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13
Assessment and Propagation of Model Uncertainty
, 1995
"... 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 ..."
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Cited by 120 (0 self)
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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.
Bayesian estimation of a multilevel IRT model using Gibbs sampling
 Psychometrika
, 2001
"... In this article, atwolevel regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather an observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficu ..."
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Cited by 28 (5 self)
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In this article, atwolevel regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather an observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement rror. Another advantage is that, contrary to observed scores, latent scores are testindependent, which offers the possibility of using results from different tests in one analysis where the parameters of the IRT model and the multilevel model can be concurrently estimated. The twoparameter no mal ogive model is used for the IRT measurement model. It will be shown that he parameters of the twoparameter normal ogive model and the multilevel model can be estimated in a Bayesian framework using Gibbs sampling. Examples using simulated and real data are given.
Inference and Hierarchical Modeling in the Social Sciences
, 1995
"... this paper I (1) examine three levels of inferential strength supported by typical social science datagathering 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 effective ..."
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Cited by 22 (6 self)
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this paper I (1) examine three levels of inferential strength supported by typical social science datagathering 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 metaanalysis from the perspective of causal inference; and (3) recommend the increased use of Gibbs sampling and other Markovchain Monte Carlo (MCMC) methods in the application of HMs in the social sciences, so that comparisons between MCMC and betterestablished fitting methodsincluding full or restricted maximum likelihood estimation based on the EM algorithm, Fisher scoring or iterative generalized least squaresmay be more fully informed by empirical practice.
Examining Relationships Between Where Students Start and How Rapidly They Progress: Implications for Constructing Indicators That Help Illuminate the Distribution of Achievement Within Schools
 University of California, National Center for
, 2001
"... 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. ..."
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Cited by 13 (1 self)
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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.
Residuals and Outliers in Repeated Measures Random Effects Models
 Expected Total
, 1995
"... 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 d ..."
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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, GoodnessofFit, 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 900951772 U.S....
Constrained Homogeneity Analysis With Applications To Hierarchical Data
 Hierarchical Data,” UCLA Statistical Series, #207
, 1996
"... . 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 withingroups and betweengrou ..."
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Cited by 3 (3 self)
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. 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 withingroups and betweengroups 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...
Bayesian modeling of measurement error in predictor variables using item response theory. Psychometrika 2003; 68:169191
"... It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, axe treated as latent variables. The normal ogive model is used to describe the relation between t ..."
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Cited by 3 (1 self)
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It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, axe treated as latent variables. The normal ogive model is used to describe the relation between the latent variables and dichotomous observed variables, which may be responses to tests or questionnaires. It will be shown that the multilevel model with measurement error in the observed predictor variables can be estimated in a Bayesian framework using Gibbs sampling. In this article, handling measurement error via the normal ogive model is compared with alternative approaches using the classical true score model. Examples using real data are given.
Reexamining, reaffirming and improving the application of hierarchical models
 Journal of Educational and Behavioral Statistics
, 1995
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Residuals and Outliers in Bayesian Random Effects Models
, 1994
"... Common repeated measures random effects models contain two random components, a random person effect and timevarying 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 ..."
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Common repeated measures random effects models contain two random components, a random person effect and timevarying 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 goodnessoffit tests are also developed. Distribution theory is given, along with some geometric intuition. Key Words: Bayesian Data Analysis, GoodnessofFit, Hierarchical Models, Observed Errors, Repeated Measures. 1 Introduction...
Strategies for Inference Robustness in Complex Modelling: An Application to Longitudinal Performance Measures.
, 1999
"... 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 t ..."
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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 fourstage 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 semiformal, in that they are embedded in a decisiontheoretic framework but require substantive input for any specific application. The ideas are illustrated on a dataset comprising the success rates of 46 invitro 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 nonlinear 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 lesssupported models, these would not be any more parsimonious. Technical issues include fitting mixture models of alternative hierarchical longitudinal models, t...