There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not necessarily having a probabilistic basis and statistical models having unobservables with a probabilistic basis. Another concerns likelihood-based inference for statistical models with unobservables. This needs an extended-likelihood framework, and we show how one such extension, hierarchical likelihood, allows this to be done. Modeling of unobservables leads to rich classes of new probabilistic models from which likelihood-type inferences can be made naturally with hierarchical likelihood.

A standard goal of model evaluation and selection is to find a model that approximates the truth well while at the same time is as parsimonious as possible. In this paper we emphasize the point of view that the models under consideration are almost always false, if viewed realistically, and so we should analyze model adequacy from that point of view. We investigate this issue in large samples by looking at a model credibility index, which is designed to serve as a one-number summary measure of model adequacy. We define the index to be the maximum sample size at which samples from the model and those from the true data generating mechanism are nearly indistinguishable. We use standard notions from hypothesis testing to make this definition precise. We use data subsampling to estimate the index. We show that the definition leads us to some new ways of viewing models as flawed but useful. The concept is an extension of the work of Davies [Statist. Neerlandica 49 (1995) 185–245].

Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions and thus is a rich and flexible nonparametric class of distributions. Further, the MLE exists and can be computed with readily available algorithms. Thus, no tuning parameter, such as a bandwidth, is necessary for estimation. Due to these attractive properties, there has been considerable recent research activity concerning the theory and applications of log-concave distributions. This article gives a review of these results.

We review some aspects of Bayesian and frequentist interval estimation, focusing first on their relative strengths and weaknesses when used in “clean” or “textbook” contexts. We then turn attention to observational-data situations which are “messy,” where modeling that acknowledges the limitations of study design and data collection leads to nonidentifiability. We argue, via a series of examples, that Bayesian interval estimation is an attractive way to proceed in this context even for frequentists, because it can be supplied with a diagnostic in the form of a calibration-sensitivity simulation analysis. We illustrate the basis for this approach in a series of theoretical considerations, simulations and an application to a study of silica exposure and lung cancer.

In many applications, the underlying scientific question concerns whether the variances of k samples are equal. There are a substantial number of tests for this problem. Many of them rely on the assumption of normality and are not robust to its violation. In 1960 Professor Howard Levene proposed a new approach to this problem by applying the F-test to the absolute deviations of the observations from their group means. Levene’s approach is powerful and robust to nonnormality and became a very popular tool for checking the homogeneity of variances.

This paper reviews the original method proposed by Levene and subsequent robust modifications. A modification of Levene-type tests to increase their power to detect monotonic trends in variances is discussed. This procedure is useful when one is concerned with an alternative of increasing or decreasing variability, for example, increasing volatility of stocks prices or “open or closed gramophones” in regression residual analysis. A major section of the paper is devoted to discussion of various scientific problems where Levene-type tests have been used, for example, economic anthropology, accuracy of medical measurements, volatility of the price of oil, studies of the consistency of jury awards in legal cases and the effect of hurricanes on ecological systems.

Leo A. Goodman was born on August 7, 1928 in New York City. He received his A.B. degree, summa cum laude, in 1948 from Syracuse University, majoring in mathematics and sociology. He went on to pursue graduate studies in mathematics, with an emphasis on mathematical statistics, in the Mathematics Department at Princeton University, and in 1950 he was awarded the M.A. and Ph.D. degrees. His statistics professors at Princeton were the late Sam Wilks and John Tukey. Goodman then began his academic career as a statistician, and also as a statistician bridging sociology and statistics, with an appointment in 1950 as assistant professor in the Statistics Department and the Sociology Department at the University of Chicago, where he remained, except for various leaves, until 1987. He was promoted to associate professor in 1953, and to professor in 1955. Goodman was at Cambridge University in 1953–1954 and 1959–1960 as visiting professor at Clare College and in the Statistical Laboratory. And he spent 1960–1961 as a visiting professor of mathematical statistics and sociology at Columbia University. He was also a research associate in the University of Chicago Population Research Center from 1967 to 1987. In 1970 he was appointed the Charles L. Hutchinson Distinguished Service Professor at the University of Chicago, a title that he held until 1987. He spent 1984–1985 at the Center for Advanced Study in the Behavioral Sciences in Stanford. In 1987 he was appointed the Class of 1938 Professor at the University of California, Berkeley, in the Sociology Department and the Statistics Department. Goodman’s numerous honors include honorary D.Sc. degrees from the University of Michigan and Syracuse University, and membership in the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society. He has also received numerous awards: From the American Statistical Association, the Samuel S. Wilks Medal; from the Committee of Presidents of Statistical Societies, the R. A. Fisher Lectureship; and from the Institute of Mathematical Statistics, the Henry L. Reitz Lectureship; also, from the American Sociological Association, the Samuel A. Stouffer Methodology Award and the Career of Distinguished Scholarship Award; and from the American Sociological Association Methodology Section, the inaugural Otis Dudley Duncan Lectureship. Earlier he had received a Special Creativity Award from the National Science Foundation, and fellowships from the Guggenheim Foundation, the Fulbright Commission, the Social Science Research Council and the National Science Foundation. In 2005 the American Sociological Association Methodology Section established the Leo A. Goodman Award to recognize contributions to sociological methodology, and/or innovative uses of sociological methodology, made by a scholar who is no more than fifteen years past the Ph.D.