Hierarchical or ‘‘multilevel’’ regression models typically parameterize the mean response conditional on unobserved latent variables or ‘‘random’’ effects and then make simple assumptions regarding their distribution. The interpretation of a regression parameter in such a model is the change in possibly transformed mean response per unit change in a particular predictor having controlled for all conditioning variables including the random effects. An often overlooked limitation of the conditional formulation for nonlinear models is that the interpretation of regression coefficients and their estimates can be highly sensitive to difficult-to-verify assumptions about the distribution of random effects, particularly the dependence of the latent variable distribution on covariates. In this article, we present an alternative parameterization for the multilevel model in which the marginal mean, rather than the conditional mean given random effects, is regressed on covariates. The impact of random effects model violations on the marginal and more traditional conditional parameters is compared through calculation of asymptotic relative biases. A simple two-level example from a study of teratogenicity is presented where the binomial overdispersion depends on the binary treatment assignment and greatly influences likelihood-based estimates of the treatment effect in the conditional model. A second example considers a three-level structure where attitudes toward abortion over time are correlated with person and district level covariates. We observe that regression parameters in conditionally specified models are more sensitive to random effects assumptions than their counterparts in the marginal formulation.

Genotypes of infectious organisms are becoming the foundation for epidemiologic studies of infectious disease. Central to the use of such data is a means for comparing genotypes. We develop methods for this purpose in the context of DN fingerprint genotyping of tuberculosis, but our approach is applicable to many fingerprint­based genotyping systems and/or organisms. Data available on replicate (laboratory) strains here reveal that (i) error in fingerprint band size is proportional to band size and (ii) errors are positively correlated within a fingerprint. Comparison (or matching) scores computed to account for this error structure need to be “standardized” in order to properly rank the comparisons. We demonstrate the utility of using extreme value distributions to effect such standardization. Several estimation issues for the extreme value parameters are discussed, including a lack of robustness of (approximate) maximum likelihood estimates. Interesting findings to emerge from examination of quantiles of standardized matching scores include (i) formal significance is not attainable when querying a database for a given fingerprint pattern and (ii) maximal matching probabilities are not necessarily monotonely decreasing with increasing numbers of fingerprint bands.

We propose a general class of prior distributions for arbitrary regression models. We discuss parametric and semiparametric models. The prior specification for the regression coefficients focuses on observable quantities in that the elicitation is based on the availability of historical data $D_0$ and a scalar quantity $a_0$ quantifying the uncertainty in $D_0$. Then $D_0$ and $a_0$ are used to specify a prior for the regression coefficients in a semiautomatic fashion. The most natural specification of $D_0$ arises when the raw data from a similar previous study are available. The availability of historical data is quite common in clinical trials, carcinogenicity studies, and environmental studies, where large data bases are available from similar previous studies. Although the methodology we present here is quite general, we will focus only on using historical data from similar previous studies to construct the prior distributions. The prior distributions are based on the idea of raising the likelihood function of the historical data to the power $a_0$, where $0 \le a_0 \le 1$. We call such prior distributions power prior distributions. We examine the power prior for four commonly used classes of regression models. These include generalized linear models, generalized linear mixed models, semiparametric proportional hazards models, and cure rate models for survival data. For these classes of models, we discuss the construction of the power prior, prior elicitation issues, propriety conditions, model selection, and several other properties. For each class of models, we present real data sets to demonstrate the proposed methodology.

Forestry statistics is an important field of applied statistics with a long tradition. Many forestry problems can be solved by means of point processes or marked point processes. There, the “points ”are tree locations and the “marks ” are tree characteristics such as diameter at breast height or degree of damage by environmental factors. Point process characteristics are valuable tools for exploratory data analysis in forestry, for describing the variability of forest stands and for understanding and quantifying ecological relationships. Models of point processes are also an important basis of modern single-tree modeling, that gives simulation tools for the investigation of forest structures and for the prediction of results of forestry operations such as plantation and thinning.

John Wilder Tukey, Donner Professor of Science Emeritus at Princeton University, was born in New Bedford, Massachusetts, on June 16,1915. After earning bachelor’s and master’s degrees in chemistry at Brown University in 1936 and 1937, respectively, he started his career at Princeton University with a Ph.D.in mathematics in 1939 followed by an immediate appointment as Henry B.Fine Instructor in Mathematics. A decade later, at age 35, he was advanced to a full professorship. He directed the Statistical Research Group at Princeton University from its founding in 1956;when the Department of Statistics was formed in 1965, he was named its first chairman and held that post until 1970. He was appointed to the Donner Chair in 1976 and remained at Princeton until reaching emeritus status in 1985. At the same time, he was a Member of Technical Staff at AT&T Bell Laboratories since 1945, advancing to Assistant Director of Research, Communications Principles, in 1958 and, in 1961, to Associate Executive Director, Research Information Sciences, a position he held until retirement in 1985.

Throughout World War II he participated in projects assigned to the Princeton Branch of the Frankford Arsenal Fire Control Design Division. This wartime service marked the beginning of his close and continuing association with governmental committees and agencies. Among other activities he was a member of the U.S. Delegation to the Conference on the Discontinuance of Nuclear Weapons Tests in Geneva in 1959, served on the President’s Science Advisory Committee from 1960 to 1964 and was a member of President Johnson’s Task Force on Environmental Pollution and President Nixon’s Task Force on Air Pollution. The long list of awards and honors that Tukey has received includes the S.S.Wilks Medal from the American Statistical Association (ASA)(1965), the National Medal of Science (1973), the Medal of Honor from the IEEE (1982), the Deming Medal from the American Society of Quality Control (1983) and the Educational Testing Service Award (1990). He holds honorary degrees from Case Institute of Technology, the University of Chicago and Brown, Temple, Yale and Waterloo Universities; in June 1998, he was awarded an honorary degree from Princeton University. He has led the way to the fields of exploratory data analysis (EDA) and robust estimation. His contributions to the spectral analysis of time series and other aspects of digital signal processes have been widely used in engineering and science. His collaboration with a fellow mathematician resulted in the discovery of the fast Fourier transform (FFT) algorithm. Author of Exploratory Data Analysis and eight volumes of collected papers, he has contributed to a wide variety of areas and has coauthored several books. He has guided more than 50 graduate students to successful Ph.D.’s and inspired their careers. A detailed list of his students as well as a complete curriculum vitae can be found in The Practice of Data Analysis (1997), edited by D. Brillinger, L. Fernholz, and S.Morgenthaler, Princeton University Press.

John W. Tukey married Elizabeth Louise Rapp in 1950. Before their marriage, she was Personnel Director of the Educational Testing Service in Princeton, New Jersey.