# Sum-score effect sizes for multilevel Bayesian cumulative probit models

This is a follow-up to my earlier post, Notes on the Bayesian cumulative probit. This time, the topic we’re addressing is: After you fit a full multilevel Bayesian cumulative probit model of several Likert-type items from a multi-item questionnaire, how can you use the model to compute an effect size in the sum-score metric?

# Just use multilevel models for your pre/post RCT data

I’ve been thinking a lot about how to analyze pre/post control group designs, lately. Happily, others have thought a lot about this topic, too. The goal of this post is to introduce the change-score and ANCOVA models, introduce their multilevel-model counterparts, and compare their behavior in a couple quick simulation studies. Spoiler alert: The multilevel variant of the ANCOVA model is the winner.

# Example power analysis report, II

In an earlier post, I gave an example of what a power analysis report could look like for a multilevel model. At my day job, I was recently asked for a rush-job power analysis that required a multilevel model of a different kind and it seemed like a good opportunity to share another example.

# Notes on the Bayesian cumulative probit

In this post, I have reformatted my personal notes into something of a tutorial on the Bayesian cumulative probit model. Using a single psychometric data set, we explore a variety of models, starting with the simplest single-level thresholds-only model and ending with a conditional multilevel distributional model.

# Use emmeans() to include 95% CIs around your lme4-based fitted lines

You’re an R user and just fit a nice multilevel model to some grouped data and you’d like to showcase the results in a plot. In your plots, it would be ideal to express the model uncertainty with 95% interval bands. If you’re a frequentist and like using the popular lme4 package, you might be surprised how difficult it is to get those 95% intervals. I recently stumbled upon a solution with the emmeans package, and the purpose of this blog post is to show you how it works.

# Got overdispersion? Try observation-level random effects with the Poisson-lognormal mixture

It turns out that you can use random effects on cross-sectional count data. Yes, that’s right. Each count gets its own random effect. Some people call this observation-level random effects and it can be a tricky way to handle overdispersion. The purpose of this post is to show how to do this and to try to make sense of what it even means.

# Example power analysis report

If you plan to analyze your data with anything more complicated than a t-test, the power analysis phase gets tricky. I’m willing to bet that most applied researchers have never done a power analysis for a multilevel model and probably have never seen what one might look like, either. The purpose of this post is to give a real-world example of just such an analysis.

# Make ICC plots for your brms IRT models

The purpose of this blog post is to show how one might make ICC and IIC plots for brms IRT models using general-purpose data wrangling steps.

When your MCMC chains look a mess, you might have to manually set your initial values. If you’re a fancy pants, you can use a custom function.

# Effect sizes for experimental trials analyzed with multilevel growth models: Two of two

This post is the second of a two-part series. In the first post, we explored how one might compute an effect size for two-group experimental data with only 2 time points. In this second post, we fulfill our goal to show how to generalize this framework to experimental data collected over 3+ time points. The data and overall framework come from Feingold (2009).

# Effect sizes for experimental trials analyzed with multilevel growth models: One of two

The purpose of this series is to show how to compute a Cohen’s-d type effect size when you have longitudinal data on 3+ time points for two experimental groups. In this first post, we’ll warm up with the basics. In the second post, we’ll get down to business. The data and overall framework come from Feingold (2009).

# Regression models for 2-timepoint non-experimental data

I recently came across Jeffrey Walker’s free text, Elements of statistical modeling for experimental biology, which contains a nice chapter on 2-timepoint experimental designs. Inspired by his work, this post aims to explore how one might analyze non-experimental 2-timepoint data within a regression model paradigm.

# Time-varying covariates in longitudinal multilevel models contain state- and trait-level information: This includes binary variables, too

When you have a time-varying covariate you’d like to add to a multilevel growth model, it’s important to break that variable into two. One part of the variable will account for within-person variation. The other part will account for between person variation. Keep reading to learn how you might do so when your time-varying covariate is binary.

# Would you like all your posteriors in one plot?

In response to a DM question, here we practice a few different ways you can combine the posterior samples from your Bayesian models into a single plot.

# Stein’s Paradox and What Partial Pooling Can Do For You

In many instances, partial pooling leads to better estimates than taking simple averages will, a finding sometimes called Stein’s Paradox. In 1977, Efron and Morris published a great paper discussing the phenomenon. In this post, I’ll walk out Efron and Morris’s baseball example and then link it to contemporary Bayesian multilevel models.