On the correspondence from Bayesian log-linear modelling to logistic regression modelling with gg-priors

Consider a set of categorical variables where at least one of them is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the outcome. Within the Bayesian framework, the $g$-prior and mixtures of $g$-priors are commonly assigned to the parameters of a generalized linear model. We prove that assigning a $g$-prior (or a mixture of $g$-priors) to the parameters of a certain log-linear model designates a $g$-prior (or a mixture of $g$-priors) on the parameters of the corresponding logistic regression. By deriving an asymptotic result, and with numerical illustrations, we demonstrate that when a $g$-prior is adopted, this correspondence extends to the posterior distribution of the model parameters. Thus, it is valid to translate inferences from fitting a log-linear model to inferences within the logistic regression framework, with regard to the presence of main effects and interaction terms.Comment: 27 page

Exploring dependence between categorical variables: benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms

This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist log-linear model determination, demonstrating advantages and limitations with simulated and real data sets. The main advantage concerns sparse contingency tables. Inferences from clustering can potentially reduce the number of covariates considered and, subsequently, the number of competing log-linear models, making the exploration of the model space feasible. Variable selection within clustering can inform on marginal independence in general, thus allowing for a more efficient exploration of the log-linear model space. However, we show that the clustering structure is not informative on the existence of interactions in a consistent manner. This work is of interest to those who utilize log-linear models, as well as practitioners such as epidemiologists that use clustering models to reduce the dimensionality in the data and to reveal interesting patterns on how covariates combine.Comment: Preprin

Premium: An R package for profile regression mixture models using dirichlet processes

PReMiuM is a recently developed R package for Bayesian clustering using a Dirichlet process mixture model. This model is an alternative to regression models, nonparametrically linking a response vector to covariate data through cluster membership (Molitor, Papathomas, Jerrett, and Richardson 2010). The package allows binary, categorical, count and continuous response, as well as continuous and discrete covariates. Additionally, predictions may be made for the response, and missing values for the covariates are handled. Several samplers and label switching moves are implemented along with diagnostic tools to assess convergence. A number of R functions for post-processing of the output are also provided. In addition to fitting mixtures, it may additionally be of interest to determine which covariates actively drive the mixture components. This is implemented in the package as variable selection

A life history analysis of a male athlete with an eating disorder

An exploratory investigation, employing the life history method, was conducted with a male athlete with an eating disorder. The focus of the life history is Mike (pseudonym), an individual with a strong athletic identity, who developed bulimia amidst aspirations to be an elite sports performer. Interviews were structured around the life course, beginning with early childhood memories and ultimately reaching the present day. His narrative suggests the achievement threats and weight-based performance pressures associated with competitive sport played a role in precipitating the onset of bulimia nervosa. When such performance pressures were removed the eating disorder remained and evolved, suggesting that disordered eating in sport can have deeper roots as opposed to being primarily situational. Recovery coincided with the cessation of sport participation and the opening up of a foreclosed identity

Eating Disorders in Sport : a call for methodological diversity

From the emergence of isolated studies in the early 1980s to the concentrated and burgeoning research base of the present day, scholars within sport psychology have been motivated to address the problem of eating disorders in sport. Heavily influenced by the medical model of scientific inquiry, the extant literature offers important insights into prevalence and aetiology. Despite this progress, there is much that is poorly understood about athlete eating disorders and existing approaches are vulnerable to considerable critique. This paper highlights some of the fundamental problems with the medical model and argues that its current dominance has created an overly narrow knowledge base. It is proposed that an increase in qualitative, interpretive accounts, that prioritize the subjectivity of experience over the serialization of symptoms, is necessary if we are to achieve a balanced and more complete understanding of eating disorders in sport

On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling

Funding: The first author would like to acknowledge the support of the School of Mathematics and Statistics, as well as CREEM, at the University of St Andrews, and the University of St Andrews St Leonard’s 7th Century Scholarship.Consider a set of categorical variables P where at least one, denoted by Y, is binary. The log-linear model that describes the contingency table counts implies a logistic regression model, with outcome Y. Extending results from Christensen (1997, Log-linear models and logistic regression, 2nd edn. New York, NY, Springer), we prove that the maximum-likelihood estimates (MLE) of the logistic regression parameters equals the MLE for the corresponding log-linear model parameters, also considering the case where contingency table factors are not present in the corresponding logistic regression and some of the contingency table cells are collapsed together. We prove that, asymptotically, standard errors are also equal. These results demonstrate the extent to which inferences from the log-linear framework translate to inferences within the logistic regression framework, on the magnitude of main effects and interactions. Finally, we prove that the deviance of the log-linear model is equal to the deviance of the corresponding logistic regression, provided that no cell observations are collapsed together when one or more factors in P∖{Y} become obsolete. We illustrate the derived results with the analysis of a real dataset.Publisher PDFPeer reviewe

Bela Julesz in Depth

A brief tribute to Bela Julesz (1928−2003) is made in words and images. In addition to a conventional stereophotographic portrait, his major contributions to vision research are commemorated by two ‘perceptual portraits’, which try to capture the spirit of his main accomplishments in stereopsis and the perception of texture