If you have a Windows-based laptop that you will be using in class, please do the following.

  1. Download and install Program MARK from the site that Evan Cooch maintains for the program,

  2. Install/update R and RStudio to the latest versions (software links are available from the course software site),

  3. Catch up on reading through the handouts, R Notebook exercises, and readings for this week,

  4. 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)).

  5. 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.