- Bayesian data analysis
- Prior selection and justification
- Prior predictive checks
- Posterior predictions
- Marginal effects
Project Summary
This post explains a data science project I have worked on. The complete analysis code is available on GitHub. A paper detailing the analysis is currently in the works. I will present the work in progress at the 2025 VA Atlanta Joint Research Symposium.
This projects uses advanced statistics to describe the relationship between trauma and functioning. I used data from three surveys collected over 4 years. The first asks about the relationship between PTSD and functioning. The second focuses on a different kind of trauma, moral injury. The third data set has both PTSD and moral injury. This analysis could help clinicians working with military veterans to understand how different kinds of trauma affect daily living.
There were several challenges to this analysis:
- The data was messy: Answers were missing and some responses were straight-lined or Christmas-treed. All three data sets required cleaning and screening. See my other portfolio post to learn how I tackled this challenge.
- The data was zero-inflated: There were lots of 0s in the data, which is a problem for linear models. To overcome this, I fit a zero-inflated gamma regression.
- I had three similar but not identical data sets: I used Bayesian methods to integrate the findings.
Real-World Applications
People Listening: Survey data is often messy and of questionable quality. Cleaning and screening methods give confidence to analysts and stakeholders. They make results from employee surveys more accurate and credible.
People Analytics: In real-world settings, testing hypotheses is often less important than quantifying relationships. Bayesian methods is particularly useful for the later.
Health and Well-being: We know that mental disorders are bad for people, but just how bad? How do different disorders compare to each other? Comparing the impact of different kinds of trauma can be useful for clinicians and support programs to tailor programs appropriately.
Key Highlights
Prior Predictive Checks
Bayesian methods make use of external information: “the prior.” This external information can help models to “regularize” — give plausible values rather than extreme ones, especially when data is sparse.
However, priors are often criticized (unfairly) as being completely subjective, akin to falsifying data. While that’s a wrong way of looking at priors, you still need to pick good ones and justify them.
Sampled from the prior only
Used visualizations to assess if priors were reasonable
Zero-Inflated Hurdle Models
Lots of data are “zero-inflated” meaning they have too-many 0s. That makes typical statistical models a poor fit for the data.
visualizations of distributions
model selection and comparison
interpreting results
Interpreting Complex Models
Bayesian models are fairly easy to understand.
Complex models such as zero-inflated hurdle models are more difficult to understand.
Visualizing and Summarizing Posterior Predictive Distributions, Marginal Effects