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Cross-Classified Data Analysis: Nested vs Crossed Random Effects

Explore the differences between nested and crossed random effects in statistical modeling and learn how to specify these effects. Use R to perform logistic regression on cross-classified data.

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Cross-Classified Data Analysis: Nested vs Crossed Random Effects

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  1. Stat 414 – Day 32 Lab 2 Projects

  2. Cross-classified data

  3. https://stats.stackexchange.com/questions/228800/crossed-vs-nested-random-effects-how-do-they-differ-and-how-are-they-specifiedhttps://stats.stackexchange.com/questions/228800/crossed-vs-nested-random-effects-how-do-they-differ-and-how-are-they-specified

  4. Lab 2A • Just don’t specify that the two classification variables are nested • Automatic if uniquely numbered! • Adjust notation if writing out the model • Will want to compare (c) to (d) • (g) Random slopes for vrq (centered) • What if for just one of the classification variables? • Could also then try gender • Tell a story with the data

  5. Lab 2B – Logistic Regression • Notice don’t have an epsilon term! • e.g., student to student variation or measurement to measurement variation • Assuming the same probability for all the women in the same community • Have to use R! • Use provided R script • Tell a story with the data

  6. Project advice • Tell a story with the data • Clearly identify primary variables (e.g., RV) • Don’t just list numbers • Don’t assume audience is familiar with your data • Use graphs to help tell your story • How the graphs and the model agree • Concern vs. interesting feature • Model vs. data • Start simple (impress with visuals, quality) • Why multilevel, structure of the data, assumptions (audience) • Null model, ICC • Be ready to justify choices • Keep audience’s interest

  7. Leftovers • JMP’s actual vs. predicted graph • Features of “final model” • Includes important EVs (research question, covariates) • Potential interactions have been investigated • Variables are centered where can enhance interpretation • Unnecessary terms have been removed • Checked validity using residual plots • Defensible/context

  8. Leftovers • Typically only worry about random slopes at lower levels • Typically cross higher level variables with lower level variables with random slopes

  9. Leftovers ethnicity hospital Level Variable Categorical variable and specific categories have distinct meanings Might predict different results in advance Ordinal or continuous variable Wouldn’t really make sense to be the unit of analysis • Categorical variables whose categories have no special meaning • Ahead of time, no real predictions of how compare • Would make sense to be the observational unit in a regression model (agg.) • Large number of categories • Willing to assume drawn from some distribution

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