Mike Hughes writes: I have been looking a your blog entries from about 8 years ago in which you comment on the number of groups that is appropriate in multilevel regression. I have a research problem in which I have 6 groups and would like to use multilevel regression. Here is the situation. I have […]

**Multilevel Modeling**category.

## My quick answer is that I would analyze all 10 outcomes using a multilevel model.

David Shor writes: Suppose you’re conducting an experiment on the effectiveness of a pain medication, but in the post survey, measure a large number of indicators of well being (Sleep quality, self reported pain, ability to get tasks done, anxiety levels, etc). After the experiment, the results are insignificant (or the posterior effect size isn’t […]

## Actually, I’d just do full Bayes

Dave Clark writes: I was hoping for your opinion on a topic related to hierarchical models. I am an actuary and have generally worked with the concept of hierarchical models in the context of credibility theory. The text by Bühlmann and Gisler (A Course in Credibility Theory; Springer) sets up the mixed models under the […]

## Mister P: Challenges in Generalizing from Sample to Population (my talk at the Ross-Royall Symposium at Johns Hopkins this Friday)

Mister P: Challenges in Generalizing from Sample to Population Andrew Gelman, Department of Statistics and Department of Political Science, Columbia University With internet surveys, nonrepresentativeness and nonresponse are bigger concerns than ever. The natural approach is to adjust for more information, demographic and otherwise, to align the sample with the population. We demonstrate the effectiveness […]

## Hierarchical models for phylogeny: Here’s what everyone’s talking about

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 am hoping that you can help me settle a debate. My collaborators and I have […]

## Pooling is relative to the model

Ryan Raaum writes: I’m hoping you’ll be willing to shed some light on a question I have regarding “pooling” in modeling. In your book with Jennifer Hill, you lay out two ends of a spectrum for dealing with structured data: (1) “Complete pooling” – ignoring the groups and pooling everything together for an overall average […]

## Forking paths vs. six quick regression tips

Bill Harris writes: I know you’re on a blog delay, but I’d like to vote to raise the odds that my question in a comment to http://andrewgelman.com/2015/09/15/even-though-its-published-in-a-top-psychology-journal-she-still-doesnt-believe-it/gets discussed, in case it’s not in your queue. It’s likely just my simple misunderstanding, but I’ve sensed two bits of contradictory advice in your writing: fit one complete model all at […]

## Where the fat people at?

Pearly Dhingra points me to this article, “The Geographic Distribution of Obesity in the US and the Potential Regional Differences in Misreporting of Obesity,” by Anh Le, Suzanne Judd, David Allison, Reena Oza-Frank, Olivia Affuso, Monika Safford, Virginia Howard, and George Howard, who write: Data from BRFSS [the behavioral risk factor surveillance system] suggest that […]

## Stunning breakthrough: Using Stan to map cancer screening!

Paul Alper points me to this article, Breast Cancer Screening, Incidence, and Mortality Across US Counties, by Charles Harding, Francesco Pompei, Dmitriy Burmistrov, Gilbert Welch, Rediet Abebe, and Richard Wilson. Their substantive conclusion is there’s too much screening going on, but here I want to focus on their statistical methods: Spline methods were used to […]

## One thing I like about hierarchical modeling is that is not just about criticism. It’s a way to improve inferences, not just a way to adjust p-values.

In an email exchange regarding the difficulty many researchers have in engaging with statistical criticism (see here for a recent example), a colleague of mine opined: Nowadays, promotion requires more publications, and in an academic environment, researchers are asked to do more than they can. So many researchers just work like workers in a product […]

## “Once I was told to try every possible specification of a dependent variable (count, proportion, binary indicator, you name it) in a regression until I find a significant relationship. That is it, no justification for choosing one specification over another besides finding significance. . . . In another occasion I was asked to re-write a theory section of a paper to reflect an incidental finding from our analysis, so that it shows up as if we were asking a question about the incidental finding and had come up with the supported hypothesis a priori. . . .”

Ethan Bolker points me to this discussion. My reply: As discussed in my paper with Hill and Yajima, I think the best approach is to analyze all comparisons rather than picking just some. If there is prior understanding that some comparisons are more important than others, that understanding can be included as predictors in the […]

## Hierarchical modeling when you have only 2 groups: I still think it’s a good idea, you just need an informative prior on the group-level variation

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 question about hierarchical modeling. If you have the time, I would greatly appreciate any advice […]

## Judea Pearl and I briefly discuss extrapolation, causal inference, and hierarchical modeling

OK, I guess it looks like the Buzzfeed-style headlines are officially over. Anyway, Judea Pearl writes: I missed the discussion you had here about Econometrics: Instrument locally, extrapolate globally, which also touched on my work with Elias Bareinboim. So, please allow me to start a new discussion about extrapolation and external validity. First, two recent […]

## How does Brad Cooper analyze hierarchical survey data with post-stratification?

Laura Holder writes: I am working on a project involving a large survey data set and am interested in applying a model-based approach in the context of post-stratification (as you frequently discuss). I’m attempting to determine the most suitable approach for my circumstance. The data set I am working with is collected via a two […]

## Inference from an intervention with many outcomes, not using “statistical significance”

Kate Casey writes: I have been reading your papers “Type S error rates for classical…” and “Why We (Usually) Don’t Have to Worry…” with great interest and would be grateful for your views on the appropriateness of a potentially related application. I have a non-hierarchical dataset of 28 individuals who participated in a randomized control […]

## You won’t believe these stunning transformations: How to parameterize hyperpriors in hierarchical models?

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 that I’d like to ask. I’ve been trying to understand one of the hierarchical models […]