Graphical hierarchical model checking and type-M errors
Two excellent blog posts by Andrew Gelman that I thought I’d pass on:
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At stats beers the question of how to visualize or check a mixed-effect or hierarchical model often comes up. Andrew Gelman is one of the best at this. He and the primary author, a post doc of his (Kenneth Shirley), have a new paper out that serves as a fantastic example of graphical model checking of a hierarchical model. It’s worth scanning through the figures for ideas. [1]
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Gelman often discusses type-M errors. Essentially, these errors describe how you will tend to overestimate effect sizes when you look at statistically significant test results with low power. This is relevant to much of what we do, especially working with small sample sizes, and given that many biological effects are in reality small.
In a blog post Gelman links to three articles describing type-M errors of increasing complexity. The American Scientist article “Of Beauty, Sex and Power” in particular might be a good fun read for people in the lab. It discusses widely-publicized and wonky claims about factors affecting human sex ratios due to type-M errors.