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Archive of posts filed under the Multilevel Modeling category.

Routine hospital-based SARS-CoV-2 testing outperforms state-based data in predicting clinical burden.

Len Covello, Yajuan Si, Siquan Wang, and I write: Throughout the COVID-19 pandemic, government policy and healthcare implementation responses have been guided by reported positivity rates and counts of positive cases in the community. The selection bias of these data calls into question their validity as measures of the actual viral incidence in the community […]

“They adjusted for three hundred confounders.”

Alexey Guzey points to this post by Scott Alexander and this research article by Elisabetta Patorno, Robert Glynn, Raisa Levin, Moa Lee, and Krista Huybrechts, and writes: I [Guzey] am extremely skeptical of anything that relies on adjusting for confounders and have no idea what to think about this. My intuition would be that because […]

Include all design information as predictors in your regression model, then postratify if necessary. No need to include survey weights: the information that goes into the weights will be used in any poststratification that is done.

David Kaplan writes: I have a question that comes up often when working with people who are analyzing large scale educational assessments such as NAEP or PISA. They want to do some kind of multilevel analysis of an achievement outcome such as mathematics ability predicted by individual and school level variables. The files contain the […]

Flaxman et al. respond to criticisms of their estimates of effects of anti-coronavirus policies

As youall know, as the coronavirus has taken its path through the world, epidemiologists and social scientists have tracked rates of exposure and mortality, studied the statistical properties of the transmission of the virus, and estimated effects of behaviors and policies that have been tried to limit the spread of the disease. All this is […]

“Inferring the effectiveness of government interventions against COVID-19”

John Salvatier points us to this article by Jan Brauner et al. that states: We gathered chronological data on the implementation of NPIs [non-pharmaceutical interventions, i.e. policy or behavioral interventions] for several European, and other, countries between January and the end of May 2020. We estimate the effectiveness of NPIs, ranging from limiting gathering sizes, […]

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 […]