(This is Dan, but in quick mode) I was on the subway when I saw Andrew’s last post and it doesn’t strike me as a particularly great idea. So let’s take a look at the suggestion for 8 schools using … Continue reading
So. For awhile now we’ve moved away from the uniform (or, worse, inverse-gamma!) prior distributions for hierarchical variance parameters. We’ve done half-Cauchy, folded t, and other options; now we’re favoring unit half-normal. We also have boundary-avoiding priors for point estimates, … Continue reading
Ed Vul writes: In the course of tinkering with someone else’s hairy dataset with a great many candidate explanatory variables (some of which are largely orthogonal factors, but the ones of most interest are competing “binning” schemes of the same … Continue reading
Chris Che-Castaldo writes: I am trying to compute variance components for a hierarchical model where the group level has two binary predictors and their interaction. When I model each of these three predictors as N(0, tau) the model will not … Continue reading
This whole exchange is interesting and is closely related to our current research on prior distributions and Bayesian inference for varying-intercept, varying-slope models.
It all started when Sean Zhang asked,
I am using your book to self-teach myself using R for multilevel modeling.
One question I have is that why lmer cannot provide var-cov matrix of estimates of random components. You mentioned in your book that lmer can only provide point estimates for variance component and that is one of the reasons to go Bayesian and use Bugs.
I am running a simple random intercept model using SAS glimmix and found that glimmix provides standard error for variance estimate of random intercept. I looked into glimmix document(see attachment, page 121, theta contains random effect parameters) and can imagine that SAS may use hessian or outer produce of gradient (see page for their likelihood function) to get them.
My question is then why lmer cannot do similar thing as SAS to report var-cov matrix of estimates of random components?
I replied, Continue reading
Since we’re talking about the scaled inverse Wishart . . . here’s a recent message from Chris Chatham: I have been reading your book on Bayesian Hierarchical/Multilevel Modeling but have been struggling a bit with deciding whether to model my … Continue reading
Marcus Brubaker writes:
I am currently working on a problem in computational biology using Bayesian inference and I’ve come to a question for which I hope you have an answer. In this problem there are a large number of noisy 2D images of a molecule, from which we wish to infer the 3D structure. Much of the modeling is straightforward but I have hit a roadblock. Specifically, the noise parameters for these images.
Fully Bayesian analyses of hierarchical linear models have been considered for at least forty years. A persistent challenge has been choosing a prior distribution for the hierarchical variance parameters. Proposed models include uniform distributions (on various scales), inverse-gamma distributions, and … Continue reading
Someone who would like to remain anonymous writes: I’m a student during the school year, but am working in industry this summer. I am currently attempting to overhaul my company’s model of retail demand. We advise suppliers to national retailers, … Continue reading
Elliott writes: My boss asks me: For our model to predict excess mortality around the world, we want to calculate a confidence interval around our mean estimate for total global excess deaths. We have real excess deaths for like 60 … Continue reading
The title Data Analysis Using Regression and Multilevel/Hierarchical Models hints at the problem, which is that there are a lot of names for models with hierarchical structure. Ways of saying “hierarchical model” hierarchical model a multilevel model with a single … Continue reading
Tim Disher writes: I have been asked to run some regularized regressions on a small N high p situation, which for the primary outcome has lead to more realistic coefficient estimates and better performance on cv (yay!). Rstanarm made this … Continue reading
An economist wrote in, asking why it would make sense to fit Bayesian hierarchical models instead of frequentist random effects. My reply: Short answer is that anything Bayesian can be done non-Bayesianly: just take some summary of the posterior distribution, … Continue reading
Given that Andrew started the Gremlin theme, I thought it would only be fitting to link to the following amusing blog post: Chris Brown: Choosing R packages for mixed effects modelling based on the car you drive (on the seascape … Continue reading
The other day on the Stan users list, we had a long discussion on hierarchical models in phylogeny that I thought might be of general interest, so I’m reconstructing it here. It started with this question from Ben Lambert: I … Continue reading
Dan Chamberlain writes: I am working on a Bayesian analysis of some data from a randomized controlled trial comparing two different drugs for treating seizures in children. I have been using your book as a resource and I have a … Continue reading
Isaac Armstrong writes: I was working through your textbook “Data Analysis Using Regression and Multilevel/Hierarchical Models” but wanted to learn more and started working through your “Bayesian Data Analysis” text. I’ve got a few questions about your rat tumor example … Continue reading
The Stan Model of the Week showcases research using Stan to push the limits of applied statistics. If you have a model that you would like to submit for a future post then send us an email. Our inaugural post … Continue reading
Alexander Volfovsky and Peter Hoff write: ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects … Continue reading
In a link to our back-and-forth on causal inference and the use of hierarchical models to bridge between different inferential settings, Elias Bareinboim (a computer scientist who is working with Judea Pearl) writes: In the past week, I have been … Continue reading