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Archive of posts filed under the Multilevel Modeling category.

Hamiltonian Monte Carlo using an adjoint-differentiated Laplace approximation: Bayesian inference for latent Gaussian models and beyond

Charles Margossian, Aki Vehtari, Daniel Simpson, Raj Agrawal write: Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the geometry of the resulting posterior distribution and can be prohibitively slow. […]

Further formalization of the “multiverse” idea in statistical modeling

Cristobal Young and Sheridan Stewart write: Social scientists face a dual problem of model uncertainty and methodological abundance. . . . This ‘uncertainty among abundance’ offers spiraling opportunities to discover a statistically significant result. The problem is acute when models with significant results are published, while those with non-significant results go unmentioned. Multiverse analysis addresses […]

Mister P for the 2020 presidential election in Belarus

An anonymous group of authors writes: Political situation Belarus is often called the “last dictatorship” in Europe. Rightly so, Aliaskandr Lukashenka has served as the country’s president since 1994. In the 26 years of his rule, Lukashenka has consolidated and extended his power, which is today absolute. Rigging referendums has been an effective means of […]

You don’t need a retina specialist to know which way the wind blows

Jayakrishna Ambati writes: I am a retina specialist and vision scientist at the University of Virginia. I am writing to you with a question on Bayesian statistics. I am performing a meta analysis of 5 clinical studies. In addition to a random effects meta analysis model, I am running Bayesian meta analysis models using half […]

Bayesian Workflow

Aki Vehtari, Daniel Simpson, Charles C. Margossian, Bob Carpenter, Yuling Yao, Paul-Christian Bürkner, Lauren Kennedy, Jonah Gabry, Martin Modrák, and I write: The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and […]

Merlin and me talk on the Bayesian podcast about forecasting the election

Alex Androrra interviewed us, and I guess it makes sense to post the link before the election is over. A couple months ago, Alex interviewed Jennifer, Aki, and me to talk about our book, Regression and Other Stories. I can’t figure out how to directly link to that; you’ll have to follow the above link, […]

Concerns with our Economist election forecast

A few days ago we discussed some concerns with Fivethirtyeight’s election forecast. This got us thinking again about some concerns with our own forecast for The Economist (see here for more details). Here are some of our concerns with our forecast: 1. Distribution of the tails of the national vote forecast 2. Uncertainties of state […]

Between-state correlations and weird conditional forecasts: the correlation depends on where you are in the distribution

Yup, here’s more on the topic, and this post won’t be the last, either . . . Jed Grabman writes: I was intrigued by the observations you made this summer about FiveThirtyEight’s handling of between-state correlations. I spent quite a bit of time looking into the topic and came to the following conclusions. In order […]

Randomized but unblinded experiment on vitamin D as a coronavirus treatment. Let’s talk about what comes next. (Hint: it involves multilevel models.)

Under the heading, “Here we go again,” Dale Lehman writes: If you want to blog on the continuing theme – try this (it’s from Marginal Revolution, the citation): Vitamin D Can Likely End the COVID-19 Pandemic What is striking is the analysis by the Rootclaim group – repeated reliance on p values as […]

“Congressional Representation: Accountability from the Constituent’s Perspective”

Steve Ansolabehere and Shiro Kuriwaki write: The premise that constituents hold representatives accountable for their legislative decisions undergirds political theories of democracy and legal theories of statutory interpretation. But studies of this at the individual level are rare, examine only a handful of issues, and arrive at mixed results. We provide an extensive assessment of […]

epidemia: An R package for Bayesian epidemiological modeling

Jamie Scott writes: I am a PhD candidate at Imperial College, and have been working with colleagues here to write an R package for fitting Bayesian epidemiological models using Stan. We thought this might interest readers of your blog, as it is based on work previously featured there. The package is similar in spirit to […]

Some thoughts inspired by Lee Cronbach (1975), “Beyond the two disciplines of scientific psychology”

I happened to come across this article today. It’s hardly obscure—it has over 3000 citations, according to Google scholar—but it was new to me. It’s a wonderful article. You should read it right away. OK, click on the above link and read the article. Done? OK, then read on.


It’s a busy day for Bayesians. John Haman writes: The Institute for Defense Analyses – Operational Evaluation Division (OED) is looking for a Bayesian statistician to join its Test Science team.  Test Science is a group of statisticians, data scientists, and psychologists that provides expertise on experimentation to the DoD. In particular, we are looking […]

Thinking about election forecast uncertainty

Some twitter action Elliott Morris, my collaborator (with Merlin Heidemanns) on the Economist election forecast, pointed me to some thoughtful criticisms of our model from Nate Silver. There’s some discussion on twitter, but in general I don’t find twitter to be a good place for careful discussion, so I’m continuing the conversation here. Nate writes: […]

BMJ update: authors reply to our concerns (but I’m not persuaded)

Last week we discussed an article in the British Medical Journal that seemed seriously flawed to me, based on evidence such as the above graph. At the suggestion of Elizabeth Loder, I submitted a comment to the paper on the BMJ website. Here’s what I wrote: I am concerned that the model does not fit […]

Dispelling confusion about MRP (multilevel regression and poststratification) for survey analysis

A colleague pointed me to this post from political analyst Nate Silver: At the risk of restarting the MRP [multilevel regression and poststratification] wars: For the last 3 models I’ve designed (midterms, primaries, now revisiting stuff for the general) trying to impute how a state will vote based on its demographics & polls of voters […]

“To Change the World, Behavioral Intervention Research Will Need to Get Serious About Heterogeneity”

Beth Tipton, Chris Bryan, and David Yeager write: The increasing influence of behavioral science in policy has been a hallmark of the past decade, but so has a crisis of confidence in the replicability of behavioral science findings. In this essay, we describe a nascent paradigm shift in behavioral intervention research—a heterogeneity revolution—that we believe […]

The value of thinking about varying treatment effects: coronavirus example

Yesterday we discussed difficulties with the concept of average treatment effect. Part of designing a study is accounting for uncertainty in effect sizes. Unfortunately there is a tradition in clinical trials of making optimistic assumptions in order to claim high power. Here is an example that came up in March, 2020. A doctor was designing […]

“Why do the results of immigrant students depend so much on their country of origin and so little on their country of destination?”

Aleks points us to this article from 2011 by Julio Carabaña. Carabaña’s article has three parts. First is a methodological point that much can be learned from a cross-national study that has data at the level of individual students, as compared to the usual “various origins-one destination” design. Second is the empirical claim, based on […]

Resolving confusions over that study of “Teacher Effects on Student Achievement and Height”

Someone pointed me to this article by Marianne Bitler, Sean Corcoran, Thurston Domina, and Emily Penner, “Teacher Effects on Student Achievement and Height: A Cautionary Tale,” which begins: Estimates of teacher “value-added” suggest teachers vary substantially in their ability to promote student learning. Prompted by this finding, many states and school districts have adopted value-added […]