scholarly journals Simulation-based Bayesian inference for latent traits of item response models: Introduction to the ltbayes package for R

2014 ◽  
Vol 47 (4) ◽  
pp. 1309-1327 ◽  
Author(s):  
Timothy R. Johnson ◽  
Kristine M. Kuhn
Keyword(s):  
Bayesian Inference ◽  
Item Response ◽  
Response Models ◽  
Item Response Models ◽  
Simulation Based ◽  
Latent Traits

scholarly journals Fitting Bayesian item response models in Stata and Stan

2017 ◽  
Vol 17 (2) ◽  
pp. 343-357 ◽  
Author(s):  
Robert L. Grant ◽  
Daniel C. Furr ◽  
Bob Carpenter ◽  
Andrew Gelman
Keyword(s):  
Monte Carlo ◽  
Education Research ◽  
Bayesian Inference ◽  
Item Response ◽  
Bayesian Methods ◽  
Rasch Model ◽  
Response Models ◽  
Item Response Models ◽  
The Rasch Model ◽  
General Range

Stata users have access to two easy-to-use implementations of Bayesian inference: Stata's native bayesmh command and StataStan, which calls the general Bayesian engine, Stan. We compare these implementations on two important models for education research: the Rasch model and the hierarchical Rasch model. StataStan fits a more general range of models than can be fit by bayesmh and uses a superior sampling algorithm, that is, Hamiltonian Monte Carlo using the no-U-turn sampler. Furthermore, StataStan can run in parallel on multiple CPU cores, regardless of the flavor of Stata. Given these advantages and given that Stan is open source and can be run directly from Stata do-files, we recommend that Stata users interested in Bayesian methods consider using StataStan.

Higher-Order Item Response Models for Hierarchical Latent Traits

2013 ◽  
Vol 37 (8) ◽  
pp. 619-637 ◽  
Author(s):  
Hung-Yu Huang ◽  
Wen-Chung Wang ◽  
Po-Hsi Chen ◽  
Chi-Ming Su
Keyword(s):  
Item Response ◽  
Higher Order ◽  
Response Models ◽  
Item Response Models ◽  
Latent Traits

scholarly journals Estimating Parameters of Dichotomous and Ordinal Item Response Models with Gllamm

2007 ◽  
Vol 7 (3) ◽  
pp. 313-333 ◽  
Author(s):  
Xiaohui Zheng ◽  
Sophia Rabe-Hesketh
Keyword(s):  
Item Response ◽  
Latent Variable ◽  
Rating Scale ◽  
Ordinal Scale ◽  
Response Models ◽  
Item Response Models ◽  
Explanatory Variables ◽  
Test Items ◽  
Measurement Models ◽  
Latent Traits

Item response theory models are measurement models for categorical responses. Traditionally, the models are used in educational testing, where responses to test items can be viewed as indirect measures of latent ability. The test items are scored either dichotomously (correct–incorrect) or by using an ordinal scale (a grade from poor to excellent). Item response models also apply equally for measurement of other latent traits. Here we describe the one- and two-parameter logit models for dichotomous items, the partial-credit and rating scale models for ordinal items, and an extension of these models where the latent variable is regressed on explanatory variables. We show how these models can be expressed as generalized linear latent and mixed models and fitted by using the user-written command gllamm.

scholarly journals Scale Alignment in the Between-Item Multidimensional Partial Credit Model

2021 ◽  
pp. 014662162110131
Author(s):  
Leah Feuerstahler ◽  
Mark Wilson
Keyword(s):  
Item Response ◽  
Kindergarten Readiness ◽  
Latent Trait ◽  
Individual Development ◽  
Partial Credit Model ◽  
Partial Credit ◽  
Response Models ◽  
Item Response Models ◽  
Item Parameters ◽  
Polytomous Item Response

In between-item multidimensional item response models, it is often desirable to compare individual latent trait estimates across dimensions. These comparisons are only justified if the model dimensions are scaled relative to each other. Traditionally, this scaling is done using approaches such as standardization—fixing the latent mean and standard deviation to 0 and 1 for all dimensions. However, approaches such as standardization do not guarantee that Rasch model properties hold across dimensions. Specifically, for between-item multidimensional Rasch family models, the unique ordering of items holds within dimensions, but not across dimensions. Previously, Feuerstahler and Wilson described the concept of scale alignment, which aims to enforce the unique ordering of items across dimensions by linearly transforming item parameters within dimensions. In this article, we extend the concept of scale alignment to the between-item multidimensional partial credit model and to models fit using incomplete data. We illustrate this method in the context of the Kindergarten Individual Development Survey (KIDS), a multidimensional survey of kindergarten readiness used in the state of Illinois. We also present simulation results that demonstrate the effectiveness of scale alignment in the context of polytomous item response models and missing data.

scholarly journals Introducing the StataStan Interface for Fast, Complex Bayesian Modeling Using Stan

2017 ◽  
Vol 17 (2) ◽  
pp. 330-342 ◽  
Author(s):  
Robert L. Grant ◽  
Bob Carpenter ◽  
Daniel C. Furr ◽  
Andrew Gelman
Keyword(s):  
Bayesian Inference ◽  
Item Response Theory ◽  
Open Source ◽  
Item Response ◽  
Bayesian Modeling ◽  
Inference Engine ◽  
Software Components ◽  
Statistical Software ◽  
Simulation Based ◽  
Item Response Theory Models

In this article, we present StataStan, an interface that allows simulation-based Bayesian inference in Stata via calls to Stan, the flexible, open-source Bayesian inference engine. Stan is written in C++, and Stata users can use the commands stan and windowsmonitor to run Stan programs from within Stata. We provide a brief overview of Bayesian algorithms, details of the commands available from Statistical Software Components, considerations for users who are new to Stan, and a simple example. Stan uses a different algorithm than bayesmh, BUGS, JAGS, SAS, and MLwiN. This algorithm provides considerable improvements in efficiency and speed. In a companion article, we give an extended comparison of StataStan and bayesmh in the context of item response theory models.

Stochastic Approximation Methods for Latent Regression Item Response Models

2010 ◽  
Vol 35 (2) ◽  
pp. 174-193 ◽  
Author(s):  
Matthias von Davier ◽  
Sandip Sinharay
Keyword(s):  
Item Response ◽  
Stochastic Approximation ◽  
Latent Variable ◽  
Reading Assessment ◽  
Mathematics Assessment ◽  
National Assessment ◽  
Variable Model ◽  
Response Models ◽  
Item Response Models ◽  
Latent Regression

This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates serving as predictors of the conditional distribution of ability. Applications to estimating latent regression models for National Assessment of Educational Progress (NAEP) data from the 2000 Grade 4 mathematics assessment and the Grade 8 reading assessment from 2002 are presented and results of the proposed method are compared to results obtained using current operational procedures.

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