Hi all, Thanks to everyone who contributed to this thread. Each comment and query was helpful, not just for my immediate needs, but for a general troubleshooting of mixed models. I've modified the original equation somewhat by removing Language as a predictor and allowing association to vary by participant. For anyone interested, the best fit model--both conceptually and statistically--is: correct response to a sentential listening prompt ~ isolated speech task 1 + isolated speech task 2 + association + (association | participant) + (1|item). This yields the following: *Predictors Odds Ratios CI p* (Intercept) 3.25 1.82 ? 5.79 <0.001 bVt Transcription 1.03 1.01 ? 1.05 0.006 Oddity 1.04 1.02 ? 1.06 <0.001 Association?opposite 0.34 0.21 ? 0.55 <0.001 Association?same 3.33 2.03 ? 5.47 <0.001 John, Simpson's paradox is a keen take and something to keep my eye on for subsequent related work. For unbalanced designs, you wouldn't say this is something common with mixed models? Is this not one of its main advantages over something like a traditional (or repeated measures) analysis of variance? Ben, I really like this approach. We've controlled pretty well for "word type" and have a fairly tight understanding of which (types of) words lead to perceptual issues in second language learners, but this could perhaps be something to use down the line in another capacity. Thanks for the suggestion and please feel free to email me if this is something you're interested in. All the best, John Jones E: johnathan.jones at gmail.com SM: linkedin.com/in/johnathanjones
contradictory odds ratios--a problem with the equation or the interpretation?
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