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.     

The Farm Crisis and Mental Health: A Longitudinal Study of the 1980s1

Abstract This paper examines rural/urban differences and trends in mental health during the farm crisis of the 1980s in a large panel sample from a midwestern state. A community research perspective, which attributes differences to life styles, culture, and community context, is contrasted with an economic stress perspective, which focuses on individual differences in economic circumstances as determinants of rural-urban differences in mental health. Survey samples from 1981, 1986, and 1989 are used to examine differences among seven categories of community type. Multiple regression analysis of the trend and panel data provide support for both the individual economic distress and community context models.     

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.     

Evaluation of an educational intervention upon knowledge, attitudes, and behavior concerning drinking/drugged driving.

The Contra Costa County educational program for juveniles found guilty of driving under the influence (DUI) was evaluated. Over 600 juveniles convicted of DUI from 1983 to 1988 formed the study group for this research and of these over 100 participated in the educational program. Assessment of program participants was conducted for knowledge, attitudes and behavior. Participants demonstrated increased knowledge, stronger attitudes against driving under the influence, and less risky alcohol and automobile related behaviors. County juvenile records analyzed by the logit procedure showed that class participants had a significantly lower number of repeat offenses compared to non-program participants that could not be explained by race, offense severity, age or gender.     

A note on inverse estimation in non-linear models

The problem of estimating the value of an x variable for a given proportion of an observed value of the y variable is consdered for a non-linear model. Asymptotic confidence limits are obtained and an application of the method is illustrated witreal data.