--- title: "Logistic Regression for Binomial Counts" output: html_document --- ```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) ``` ## Logistic Regression for Binomial Counts Read in the data ```{r} require(Sleuth3) krunnit <- case2101 ``` Let's plot the logits of the proportions vs. the logits of the probability of going extinct. ```{r message=F} require(gtools) require(ggplot2) krunnit$pi_hat <- krunnit$Extinct/krunnit$AtRisk ``` ```{r} qplot(log(Area), logit(pi_hat), data=krunnit) ``` (Note: here, the interpretation is that the total number of species is AtRisk, and out of those, the number of specise that went extinct is Extinct) ```{r} fit <- glm( cbind(Extinct, AtRisk-Extinct) ~ log(Area), family="binomial", data=krunnit) summary(fit) ``` ```{r} fit.sq <- glm(cbind(Extinct, AtRisk - Extinct) ~ log(Area) + I(log(Area)^2), family= "binomial", data= krunnit) summary(fit.sq) ``` (Note: if you do not enclose log(Area)^2 in `I()`, things don't work. You have to either do that or add an additional column to the data frame with the value `log(Area)^2`) (We haven't covered this, but BIC is used similarly to AIC) ```{r} BIC(fit) BIC(fit.sq) ```