On the Bayesian Nonparametric Generalization of IRT-Type Models

Martı́n, Ernesto San; Jara, Alejandro; Rolin, Jean-Marie; Mouchart, Michel

doi:10.1007/s11336-011-9213-9

Cited by 25 publications

(34 citation statements)

References 49 publications

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“…Specifically, it is important to stress that under parametrization (2), β R represents the mean of random effects, and b i represents the subject-specific deviation from the mean. It follows that fixing the mean of the normal prior distribution for the random effects b at zero in the parametric context corresponds to an identification restriction for the model parameters (see e.g., Newton, 1994; San Martín, Jara, Rolin, and Mouchart, 2007). Equivalently, the random probability measure must be appropriately restricted in a semiparametric GLMM specification.…”

Section: Implemented Modelsmentioning

confidence: 99%

“…We consider semiparametric versions of the models where the abilities distribution G is modeled using DP, PT and DPM priors. To avoid identification problems in the semiparametric specification of the model (see, San Martín et al , 2007), we fixed the first difficulty parameter at 0 and consider a normal prior for the remaining elements in the vector

{bold-italic β}_{2 : p} ∣ {bold-italic β}_{0}, {bold-italicS}_{β_{0}} ~ N_{p - 1} (β_{0}, S_{β_{0}}) .

…”

Section: Implemented Modelsmentioning

confidence: 99%

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DPpackage: Bayesian Semi- and Nonparametric Modeling inR

Hanson²,

et al. 2011

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Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on a function space, such as the space of all probability distributions or the space of all regression functions. Unfortunately, posterior distributions ranging over function spaces are highly complex and hence sampling methods play a key role. This paper provides an introduction to a simple, yet comprehensive, set of programs for the implementation of some Bayesian non- and semi-parametric models in , DPpackage. Currently DPpackage includes models for marginal and conditional density estimation, ROC curve analysis, interval-censored data, binary regression data, item response data, longitudinal and clustered data using generalized linear mixed models, and regression data using generalized additive models. The package also contains functions to compute pseudo-Bayes factors for model comparison, and for eliciting the precision parameter of the Dirichlet process prior. To maximize computational efficiency, the actual sampling for each model is carried out using compiled FORTRAN.

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Section: Implemented Modelsmentioning

confidence: 99%

{bold-italic β}_{2 : p} ∣ {bold-italic β}_{0}, {bold-italicS}_{β_{0}} ~ N_{p - 1} (β_{0}, S_{β_{0}}) .

…”

Section: Implemented Modelsmentioning

confidence: 99%

DPpackage: Bayesian Semi- and Nonparametric Modeling inR

Hanson²,

et al. 2011

Self Cite

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show abstract

“…Recently, San Martín, Jara, Rolin, and Mouchart (2011) provided a rigorous discussion of the identification of IRT-type models. They pointed out that the identification of the measurement equation and the structural equation does not imply the identification of the whole model.…”

Section: A Generalized Semiparametric Semmentioning

confidence: 99%

“…This result is in general true. The theories and methodologies developed by Jara et al (2008) and San Martín et al (2011) may also be used to help provide a rigorous proof for the identification of the proposed model. Further research is required for this investigation.…”

Section: A Generalized Semiparametric Semmentioning

confidence: 99%

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

Song

Cai

et al. 2013

Psychometrika

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In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types—continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.

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“…The purpose of this paper is not to address the issue of identifiability for any of the models above in much detail, nor is it to derive sufficient restrictions to identify these models. Discussions of those topics may be found, for instance, in , Verhelst (2002), Fischer (2004), , ), Reiersøl (1950, ), San Martín, Gonzáles, and Tuerlinckx (2009), San Martín, Jara, Rolin, and Mouchart (2011, and . However, as parameter linking, which is the focus of this paper, is required due to lack of identifiability, we present some concepts related to identifiability and then present a few examples that demonstrate the lack of identifiability of polytomous IRT models.…”

Section: The Need To Linkmentioning

confidence: 99%

Response model parameter linking

Barrett¹

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On the Bayesian Nonparametric Generalization of IRT-Type Models

Abstract: Bayesian identification, Bayesian consistency, Rasch model, Rasch Poisson counts model, Dirichlet processes, Pólya tree processes,

Cited by 25 publications

References 49 publications

DPpackage: Bayesian Semi- and Nonparametric Modeling inR

DPpackage: Bayesian Semi- and Nonparametric Modeling inR

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

Response model parameter linking

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