Bayesian inference for Poisson and multinomial log-linear models

Categorical data frequently arise in applications in the Social Sciences. In such applications, the class of log-linear models, based on either a Poisson or (product) multinomial response distribution, is a flexible model class for inference and prediction. In this paper we consider the Bayesian analysis of both Poisson and multinomial log-linear models. It is often convenient to model multinomial or product multinomial data as observations of independent Poisson variables. For multinomial data, Lindley (1964) [20] showed that this approach leads to valid Bayesian posterior inferences when the prior density for the Poisson cell means factorises in a particular way. We develop this result to provide a general framework for the analysis of multinomial or product multinomial data using a Poisson log-linear model. Valid finite population inferences are also available, which can be particularly important in modelling social data. We then focus particular attention on multivariate normal prior distributions for the log-linear model parameters. Here, an improper prior distribution for certain Poisson model parameters is required for valid multinomial analysis, and we derive conditions under which the resulting posterior distribution is proper. We also consider the construction of prior distributions across models, and for model parameters, when uncertainty exists about the appropriate form of the model. We present classes of Poisson and multinomial models, invariant under certain natural groups of permutations of the cells. We demonstrate that, if prior belief concerning the model parameters is also invariant, as is the case in a ‘reference’ analysis, then the choice of prior distribution is considerably restricted. The analysis of multivariate categorical data in the form of a contingency table is considered in detail. We illustrate the methods with two examples.     

Cigarette Use Among Young Adults: Comparisons Between 2-Year College Students, 4-Year College Students,and Those Not in College

Abstract

Objective: To examine cigarette smoking among young adults based on education status. Participants: Community-based sample of 2,694 young adults in the United States Methods: The authors compared 3 groups—those not in college with no college degree, 2-year college students/graduates, 4-year college students/graduates—on various smoking measures: ever smoked, smoked in past month, smoked in past week, consider self a smoker, began smoking before age 15, smoked over 100 cigarettes in lifetime, ever tried to quit, and plan to quit in next year. Results: The authors found that for nearly all the smoking measures, the 4-year college group was at lowest risk, the noncollege group was at highest risk, and the 2-year college group represented a midpoint. Differences between groups remain after adjusting for parents’ education and other potential confounding factors. Conclusions: Smoking behaviors clearly differ between the 2-year, 4-year, and no college groups. Interventions should be tailored for each group.     

Communities and academics: A developing dialogue

Intentional communities have been described as laboratories for testing and demonstrating new ideologies and social structures. This paper focuses on the part played by academics in disseminating the results of these ‘social experiments’ to a wider audience. The relationship between intentional communities and academics has often been difficult, with mistrust on both sides. By looking at the underlying needs of both, this paper intends to throw light on the source of some of the difficulties, so that both may better fulfil their important social functions. A case study is reported to illustrate the main points. The paper concludes with advice to both intentional communities and academics for building better relationships and developing co-operative projects.     

Biases in bias elicitation

Abstract

We consider the biases that can arise in bias elicitation when expert assessors make random errors. After presenting a general framework of the phenomenon, we illustrate it for two examples: the case of omitting variables bias and that of the bias arising in adjusting relative risks. Results show that, even when assessors’ elicitations of bias have desirable properties, the nonlinear nature of biases can lead to elicitations of bias that are, themselves, biased. We show the corrections which can be made to remove this bias and discuss the implications for the applied literature which employs these methods.     

Operationalising caseload midwifery in the Australian public maternity system: Findings from a national cross-sectional survey of maternity managers

Background

Despite high-level evidence of the benefits of caseload midwifery for women and babies, little is known about specific practice arrangements, organisational barriers and facilitators, nor about workforce requirements of caseload. This paper explores how caseload models across Australia operate.