this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the U.S. Space Shuttle.

this paper I (1) examine three levels of inferential strength supported by typical social science data-gathering methods, and call for a greater degree of explicitness, when HMs and other models are applied, in identifying which level is appropriate; (2) reconsider the use of HMs in school effectiveness studies and meta-analysis from the perspective of causal inference; and (3) recommend the increased use of Gibbs sampling and other Markov-chain Monte Carlo (MCMC) methods in the application of HMs in the social sciences, so that comparisons between MCMC and better-established fitting methods---including full or restricted maximum likelihood estimation based on the EM algorithm, Fisher scoring or iterative generalized least squares---may be more fully informed by empirical practice.

Attending to school mean rates of change and to differences in rates of change for various demographic groups is of central importance in monitoring school performance.

An approach for developing Bayesian outlier and goodness of fit statistics is presented for the linear model and extended to a hierarchical random effects model for repeated measures data. Diagnostics for univariate outliers, missing covariates, multivariate outliers and global goodness of fit are developed. Distribution theory for the posterior of the residuals is worked out. A local approach is used to show how omitted covariates and fixed and random effects affect residual summaries. Standard plots are interpreted in light of these understandings. Key Words: Bayesian Data Analysis, Goodness-of-Fit, Hierarchical Models, Longitudinal Data, Outlier, Philosophy of Statistics, Shrinkage. 1 Introduction. This paper develops a Bayesian approach to residual analysis and extends the approach to the random effects model (REM) used to model repeated Robert E. Weiss is Assistant Professor, Department of Biostatistics, Box 177220; UCLA School of Public Health; Los Angeles CA 90095-1772 U.S....

. In this paper we extend the techniques of homogeneity analysis and nonlinear principal components analysis to a multilevel sampling design framework. We also propose some models that take advantage of the multilevel nature of the sampling design, and allow us to make within-groups and between-groups comparisons. Furthermore, it is shown that several models proposed in the literature for panel and event history data, can be casted naturally into our framework. A data set from the National Educational Longitudinal Study (NELS:88) is used to illustrate the techniques introduced in the paper. 1 2 GEORGE MICHAILIDIS AND JAN DE LEEUW 1. Introduction to Homogeneity Analysis The basic technique studied in this paper is known under many different names. For example, we have principal components of scale analysis [19, 20], factorial analysis of qualitative data [7], second method of quantification [21], multiple correspondence analysis [2, 17, 27] and homogeneity analysis [10, 15]. The tec...

Advances in computation mean it is now possible to fit a wide range of complex models, but selecting a model on which to base reported inferences is a difficult problem. Following an early suggestion of Box and Tiao, it seems reasonable to seek `inference robustness' in reported models, so that alternative assumptions that are reasonably well supported would not lead to substantially different conclusions. We propose a four-stage modelling strategy in which we: iteratively assess and elaborate an initial model, measure the support for each of the resulting family of models, assess the influence of adopting alternative models on the conclusions of primary interest, and identify whether an approximate model can be reported. These stages are semi-formal, in that they are embedded in a decision-theoretic framework but require substantive input for any specific application. The ideas are illustrated on a dataset comprising the success rates of 46 in-vitro fertilisation clinics over three years. The analysis supports a model that assumes 43 of the 46 clinics have odds on success that are evolving at a constant proportional rate (i.e. linear on a logit scale), while three clinics are outliers in the sense of showing non-linear trends. For the 43 `linear' clinics, the intercepts and gradients can be assumed to follow a bivariate normal distribution except for one outlying intercept: the odds on success are significantly increasing for four clinics and significantly decreasing for three. This model displays considerable inference robustness and, although its conclusions could be approximated by other less-supported models, these would not be any more parsimonious. Technical issues include fitting mixture models of alternative hierarchical longitudinal models, t...

Common repeated measures random effects models contain two random components, a random person effect and time-varying errors. An observation can be an outlier due to either an extreme person effect or an extreme time varying error. Outlier statistics are presented that can distinguish between these types of outliers. For each person there is one statistic per observation, plus one statistic per random effect. Methodology is developed to reduce the explosion of statistics to two summary outlier statistics per person; one for the random effects and one for the time varying errors. If either of these screening statistics are large, then individual statistics for each observation or random effect can be inspected. Multivariate, targeted outlier statistics and goodness-of-fit tests are also developed. Distribution theory is given, along with some geometric intuition. Key Words: Bayesian Data Analysis, Goodness-of-Fit, Hierarchical Models, Observed Errors, Repeated Measures. 1 Introduction...

Variables Using Stata will prove indispensable as a guide for analyzing categorical data using Stata. This book is suitable for new users and seasoned programmers alike and is certain to inspire researchers to move beyond reporting effects toward uncovering and elaborating important aspects of the relationship between independent variables and outcomes in models for categorical data. The book is also an excellent resource for students and instructors in courses on categorical data modeling. All of the examples used in this book, as well as examples from Long (1997), can be downloaded from the authors’ Web site. Stata is well known for being a state-of-the-art statistical package, due in part to a growing number of contributions from a large and diverse user base. In fact, many current Stata estimation procedures for categorical data models are implemented as user-contributed “macros” in the form of ado files. The authors augment Stata’s rich set of existing

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