Overview

The use of random effects models in practice, often in the form of Bayesian hierarchical models, is growing rapidly because of major developments in computational methods for these models. In this short course we present models and building methods for data with random location and scale effects. Data visualization methods play a fundamental role in all phases of this model building: data exploration, model identification, and model checking. From the model building stage we move to Bayesian models for the data because, as a practical matter, the location and scale distributions fit readily into a hierarchical Bayesian framework. We describe computational methods for fitting these models.

Example

Several data sets will be used to motivate the models and methods. One example of such data, which occurs widely in the social and business sciences is rater data: respondents in a survey rate attributes on a subjective scale from 1 to10.

What's New

Random-effects models with measurements of a response on a continuous measurement scale typically specify the random effects as location effects; the number of treatments of random scale effects we have been able to uncover amount to about a dozen. But the data sets with random location effects can also have random scale effects. Our presentation includes models and methods for both location and scale effects. Typically, random location effects are taken to be normal and random scale effects to be square root inverse gamma. But in practice, other distributions often occur. Our presentation describes methods for identifying the random effects distributions.

Biographies

William Cleveland is a member of the Statistics Research Department of Bell Labs, the research and development part of Lucent Technologies. Bill's areas of research have included data visualization, model building, smoothing, Bayesian statistics, the foundations of data analysis, time series, data network measurement, graphical perception, environnmental science, and customer opinion polling. Bill has published 110 papers in these areas and three books on data visualization. He is a fellow of the ASA, IMS, AAAS, and a member of the ISI. In 1996 he was chosen as the statistcian of the year by the Chicago chapter of the ASA. Bill has taught short courses extensively during the past 20 years for many organizations including the ASA, ACM, Icon Multimedia Publishing, CSIRO, George Washington University, Institut fuer Datenanalyse, and Versuchsplanung, and U.S. Army.

Lorraine Denby is a member of the Statistics Research Department of Bell Labs, the research and development part of Lucent Technologies. Lorraine's areas of research include graphical analysis, data analysis, regression modelling and diagnostics, graphical user interface for statistical analysis, and customer opinion polling. She is a fellow of the ASA and an elected member of ISI. She has served on the ASA Board of Directors. Lorraine has taught short courses at the ASA annual and winter conferences, NCTM annual meeting, ASA chapter meetings, and NCGA.

Chuanhai Liu is a member of the Statistics Research Department of Bell Labs, the research and development part of Lucent Technologies. Chuanhai received his Ph.D. from Harvard University in 1994. His research interests include Bayesian statistics, scientific model building and checking, missing data and multiple imputation, expectation-maximization (EM) algorithms, Markov chain Monte Carlo (MCMC) methods, and time series.