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.     

Drivers and Performance Outcomes of Supplier Innovation Generation in Customer–Supplier Relationships: The Role of Power‐Dependence

While innovations generated by supply channel relationships, as opposed to individual partners, play an increasingly important role in the success of all supply chain partners, there has been a dearth of research in the literature on how supply chain relationships cultivate the process of such innovation generation. We explore supplier market knowledge acquisition, relationship learning, systems collaboration, and technological uncertainty as antecedents of supplier innovation generation, which is in turn hypothesized to positively affect the relationship performance of the supplier. Furthermore, supplier dependence on the buyer is investigated as a moderator of the effects of such antecedents on supplier innovation generation. Empirical tests, which used a sample of 236 Taiwanese executives, supported most of the hypotheses, and some implications of the results are discussed.     

CLASH OF CAREER AND FAMILY: FERTILITY DECISIONS AFTER JOB DISPLACEMENT

In this paper we investigate how career considerations may affect fertility decisions in the presence of a temporary employment shock. We compare the birth rates of women displaced by a plant closure with those of women unaffected by job loss after establishing the pre‐displacement comparability of these groups. Our results reveal that job displacement reduces average fertility by 5%–10%, and that these effects are largely explained by the response of women in more skilled occupations. We offer an explanation of our results based on career interruptions of women.     

Addressing self-selection effects in evaluations of mutual help groups and professional mental health services: An introduction to two-stage sample selection models

Because random assignment to conditions is often neither possible nor desirable in longitudinal evaluations of mutual help organizations, the influence of self-selection effects must be assessed in order to accurately interpret outcome data. One approach to adjusting for self-selection effects is to control for covariates that predict outcome using statistical procedures such as analysis of covariance (ANCOVA), partial correlations, and hierarchical regression. This approach has considerable power, but is less useful when an evaluator is interested in directly modeling the process of entry into a program and incorporating information on the factors affecting self-selection into estimation of program effects. Two-stage sample selection models are designed to address such situations. These models rely on regression procedures in which program participation is modeled in an initial equation, which yields a sample selection correction factor. The correction factor is included with participation in a second equation that predicts outcome. This two-stage procedure allows the evaluator to interpret the observed effects of a professional service or a self-help group in the context of the magnitude and direction of selection effects. We compare and contrast the covariate control and sample selection models in a longitudinal study of the effects of participation in Alcoholics Anonymous on drinking behavior.