We are using a dataset with ~2,000 households across 20 different sites across the world. We are using a Mixed Effects Logistic Regression to examine the effect of income groups (categorical IV) on food insecurity (binary DV). We include other variables in the models, but this is our principal relationship of interest. We are using site as a grouping variable. Based on our theoretical understanding – we include a random intercept as well as a random slope term, because we expect the effect of income group to vary across sites.
We have produced the fixed effects (e.g., income group, and other relevant variables) as well as the random effects (site and income group). The fixed effect Odds Ratios tell us the “average” effect of IV on D, accounting for other variables in the model. When we plot the random effects as Odds Ratios, we understand this as meaning how the Odds Ratios vary across sites – or what is the effect of IV on D in a specific site. However, we also recognize that this is different than running site-wise regression models. We have several interpretational questions as it relates to the full model (~2000) effect of IV of D, the random effects, and the site-wise models (which we also ran, i.e., 20 logistic regressions):
What is the difference between running individual site-specific models (20), and using the random slopes extracted from the full model to investigate site-wise differences? That is, we know the individual site models are different from what we see as the random slopes -- but how are these different?
The random slopes for each site are sometimes inconsistent from the full model slope. We are interested in giving attention to the average or full model slope, but not at the expense of overshadowing particular sites if those are very different. Can anyone provide interpretational guidance here?
Most examples (we found) that look at individual random slopes and compare this to the ‘full’ model (fixed portion), all point generally in the same direction although their slope might vary. There are of course cases where this is more complicated; some sites could have negative slopes (or <1 OR) that run counter to the ‘full model’ effect. How can these be interpreted? If there is a large variation in random effect values across sites – how important the fixed effects values are?