Autoregressive (AR) models are some of the most widely used models in applied economics, among other disciplines, because of their generality and simplicity. However, the dynamic characteristics of real economic and financial data can change from one time period to another, limiting the applicability of linear time-series models. For example, the change of unemployment rate is a function of the state of the economy, whether it is expanding or contracting. A variety of models have been developed that allow time-series dynamics to depend on the regime of the system they are part of. The class of regime-dependent models include Markov-switching, smooth transition, and threshold autoregressive (TAR) models. Read more…

Monitoring lineages of the Omicron variant of the SARS-CoV-2 virus continues to be an important health consideration. The World Health Organization identifies BA.1, BA.1.1, and the most recent BA.2 as the most common sublineages. A recent study from Japan, Yamasoba et al. (2022), compares, among other characteristics, the transmissibility of these three Omicron lineages with the latest Delta variant. It identifies BA.2 to have the highest transmissibility of the four. Preprint of the study is available at bioarxiv.org. One interesting aspect of the study is the application of Bayesian multilevel models for representing lineage growth dynamics. In this post, I demonstrate how to use Stata’s bayesmh and bayesstats summary commands to perform similar analysis. Read more…

In this blog post, I’d like to give you a relatively nontechnical introduction to Markov chain Monte Carlo, often shortened to “MCMC”. MCMC is frequently used for fitting Bayesian statistical models. There are different variations of MCMC, and I’m going to focus on the Metropolis–Hastings (M–H) algorithm. In the interest of brevity, I’m going to omit some details, and I strongly encourage you to read the [BAYES] manual before using MCMC in practice.

Let’s continue with the coin toss example from my previous post Introduction to Bayesian statistics, part 1: The basic concepts. We are interested in the posterior distribution of the parameter \(\theta\), which is the probability that a coin toss results in “heads”. Our prior distribution is a flat, uninformative beta distribution with parameters 1 and 1. And we will use a binomial likelihood function to quantify the data from our experiment, which resulted in 4 heads out of 10 tosses. Read more…

In this blog post, I’d like to give you a relatively nontechnical introduction to Bayesian statistics. The Bayesian approach to statistics has become increasingly popular, and you can fit Bayesian models using the bayesmh command in Stata. This blog entry will provide a brief introduction to the concepts and jargon of Bayesian statistics and the bayesmh syntax. In my next post, I will introduce the basics of Markov chain Monte Carlo (MCMC) using the Metropolis–Hastings algorithm. Read more…

This post was written jointly with Yulia Marchenko, Executive Director of Statistics, StataCorp.

As of update 03 Mar 2016, bayesmh provides a more convenient way of fitting distributions to the outcome variable. By design, bayesmh is a regression command, which models the mean of the outcome distribution as a function of predictors. There are cases when we do not have any predictors and want to model the outcome distribution directly. For example, we may want to fit a Poisson distribution or a binomial distribution to our outcome. This can now be done by specifying one of the four new distributions supported by bayesmh in the likelihood() option: dexponential(), dbernoulli(), dbinomial(), or dpoisson(). Previously, the suboption noglmtransform of bayesmh‘s option likelihood() was used to fit the exponential, binomial, and Poisson distributions to the outcome variable. This suboption continues to work but is now undocumented.

For examples, see Beta-binomial model, Bayesian analysis of change-point problem, and Item response theory under Remarks and examples in [BAYES] bayesmh.

We have also updated our earlier “Bayesian binary item response theory models using bayesmh” blog entry to use the new dbernoulli() specification when fitting 3PL, 4PL, and 5PL IRT models.

This post was written jointly with Yulia Marchenko, Executive Director of Statistics, StataCorp.

Overview
1PL model
2PL model
3PL model
4PL model
5PL model
Conclusion

Item response theory (IRT) is used for modeling the relationship between the latent abilities of a group of subjects and the examination items used for measuring their abilities. Stata 14 introduced a suite of commands for fitting IRT models using maximum likelihood; see, for example, the blog post Spotlight on irt by Rafal Raciborski and the [IRT] Item Response Theory manual for more details. In this post, we demonstrate how to fit Bayesian binary IRT models by using the redefine() option introduced for the bayesmh command in Stata 14.1. We also use the likelihood option dbernoulli() available as of the update on 03 Mar 2016 for fitting Bernoulli distribution. If you are not familiar with the concepts and jargon of Bayesian statistics, you may want to watch the introductory videos on the Stata Youtube channel before proceeding.

Introduction to Bayesian analysis, part 1 : The basic concepts
Introduction to Bayesian analysis, part 2: MCMC and the Metropolis-Hastings algorithm

We use the abridged version of the mathematics and science data from DeBoeck and Wilson (2004), masc1. The dataset includes 800 student responses to 9 test questions intended to measure mathematical ability.

The irt suite fits IRT models using data in the wide form – one observation per subject with items recorded in separate variables. To fit IRT models using bayesmh, we need data in the long form, where items are recorded as multiple observations per subject. We thus reshape the dataset in a long form: we have a single binary response variable, y, and two index variables, item and id, which identify the items and subjects, respectively. This allows us to Read more…

This post was written jointly with Nikolay Balov, Senior Statistician and Software Developer, StataCorp.

A question on Statalist motivated us to write this blog entry.

A user asked if the churdle command (http://www.stata.com/stata14/hurdle-models/) for fitting hurdle models, new in Stata 14, can be combined with the bayesmh command (http://www.stata.com/stata14/bayesian-analysis/) for fitting Bayesian models, also new in Stata 14:

http://www.statalist.org/forums/forum/general-stata-discussion/general/1290426-comibining-bayesmh-and-churdle

Our initial reaction to this question was ‘No’ or, more precisely, ‘Not easily’—hurdle models are not among the likelihood models supported by bayesmh. One can write a program to compute the log likelihood of the double hurdle model and use this program with bayesmh (in the spirit of http://www.stata.com/stata14/bayesian-evaluators/), but this may seem like a daunting task if you are not familiar with Stata programming.

And then we realized, why not simply call churdle from the evaluator to compute the log likelihood? All we need is for churdle to evaluate the log likelihood at specific values of model parameters without performing iterations. This can be achieved by specifying churdle‘s options from() and iterate(0). Read more…