the COVID-19 pandemic had a significant but temporary impact on internal migration in Yakutia. Only Yakutsk has experienced population growth due to internal migration throughout the period studied. The intensity of migration in the Arctic uluses was not statistically different from central and eastern uluses, but differed from the most economically developed districts in southern and western Yakutia. The Republic was homogeneous with respect to the balance of migration inflows and outflows, but there was considerable heterogeneity in terms of the impact of migration on the size of the population.

We present an hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The model assumes that there are relevant subpopulations and that within each subpopulation the individual-level regression coefficients have a multivariate normal distribution. However, class membership is not known a priori, so the heterogeneity in the regression coefficients becomes a finite mixture of normal distributions. This approach combines the flexibility of semiparametric, latent class models that assume common parameters for each sub-population and the parsimony of random effects models that assume normal distributions for the regression parameters. The number of subpopulations is selected to maximize the posterior probability of the model being true. Simulations are presented which document the performance of the methodology for synthetic data with known heterogeneity and number of sub-populations. An application is presented concerning preferences for various aspects of personal computers.

In intertemporal and risky choice decisions, parametric utility models are widely used for predicting choice and measuring individuals’ impulsivity and risk aversion. However, parametric utility models cannot describe data deviating from their assumed functional form. We propose a novel method using cubic Bezier splines (CBS) to flexibly model smooth and monotonic utility functions that can be fit to any dataset. CBS shows higher descriptive and predictive accuracy over extant parametric models and can identify common yet novel patterns of behavior that are inconsistent with extant parametric models. Furthermore, CBS provides measures of impulsivity and risk aversion that do not depend on parametric model assumptions.

Identifying price sensitive consumers is an important problem in marketing. We develop a Bayesian multi-level factor analytic model of the covariation among household-level price sensitivities across product categories that are substitutes. Based on a multivariate probit model of category incidence, this framework also allows the researcher to model overall price sensitivity (i.e., indicated by higher-order factor scores) as a function of household-level covariates. All model parameters are estimated simultaneously to circumvent the downward bias resulting from two-stage estimation. The modeling framework is illustrated using scanner panel data from multiple categories of instant coffee.

This paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the Grade of Membership (GoM) model in representing population heterogeneity. We consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range, while keeping other population parameters fixed, in the marginal space (based on marginal probabilities) and in the full parameter space (based on cell probabilities). The case of a 2 × 2 contingency table is discussed in detail, and a generalization to 2J tables with J ≥ 3 is sketched. Our approach highlights the main distinction between the GoM model and the probabilistic mixture of classes by demonstrating geometrically the difference between the concepts of partial and probabilistic memberships. By using the geometric approach we show that, in special cases, the GoM model can be thought of as being similar to an item response theory (IRT) model in representing population heterogeneity. Finally, we show that the GoM item parameters can provide quantities analogous to more general logistic IRT item parameters. As a latent structure model, the GoM model might be considered a useful alternative for a data analysis when both classes of extreme responses, and additional heterogeneity that cannot be captured by those latent classes, are expected in the population.

We introduce a new statistical procedure for the identification of unobserved categories that vary between individuals and in which objects may span multiple categories. This procedure can be used to analyze data from a proposed sorting task in which individuals may simultaneously assign objects to multiple piles. The results of a synthetic example and a consumer psychology study involving categories of restaurant brands illustrate how the application of the proposed methodology to the new sorting task can account for a variety of categorization phenomena including multiple category memberships and for heterogeneity through individual differences in the saliency of latent category structures.

The p-median offers an alternative to centroid-based clustering algorithms for identifying unobserved categories. However, existing p-median formulations typically require data aggregation into a single proximity matrix, resulting in masked respondent heterogeneity. A proposed three-way formulation of the p-median problem explicitly considers heterogeneity by identifying groups of individual respondents that perceive similar category structures. Three proposed heuristics for the heterogeneous p-median (HPM) are developed and then illustrated in a consumer psychology context using a sample of undergraduate students who performed a sorting task of major U.S. retailers, as well as a through Monte Carlo analysis.

Multiple regression is frequently used across the various social sciences to analyze cross-sectional data. However, it can often times be challenging to justify the assumption of common regression coefficients across all respondents. This manuscript presents a heterogeneous Bayesian regression model that enables the estimation of individual-level-regression coefficients in cross-sectional data involving a single observation per response unit. A Gibbs sampling algorithm is developed to implement the proposed Bayesian methodology. A Monte Carlo simulation study is constructed to assess the performance of the proposed methodology across a number of experimental factors. We then apply the proposed method to analyze data collected from a consumer psychology study that examines the differential importance of price and quality in determining perceived value evaluations.

A new Bayesian multinomial probit model is proposed for the analysis of panel choice data. Using a parameter expansion technique, we are able to devise a Markov Chain Monte Carlo algorithm to compute our Bayesian estimates efficiently. We also show that the proposed procedure enables the estimation of individual level coefficients for the single-period multinomial probit model even when the available prior information is vague. We apply our new procedure to consumer purchase data and reanalyze a well-known scanner panel dataset that reveals new substantive insights. In addition, we delineate a number of advantageous features of our proposed procedure over several benchmark models. Finally, through a simulation analysis employing a fractional factorial design, we demonstrate that the results from our proposed model are quite robust with respect to differing factors across various conditions.

A variety of joint space multidimensional scaling (MDS) methods have been utilized for the spatial analysis of two- or three-way dominance data involving subjects’ preferences, choices, considerations, intentions, etc. so as to provide a parsimonious spatial depiction of the underlying relevant dimensions, attributes, stimuli, and/or subjects’ utility structures in the same joint space representation. We demonstrate that care must be taken with respect to a key assumption in existent joint space MDS models such that all estimated dimensions are utilized by each and every subject in the sample, as this assumption can lead to serious distortions with respect to the derived joint spaces. We develop a new Bayesian dimension selection methodology for the multidimensional unfolding model which accommodates heterogeneity with respect to such dimensional utilization at the individual subject level for the analysis of two or three-way dominance data. A consumer psychology application regarding the preference for Over-the-Counter (OTC) analgesics is provided. We conclude by discussing the practical implications of the results, as well as directions for future research.

In comparing characteristics of independent populations, researchers frequently expect a certain structure of the population variances. These expectations can be formulated as hypotheses with equality and/or inequality constraints on the variances. In this article, we consider the Bayes factor for testing such (in)equality-constrained hypotheses on variances. Application of Bayes factors requires specification of a prior under every hypothesis to be tested. However, specifying subjective priors for variances based on prior information is a difficult task. We therefore consider so-called automatic or default Bayes factors. These methods avoid the need for the user to specify priors by using information from the sample data. We present three automatic Bayes factors for testing variances. The first is a Bayes factor with equal priors on all variances, where the priors are specified automatically using a small share of the information in the sample data. The second is the fractional Bayes factor, where a fraction of the likelihood is used for automatic prior specification. The third is an adjustment of the fractional Bayes factor such that the parsimony of inequality-constrained hypotheses is properly taken into account. The Bayes factors are evaluated by investigating different properties such as information consistency and large sample consistency. Based on this evaluation, it is concluded that the adjusted fractional Bayes factor is generally recommendable for testing equality- and inequality-constrained hypotheses on variances.

SARS-CoV-2 superspreading occurs when transmission is highly efficient and/or an individual infects many others, contributing to rapid spread. To better quantify heterogeneity in SARS-CoV-2 transmission, particularly superspreading, we performed a systematic review of transmission events with data on secondary attack rates or contact tracing of individual index cases published before September 2021 prior to the emergence of variants of concern and widespread vaccination. We reviewed 592 distinct events and 9,883 index cases from 491 papers. A meta-analysis of secondary attack rates identified substantial heterogeneity across 12 chosen event types/settings, with the highest transmission (25–35%) in co-living situations including households, nursing homes, and other congregate housing. Among index cases, 67% reported zero secondary cases and only 3% (287) infected >5 secondary cases (“superspreaders”). Index case demographic data were limited, with only 55% of individuals reporting age, sex, symptoms, real-time polymerase chain reaction (PCR) cycle threshold values, or total contacts. With the data available, we identified a higher percentage of superspreaders among symptomatic individuals, individuals aged 49–64 years, and individuals with over 100 total contacts. Addressing gaps in the literature regarding transmission events and contact tracing is needed to properly explain the heterogeneity in transmission and facilitate control efforts for SARS-CoV-2 and other infections.

Meta-analyses traditionally compare the difference in means between groups for one or more outcomes of interest. However, they do not compare the spread of data (variability), which could mean that important effects and/or subgroups are missed. To address this, methods to compare variability meta-analytically have recently been developed, making it timely to review them and consider their strengths, weaknesses, and implementation. Using published data from trials in major depression, we demonstrate how the spread of data can impact both overall effect size and the frequency of extreme observations within studies, with potentially important implications for conclusions of meta-analyses, such as the clinical significance of findings. We then describe two methods for assessing group differences in variability meta-analytically: the variance ratio (VR) and coefficient of variation ratio (CVR). We consider the reporting and interpretation of these measures and how they differ from the assessment of heterogeneity between studies. We propose general benchmarks as a guideline for interpreting VR and CVR effects as small, medium, or large. Finally, we discuss some important limitations and practical considerations of VR and CVR and consider the value of integrating variability measures into meta-analyses.