If you have a Windows-based laptop that you will be using in class, please do the following.
Download and install Program MARK from the site that Evan Cooch maintains for the program,
Install/update R and RStudio to the latest versions (software links are available from the course software site),
Catch up on reading through the handouts, R Notebook exercises, and readings for this week,
Calculate the Maximum Likelihood Estimate (MLE) of the probability of success, \(p\), for a study in which the survival status of 40 individuals was monitored for 1 year and had 23 individuals survive and 17 die. Calculate the MLE using the following 3 methods using a model that assumes that \(p\) is the same for all individuals.
closed-form estimator for \(\hat{p}\),
working out the \(ln\mathcal{L}\) for potential values of \(p\) from 0, 0.01, 0.02, …, 1 and identifying which potential value of \(p\) is associated with the maximum value of \(ln\mathcal{L}\),
using R’s glm
function as shown in R Notebook 2. You will need to replace the command we used to create random values of \(y\) in the Notebook, y = rbinom(n, 1, 0.7)
with the following command: y = c(rep(1, 23), rep(0, 17))
.
Find the MLE for \(SE(\hat{p})\) using the following 2 methods.
use the closed-form estimator for \(Var(\hat{p})\) and take the square root of that value to obtain \(SE(\hat{p})\),
using R’s glm
function as shown in R Notebook 2.