statisticalrethinkin..

12.3. VARIABLE PROBABILITIES: BETA-BINOMIAL 325compare(m12.6,m12.7,nobs=sum(d$density))R code12.30k AICc w.AICc dAICcm11.7 3 233.96 1 0.00m11.6 2 274.27 0 40.31Again, we can compare the estimates to get a better idea for how the beta-binomial is improvingprediction, by accounting for heterogeneity:coeftab(m12.6,m12.7)R code12.31m11.6 m11.7a 2.54 2.21bp -2.65 -2.21tau NA 2.26nobs 48 48And again the estimated log-odds (a) are similar across both models, as well as the newestimate for the effect of predation on log-odds, bp. Predators being present reduces survivalprobability, unsurprisingly. In fact, it takes the average survival from logistic(2.2)≈ 0.9to logistic(2.2-2.2)≈ 0.5.But what is theta doing? Again, it’s describing the heterogeneity that remains. Now toplot the predictions, we’ll have to treat this somewhat like an interaction effect, making oneplot for when predators are absent and another for when predators are present. Here’s thecode to compute the mean and confidence interval, when predators are absent (I’ll leave itto the reader to modify it for when predators are present):post