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The hierarchical rater model for rated test items and its application to largescale educational assessment data. Paper presented April 23
, 1999
"... Single and multiple ratings of test items have become a stock component of standardized educational tests and surveys. For both formative and summative evaluation of raters, a number of multipleread rating designs are now commonplace (Wilson and Hoskens, 1999), including designs with as many as six ..."
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Single and multiple ratings of test items have become a stock component of standardized educational tests and surveys. For both formative and summative evaluation of raters, a number of multipleread rating designs are now commonplace (Wilson and Hoskens, 1999), including designs with as many as six raters per item (e.g. Sykes, Heidorn and Lee, 1999). As digital image based distributed rating becomes commonplace, we expect the use of multiple raters as a routine part of test scoring to grow; increasing the number of raters also raises the possibility of improving the precision of examinee proficiency estimates. In this paper we develop Patz’s (1996) hierarchical rater model (HRM) for polytomously scored item response data, and show how it can be used, for example, to scale examinees and items, to model aspects of consensus among raters, and to model individual rater severity and consistency effects. The HRM treats examinee responses to openended items as unobserved discrete variables, and it explicitly models the “proficiency ” of raters in assigning accurate scores as well as the proficiency
Multilevel Structural Equation Models for the Analysis of Comparative Data on Educational Performance
"... Ministe`re de l’Education Nationale, de l’Enseignement Supe´rieur ..."
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Ministe`re de l’Education Nationale, de l’Enseignement Supe´rieur
Data Augmentation, Frequentist Estimation, and the Bayesian Analysis of Multinomial Logit Models
, 2006
"... This article introduces a generalization of Tanner and Wong’s data augmentation algorithm which can be used when the complete data posterior distribution cannot be directly sampled. The algorithm proposes parameter values based on complete data sampling distributions of convenient frequentist estim ..."
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This article introduces a generalization of Tanner and Wong’s data augmentation algorithm which can be used when the complete data posterior distribution cannot be directly sampled. The algorithm proposes parameter values based on complete data sampling distributions of convenient frequentist estimators which ignore some information in the complete data likelihood. The proposals are filtered using a MetropolisHastings probability to produce draws from the Bayesian posterior distribution of interest. The result is a method of deriving closed form MetropolisHastings proposals which do not need to be tuned. The method is used to sample the parameters of a multinomial logit model from their posterior distribution in a manner similar to Albert and Chib’s (1993) algorithm for probit regression. The algorithm converges geometrically ergodically, and its convergence rate can be accelerated through the use of working parameter methods developed for standard data augmentation algorithms. As with standard data augmentation, the method remains useful when multinomial logit models are embedded in more complicated settings, such as hierarchical models. The algorithm’s utility in complicated settings is illustrated
Locally dependent latent trait models for polytomous responses. Manuscript submitted for publication
, 2002
"... Psychological tests often involve item dusters that are designed to solicit responses to behavioral stimuli. The dependency between individual responses within dusters beyond that which can be explained by the underlying trait sometimes reveals structures that are of substantive interest. The paper ..."
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Psychological tests often involve item dusters that are designed to solicit responses to behavioral stimuli. The dependency between individual responses within dusters beyond that which can be explained by the underlying trait sometimes reveals structures that are of substantive interest. The paper describes two general classes of models for this type of locally dependent responses. Specifically, the models indude a generalized loglinear representation and a hybrid parameterization model for polytomous data. A compact matrix notation designed to succinctly represent the system of complex multivariate polytomous responses is presented. The matrix representation creates the necessary formulation for the locally dependent kernel for polytomous item responses. Using polytomous data from an inventory of hostility, we provide illustrations as to how the locally dependent models can be used in psychological measurement. Key words: generalized loglineax model, hybrid kernel, combination dependency models, EM algorithm, social inhibition.
Posterior Sampling of Multinomial Logit Models Using Latent Exponential Variables
, 2001
"... This article describes an augmented variables method for sampling the posterior distribution of multinomial logit models, where the probability that unit i assumes the value m is proportional to exp(g m (x i jfi)). The method cycles between sampling a set of exponential random variables with rate ..."
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This article describes an augmented variables method for sampling the posterior distribution of multinomial logit models, where the probability that unit i assumes the value m is proportional to exp(g m (x i jfi)). The method cycles between sampling a set of exponential random variables with rates exp(gm (x i jfi)), proposing new parameters from a distribution estimated using transformations of the exponential variables, and accepting or rejecting the proposal according to a MetropolisHastings probability. The method requires neither tuning nor iterative root finding to construct proposal distributions. It is fast, adaptive, and accepts either categorical or continuous covariates. If the g m have distinct parameters then conditioning on the exponential variables renders the parameters of each g m independent in the complete data likelihood.
Data Augmentation for the Bayesian Analysis of Multinomial Logit Models
 IN PROCEEDINGS OF THE 39TH ANNUAL MEETING OF THE ASSOCIATION FOR COMPUTATIONAL LINGUISTICS
, 2003
"... This article introduces a Markov chain Monte Carlo (MCMC) method for sampling the parameters of a multinomial logit model from their posterior distribution. Let y i # {0, . . . , M} denote the categorical response of subject i with covariates x i = (x i1 , . . . , x ip ) . Let X = (x 1 , . . . , ..."
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This article introduces a Markov chain Monte Carlo (MCMC) method for sampling the parameters of a multinomial logit model from their posterior distribution. Let y i # {0, . . . , M} denote the categorical response of subject i with covariates x i = (x i1 , . . . , x ip ) . Let X = (x 1 , . . . , xn ) denote the design matrix, and let y = (y 1 , . . . , yn ) . Multinomial logit models relate y i to x i through p(y i = m) # exp{gm (x i #)} = # im (1) where g m (x i #) is a linear function and # is a parameter vector. Adding the same constant to each g m (x#) leaves (1) unchanged, so one commonly assumes g 0 (x#) = 0 to preserve identifiability. The general function notation masks subtleties in the linear predictor that distinguish several varieties of multinomial logit models. For example, equation (1) can be made to model either ordinal or nominal responses by suitably constraining the linear predictor. By extending x through basis expansions equation (1) includes generalized additive multinomial logit models (Abe, 1999)