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Archive of posts filed under the Multilevel Modeling category.

The Pandora Principle in statistics — and its malign converse, the ostrich

The Pandora Principle is that once you’ve considered a possible interaction or bias or confounder, you can’t un-think it. The malign converse is when people realize this and then design their studies to avoid putting themselves in a position where they have to consider some potentially important factor. For example, suppose you’re considering some policy […]

What explains my lack of openness toward this research claim? Maybe my cortex is just too damn thick and wrinkled

Diana Senechal writes: Yesterday Cari Romm reported that researchers had found a relation between personality traits and cortex shape: “People who scored higher on openness tended to have thinner and smoother cortices, while those who scored high on neuroticism had cortices that were thicker and more wrinkled.” I [Senechal] looked up the study itself (https://academic.oup.com/scan/article/doi/10.1093/scan/nsw175/2952683/Surface-based-morphometry-reveals-the) […]

Multilevel modeling: What it can and cannot do

Today’s post reminded me of this article from 2005: We illustrate the strengths and limitations of multilevel modeling through an example of the prediction of home radon levels in U.S. counties. . . . Compared with the two classical estimates (no pooling and complete pooling), the inferences from the multilevel models are more reasonable. . […]

Adding a predictor can increase the residual variance!

Chao Zhang writes: When I want to know the contribution of a predictor in a multilevel model, I often calculate how much of the total variance is reduced in the random effects by the added predictor. For example, the between-group variance is 0.7 and residual variance is 0.9 in the null model, and by adding […]

Sparse regression using the “ponyshoe” (regularized horseshoe) model, from Juho Piironen and Aki Vehtari

The article is called “Sparsity information and regularization in the horseshoe and other shrinkage priors,” and here’s the abstract: The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but has previously suffered from two problems. First, there has been no systematic way of specifying a prior for the global shrinkage […]

Analyze all your comparisons. That’s better than looking at the max difference and trying to do a multiple comparisons correction.

[cat picture] The following email came in: I’m in a PhD program (poli sci) with a heavy emphasis on methods. One thing that my statistics courses emphasize, but that doesn’t get much attention in my poli sci courses, is the problem of simultaneous inferences. This strikes me as a problem. I am a bit unclear […]

Question about the secret weapon

Micah Wright writes: I first encountered your explanation of secret weapon plots while I was browsing your blog in grad school, and later in your 2007 book with Jennifer Hill. I found them immediately compelling and intuitive, but I have been met with a lot of confusion and some skepticism when I’ve tried to use […]

Breaking the dataset into little pieces and putting it back together again

Alex Konkel writes: I was a little surprised that your blog post with the three smaller studies versus one larger study question received so many comments, and also that so many people seemed to come down on the side of three smaller studies. I understand that Stephen’s framing led to some confusion as well as […]

PhD student fellowship opportunity! in Belgium! to work with us! on the multiverse and other projects on improving the reproducibility of psychological research!!!

[image of Jip and Janneke dancing with a cat] Wolf Vanpaemel and Francis Tuerlinckx write: We at the Quantitative Psychology and Individual Differences, KU Leuven, Belgium are looking for a PhD candidate. The goal of the PhD research is to develop and apply novel methodologies to increase the reproducibility of psychological science. More information can […]

UK election summary

The Conservative party, led by Theresa May, defeated the Labour party, led by Jeremy Corbyn. The Conservative party got 42% of the vote, Labour got 40% of the vote, and all the other parties received 18% between them. The Conservatives ended up with 51.5% of the two-party vote, just a bit less than Hillary Clinton’s […]

No conf intervals? No problem (if you got replication).

This came up in a research discussion the other day. Someone had produced some estimates, and there was a question: where are the conf intervals. I said that if you have replication and you graph the estimates that were produced, then you don’t really need conf intervals (or, for that matter, p-values). The idea is […]

The Publicity Factory: How even serious research gets exaggerated by the process of scientific publication and media exposure

The starting point is that we’ve seen a lot of talk about frivolous science, headline-bait such as the study that said that married women are more likely to vote for Mitt Romney when ovulating, or the study that said that girl-named hurricanes are more deadly than boy-named hurricanes, and at this point some of these […]

U.K. news article congratulates YouGov on using modern methods in polling inference

Mike Betancourt pointed me to this news article by Alan Travis that is refreshingly positive regarding the use of sophisticated statistical methods in analyzing opinion polls. Here’s Travis: Leading pollsters have described YouGov’s “shock poll” predicting a hung parliament on 8 June as “brave” and the decision by the Times to splash it on its […]

Come to Seattle to work with us on Stan!

Our colleague Jon Wakefield in the Department of Biostatistics at the University of Washington is interested in supervising a 2-year postdoc through this training program. We’re interested in finding someone who would with Jon and another faculty member (who is assigned on the basis of interests) on exciting projects in spatio-temporal modeling and the environmental […]

The Other Side of the Night

Don Green points us to this quantitative/qualitative meta-analysis he did with Betsy Levy Paluck and Seth Green. The paper begins: This paper evaluates the state of contact hypothesis research from a policy perspective. Building on Pettigrew and Tropp’s (2006) influential meta-analysis, we assemble all intergroup contact studies that feature random assignment and delayed outcome measures, […]

#NotAll4YearOlds

I think there’s something wrong this op-ed by developmental psychologist Alison Gopnik, “4-year-olds don’t act like Trump,” and which begins, The analogy is pervasive among his critics: Donald Trump is like a child. . . . But the analogy is profoundly wrong, and it’s unfair to children. The scientific developmental research of the past 30 […]

Causal inference using Bayesian additive regression trees: some questions and answers

[cat picture] Rachael Meager writes: We’re working on a policy analysis project. Last year we spoke about individual treatment effects, which is the direction we want to go in. At the time you suggested BART [Bayesian additive regression trees; these are not averages of tree models as are usually set up; rather, the key is […]

Using Stan for week-by-week updating of estimated soccer team abilites

Milad Kharratzadeh shares this analysis of the English Premier League during last year’s famous season. He fit a Bayesian model using Stan, and the R markdown file is here. The analysis has three interesting features: 1. Team ability is allowed to continuously vary throughout the season; thus, once the season is over, you can see […]

Splines in Stan! (including priors that enforce smoothness)

Milad Kharratzadeh shares a new case study. This could be useful to a lot of people. And here’s the markdown file with every last bit of R and Stan code. Just for example, here’s the last section of the document, which shows how to simulate the data and fit the model graphed above: Location of […]

A completely reasonable-sounding statement with which I strongly disagree

From a couple years ago: In the context of a listserv discussion about replication in psychology experiments, someone wrote: The current best estimate of the effect size is somewhere in between the original study and the replication’s reported value. This conciliatory, split-the-difference statement sounds reasonable, and it might well represent good politics in the context […]