statisticalrethinkin..

324 12. MONSTERS AND MIXTURESe results are visible in FIGURE 12.3. e black estimated curves show the same skewedshape as the empirical density. is is what the beta-binomial model is capable of copyingwith, while the binomial model assumes instead a concentrated density, peaked at 0.7 onthe horizontal axis in FIGURE 12.3, with 95% of its probability between 0.67 and 0.73 (theHPDI you computed earlier). us the pure-binomial model does a poor job of describingthe heterogeneity in survival across cases, while the beta-binomial is built to do better at thiskind of job.Still, you might ask if the beta-binomial model is just doing better here, because wehaven’t yet included predictor variables to soak up some of that heterogeneity. Aer all, thecentral purpose of GLM’s is to explain variation in outcomes using variation in predictors.So let’s include some predictors, now.Adding predators. Let’s add a dummy variable for the presence of predators, which islikely to explain a lot of variation in survival. To make the dummy and fit both new models:R code12.29d$pred.yes