Generalized Laplacian approximations in Bayesian inference

This paper presents a new Laplacian approximation to the posterior density of η = g(θ). It has a simpler analytical form than that described by Leonard et al. (1989). The approximation derived by Leonard et al. requires a conditional information matrix R_η to be positive definite for every fixed η. However, in many cases, not all R_η are positive definite. In such cases, the computations of their approximations fail, since the approximation cannot be normalized. However, the new approximation may be modified so that the corresponding conditional information matrix can be made positive definite for every fixed η. In addition, a Bayesian procedure for contingency-table model checking is provided. An example of cross-classification between the educational level of a wife and fertility-planning status of couples is used for explanation. Various Laplacian approximations are computed and compared in this example and in an example of public school expenditures in the context of Bayesian analysis of the multiparameter Fisher-Behrens problem.     

Public Perceptions about Food Safety in the United States and Japan1

Abstract Consumer concerns over pesticide residues and food additives have been growing in industrialized societies, including the United States and Japan. However, little comparative research has been carried out to determine which household characteristics may be significantly associated with these heightened concerns, and whether or not the same factors are useful for understanding variation in these worries in more than one society. This paper examines food safety attitudes in Seattle, Washington, and Kobe, Japan, and discovers that while the absolute level of expressed concern is higher in Kobe, the predictive power of household characteristics in explaining attitudinal differences within countries is similar. Implications for rural areas and future research on family structures in capitalist societies are discussed.     

Mean squares in saturated fractional designs revisited

In a previous paper (Bissell, 1989) some suggestions were offered for interpreting mean squares in saturated fractional designs where no independent estimate of experimental error is available. One of the methods leads to a simple numerical test of homogeneity which provides an objective accompaniment to half-Normal plotting of effects (Daniel, 1959) in 2n designs or exponential plotting of mean squares (Bissell, 1989) in 3n designs. A table of percentage points for a convenient test statistic is provided in this paper.     

TESTING SPHERICITY UNDER A MIXTURE MODEL

The robustness of Mauchly's sphericity test criterion when sampling from a mixture of two multivariate normal distributions is studied. The distribution of the sphericity test criterion when the sample covariance matrix has a non-central Wishart density of rank one is derived in terms of Meijer's G-functions; its distribution under the mixture model is then deduced. The robustness is studied by computing actual significance levels of the test under the mixture model using the critical values under the usual normal model.     

Will taxpayers ever like taxes?: Responses to the U.S. Tax Reform Act of 1986

Major policy changes like the 1986 Tax Reform Act (TRA) in the United States provide natural experiments to study attitudinal and behavior responses to law. Surprisingly, public evaluations of the TRA became increasingly negative after passage, while general support for the tax system became more positive in response to the changes. To explain this puzzle, we propose a dynamic model of taxpayer attitudes that is consistent with the observed loose linkage between logically-connected concepts. We briefly review the political context, objectives and impacts of the 1986 Tax Reform Act, and present several studies testing the impact of self-interest, prior beliefs, and social discussion on changes in attitudes and behavior.Results suggest that the complexity of taxes and difficulty in knowing objective impacts weakens the role of self-interest in attitudinal changes, thereby strengthening the role of prior beliefs and discussion. Evaluations of tax laws are most responsive to more politically-oriented influences.     

Children's gender- and age-based categorization in similarity and induction tasks

The present studies examined children's and adults' preferences for gender- or age-based categorization using similarity and inductive inference tasks. Four-year-olds, 6-year-olds, and adults looked at pictures of people and decided which of two was more like a target (similarity condition) or which shared a novel age- or gender-related property with the target (inference condition). Age or gender-based matches were possible. The results are consistent with previous findings that gender-based classification decreases with age. However, they also demonstrate that children use gender more for judging similarity than for making inferences about novel properties. Distinct patterns emerge from the two tasks: 6-year-olds and adults in both conditions categorize more by age than gender; 4-year-olds categorize by gender more than age in the similarity task, but by age more in the induction task. Only adults differentiated by property in the inference condition. These findings suggest that the salience of gender categories cannot entirely be attributed to their inductive potential. Gender has a salience beyond what would be predicted by its power for directing novel generalizations.     

Naturally occurring play patterns in groups of latency aged children

This study examines the influence of the socialization of aggression among different gender and social class groupings and the influence of psychosocial stage on cognitive developmental play preferences among groups of school aged children. Observations of 143 play groups were coded for play preference (symbolic play, practice play, games with rules) and play performance (cooperative or competitive). Findings of the log-linear data analysis suggest a middle class and masculine bias in Piaget's cognitive model (i.e., that as age increases children prefer more games with rules). This model held only for middle class and affluent boys. Girls (both latency and prepubertal) and lower socioeconomic groups tended to prefer practice play. Girls were more likely to play cooperatively; boys more likely to play competitively. Implications for theory development and clinical practice are explored.     

Estimation of noncentrality parameters

We propose some estimators of noncentrality parameters which improve upon usual unbiased estimators under quadratic loss. The distributions we consider are the noncentral chi-square and the noncentral F. However, we give more general results for the family of elliptically contoured distributions and propose a robust dominating estimator.