MCMC is by its very nature a serial algorithm -- each iteration depends on the results of the last iteration. It is, therefore, rather difficult to parallelize MCMC code so that a single chain will run more quickly by splitting … Continue reading → [Read more...]

This post demonstrates how to tune the sampler for optimal acceptance probabilities and demonstrates that the whole sampler works. Tuning the complete sampler for acceptance rate Tuning the sampler's acceptance rates consists of running the sampler several times while tweaking … Continue reading → [Read more...]

The Bayesian 2PL IRT model we defined in Post 1 set a hyper-prior on the variance of the person ability parameters. This post implements the sampler for this parameter as a Gibbs step. We will check that Gibbs step is … Continue reading → [Read more...]

In this post, we will build the samplers for the item parameters using the generic functions developed in Post 5 and Post 6. We will check that the samplers work by running them on the fake data from Post 2, … Continue reading → [Read more...]

In this post we refactor the proposal function from the previous post into a generic normal proposal function. This allows us to implement normal proposals for the (yet to be developed) samplers for the item parameters without duplicating code. Our … Continue reading → [Read more...]

A best practice in software engineering is to re-use code instead of duplicating it. One reason for this is that it makes finding and fixing bugs easier. You only have to find the bug once instead of finding it every … Continue reading → [Read more...]

The previous post outlined the general strategy of writing a MH within Gibbs sampler by breaking the code into two levels: a high level shell and a series of lower-level samplers which do the actual work. This post discusses the … Continue reading → [Read more...]

In the chapter, we argue that a useful way to develop a Metropolis-Hastings (MH) within Gibbs sampler is to split the code into two levels. The top level is the "shell" of the MH within Gibbs algorithm, which sets up … Continue reading → [Read more...]

In order to check that an estimation algorithm is working properly, it is useful to see if the algorithm can recover the true parameter values in one or more simulated "test" data sets. This post explains how to build such … Continue reading → [Read more...]

In this post, we define the Two-Parameter Logistic (2PL) IRT model, derive the complete conditionals that will form the basis of the sampler, and discuss our choice of prior specification. We can find the appropriate values of numerically in R … Continue reading → [Read more...]

R is an interpreted programming language that makes it easy to think about statistics instead of thinking about programming. Unlike other programming languages, R is commonly used by typing commands one-at-a-time in an interactive session. RStudio is a program that … Continue reading → [Read more...]