The Dirichet-Multinomial model for multivariate randomized response data and small samples

In survey sampling the randomized response (RR) technique can be used to obtain truthful answers to sensitive questions. Although the individual answers are masked due to the RR technique, individual (sensitive) response rates can be estimated when observing multivariate response data. The beta-binomial model for binary RR data will be generalized to handle multivariate categorical RR data. The Dirichlet-multinomial model for categorical RR data is extended with a linear transformation of the masked individual categorical-response rates to correct for the RR design and to retrieve the sensitive categorical-response rates even for small data samples. This specification of the Dirichlet-multinomial model enables a straightforward empirical Bayes estimation of the model parameters. A constrained-Dirichlet prior will be introduced to identify homogeneity restrictions in response rates across persons and/or categories. The performance of the full Bayes parameter estimation method is verified using simulated data. The proposed model will be applied to the college alcohol problem scale study, where students were interviewed directly or interviewed via the randomized response technique about negative consequences from drinking. (Contains 5 tables.

Bayesian psychometric scaling

In educational and psychological studies, psychometric methods are involved in the measurement of constructs, and in constructing and validating measurement instruments. Assessment results are typically used to measure student proficiency levels and test characteristics. Recently, Bayesian item response models received considerable attention to analyze test data and to measure latent variables. Bayesian psychometric modeling allows to include prior information about the assessment in addition to information available in the observed response data. An introduction is given to Bayesian psychometric modeling, and it is shown that this approach is very flexible, provides direct estimates of student proficiencies, and depends less on asymptotic results. Various Bayesian item response models are discussed to provide insight in Bayesian psychometric scaling and the Bayesian way of making psychometric inferences. This is done according to a general multilevel modeling approach, where observations are nested in students and items, and students are nested in schools. Different examples are given to illustrate the influence of prior information, the effects of clustered response data following a PISA study, and Bayesian methods for scale construction

Bayesian Covariance Structure Modeling of Multi-Way Nested Data

A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the well-known dependence structure implied by random effects. A conjugate shifted-inverse gamma prior is proposed for the covariance parameters which ensures that the covariance matrix remains positive definite under posterior analysis. A numerically efficient Gibbs sampling procedure is defined for balanced nested designs, and is validated using two simulation studies. For a top-layer unbalanced nested design, the procedure requires an additional data augmentation step. The proposed data augmentation procedure facilitates sampling latent variables from (truncated) univariate normal distributions, and avoids numerical computation of the inverse of the structured covariance matrix. The Bayesian multivariate (linear transformation) model is applied to two-way nested interval-censored event times to analyze differences in adverse events between three groups of patients, who were randomly allocated to treatment with different stents (BIO-RESORT). The parameters of the structured covariance matrix represent unobserved heterogeneity in treatment effects and are examined to detect differential treatment effects.Comment: 30 pages, 5 figures, 4 table

Violent Frames: Analyzing Internet Movie Database Reviewers' Text Descriptions of Media Violence and Gender Differences from 39 Years of US Action, Thriller, Crime, and Adventure Movies

The Internet Movie Database (www.imdb.com) is the largest and most successful website for movie information, yet crowdsourced contents of sites like these have rarely been studied. Therefore, using IMDb synopsis texts, reviewers’ movie descriptions were analyzed regarding movie contents that have been the subject of many previous media studies: the violent behavior and victimization of male and female film characters over time. Analysis of 1,396 synopsis texts reveals that both perpetrators and victims are mainly male (both 80%) and, against expectation, violence becomes less severe and more often nonlethal over the years. For the first time, our study using IMDb texts identifies male and female stereotypes and suggests that viewers’ descriptions of what they have seen could match the findings of traditional content analyses and actual crime figure

Small and negative correlations among clustered observations: Limitations of the linear mixed effects model

The linear mixed effects model is an often used tool for the analysis of multilevel data. However, this model has an ill-understood shortcoming: it assumes that observations within clusters are always positively correlated. This assumption is not always true: individuals competing in a cluster for scarce resources are negatively correlated. Random effects in a mixed effects model can model a positive correlation among clustered observations but not a negative correlation. As negative clustering effects are largely unknown to the sheer majority of the research community, we conducted a simulation study to detail the bias that occurs when analysing negative clustering effects with the linear mixed effects model. We also demonstrate that ignoring a small negative correlation leads to deflated Type-I errors, invalid standard errors and confidence intervals in regression analysis. When negative clustering effects are ignored, mixed effects models incorrectly assume that observations are independently distributed. We highlight the importance of understanding these phenomena through analysis of the data from Lamers, Bohlmeijer, Korte, and Westerhof (2015). We conclude with a reflection on well-known multilevel modelling rules when dealing with negative dependencies in a cluster: negative clustering effects can, do and will occur and these effects cannot be ignored