MATH 620 Week 4 Homework Assignment (20 points) In this week's homework assignment, you'll be modeling data using generalized linear models, evaluating model assumptions, interpreting parameter estimates, and generating figures based on your results. Please form your responses using complete sentences where appropriate (1 point), and provide all code used to obtain the answer below each response (1 point). Question 1. Staff at an aquaculture facility were rearing two imperiled marine fish species for release into the wild to bolster natural populations. For simplicity's sake, let's call them species "A" and "B". Unfortunately, there was a colony-wide outbreak of the parasite Cryptocaryon irritans that causes "white spot disease". Although white spot disease can be fatal, it isn't clear how susceptible each fish species is to C. irritans. Therefore, the staff sent off samples from each fish to a lab to test for presence or absence of the parasite. At the time of sample collection staff recorded the ID of the tank a fish came from, the fish species being sampled, and the water temperature (C) of the tank. The presence or absence of C. irritans ("CI" in the dataset) for each sampled fish was noted as "1" or "0", respectively. These data are in the file "MATH 620 Week 4 assignment dataset 1.csv". a) Run a generalized linear model to determine whether the probability of C. irritans presence for a sampled fish is dependent on water temperature. What probability distribution did you use for your model and why? Provide an odds ratio estimate and 95% confidence interval for the effect of water temperature. Does this information suggest water temperature influences susceptibility to the parasite? Explain why or why not. Was there evidence of overdispersion in your model? How did you evaluate this assumption? (3 points) b) Run a model similar to the one you did for question 1a but predict whether the probability of C. irritans presence for a sampled fish is dependent on species. Did you find any evidence suggesting species differed in susceptibility to the parasite? Provide an odds ratio estimate and 95% confidence interval for Species B to help support your answer. Was there evidence of overdispersion in the data? Explain why or why not using support from your modeling procedure. (2 points) c) Using your above models, you've made inferences about susceptibility to C. irritans, but we may have forgotten an important aspect of the dataset: data points from the same tank are not independent. Model the data from questions 2a and 2b using the same fixed effects but include a random intercept for "tank". How do the log odds estimates and standard errors in the model outputs and odds ratio estimates with 95% confidence intervals change by including the random effect? (2 points) d) Using your models from question 1c, provide publication quality figures showing the mean predicted probability of C. irritans presence as a function of temperature and for each species with 95% confidence intervals. Interpret what these results could mean in terms of biological relevance. (2 points)