An Introduction to the DA-T Gibbs Sampler for the Two-Parameter Logistic (2PL) Model and Beyond
نویسندگان
چکیده
The DA-T Gibbs sampler is proposed by Maris and Maris (2002) as a Bayesian estimation method for a wide variety of Item Response Theory (IRT) models. The present paper provides an expository account of the DAT Gibbs sampler for the 2PL model. However, the scope is not limited to the 2PL model. It is demonstrated how the DA-T Gibbs sampler for the 2PL may be used to build, quite easily, Gibbs samplers for other IRT models. Furthermore, the paper contains a novel, intuitive derivation of the Gibbs sampler and could be read for a graduate course on sampling.
منابع مشابه
Comparison of Maximum Likelihood Estimation and Bayesian with Generalized Gibbs Sampling for Ordinal Regression Analysis of Ovarian Hyperstimulation Syndrome
Background and Objectives: Analysis of ordinal data outcomes could lead to bias estimates and large variance in sparse one. The objective of this study is to compare parameter estimates of an ordinal regression model under maximum likelihood and Bayesian framework with generalized Gibbs sampling. The models were used to analyze ovarian hyperstimulation syndrome data. Methods: This study use...
متن کاملBayesian analysis of outlier problems using the Gibbs sampler
We consider the Bayesian analysis of outlier models. We show that the Gibbs sampler brings considerable conceptual and computational simplicity to the problem of calculating posterior marginals. Although other techniques for finding posterior marginals are available, the Gibbs sampling approach is notable for its ease of implementation. Allowing the probability of an outlier to he unknown intro...
متن کاملRobit Regression: A Simple Robust Alternative to Logistic and Probit Regression
Logistic and probit regression models are commonly used in practice to analyze binary response data, but the maximum likelihood estimators of these models are not robust to outliers. This paper considers a robit regression model, which replaces the normal distribution in the probit regression model with a t-distribution with a known or unknown number of degrees of freedom. It is shown that (i) ...
متن کاملThe Analysis of Bayesian Probit Regression of Binary and Polychotomous Response Data
The goal of this study is to introduce a statistical method regarding the analysis of specific latent data for regression analysis of the discrete data and to build a relation between a probit regression model (related to the discrete response) and normal linear regression model (related to the latent data of continuous response). This method provides precise inferences on binary and multinomia...
متن کاملFixed and random effects selection in linear and logistic models.
We address the problem of selecting which variables should be included in the fixed and random components of logistic mixed effects models for correlated data. A fully Bayesian variable selection is implemented using a stochastic search Gibbs sampler to estimate the exact model-averaged posterior distribution. This approach automatically identifies subsets of predictors having nonzero fixed eff...
متن کامل