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Stan Case Studies,   Volume 5   (2018)

open-source methods and models The case studies on this page are intended to reflect best practices in

We require In this tutorial, we illustrate how to fit a multilevel linear model within a full Bayesian framework using rstanarm.

This tutorial is aimed primarily at educational researchers who have used lme4 in R to fit models to their data and who may be interested in learning how to fit Bayesian multilevel models.

However, for readers who have not used lme4 before, we briefly review the use of the package for fitting multilevel models.

data has a neighborhood structure, ICAR models provide spatial smoothing by

using simple examples based on simulation to show that all

points are far away in high dimensions and that the mode is an atypical

View (HTML) This case study discusses the common pathologies of Bayesian mixture models as well

View (HTML) This case study reviews the basics of weakly-informative priors and how the choice

View (HTML) This document details sparse exact conditional autoregressive (CAR) models in Stan as an extension of previous work on approximate sparse CAR models in Stan.

Sparse representations seem to give order of magnitude efficiency gains, scaling better for large spatial data sets.

View (HTML) This case study replicates the analysis of home radon levels using hierarchical

View (HTML) This case study documents a Stan model for the two-parameter logistic model (2PL) with hierarchical priors.

A brief simulation indicates that the Stan model successfully recovers the generating parameters.

An example using a grade 12 science assessment is provided.

View (HTML) This case study documents a Stan model for the rating scale model (RSM) and the generalized rating scale model (GRSM) with latent regression.

The latent regression portion of the models may be restricted to an intercept only, yielding a standard RSM or GRSM.

A brief simulation indicates that the Stan models successfully recover the generating parameters.

An example using a survey of public perceptions of science and technology is provided.

View (HTML) This case study documents a Stan model for the partial credit model (PCM) and the generalized partial credit model (GPCM) with latent regression.

The latent regression portion of the models may be restricted to an intercept only, yielding a standard PCM or GPCM.

A brief simulation indicates that the Stan models successfully recover the generating parameters.

An example using the TIMSS 2011 mathematics assessment is provided View (HTML) This case study documents Stan models for the Rasch and two-parameter logistic models with latent regression.

The latent regression portion of the models may be restricted to an intercept only, yielding standard versions of the models.

An example using a grade 12 science assessment is provided.

View (HTML) This case study documents a Stan model for the DINA model with independent attributes.

A Simulation indicates that the Stan model successfully recovers the generating parameters and predicts respondents’ attribute mastery.

A Stan model with no structure of the attributes is also discussed and applied to the simulated data.

An example using a subset of the fraction subtraction data is provided.

data (aka sharing strength) across items for repeated binary trial

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