Linear model extensions

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• add code chunks by clicking the Insert Chunk button on the toolbar or by pressing Ctrl+Alt+I to answer the questions!
• render your file to produce a markdown version that you can see!
• save your work often
  • commit it via git!
  • push updates to github

Overview

This practice reviews the extensions to linear models.

1

In a study considering how the presence of sea stars changed snail growth patterns, ~25 snails were grown in containers containing 0,1, or 2 seastars.
Since non-consumptive effects are often threshold based, these treatments levels should be considered as groups (not as a continuous variable!). The data is available at

https://raw.githubusercontent.com/jsgosnell/CUNY-BioStats/master/datasets/snail_modified_for_class.csv

FL is the final length of measured snails, and the treatment (coded 1-3) correspond to [1=Control (no predators). 2=1 predator treatment,3=2 predator treatment).

What method would you use to analyze this data and why? Carry out your test, stating your null hypothesis, test assumptions, p-value, and interpretation.
Describe any necessary steps and provide graphics and values as needed. If needed, can you determine which treatments differ from each other?

2

(From OZDasl) The data give the ambient temperature and the number of primary O-rings damaged for 23 of the 24 space shuttle launches before the launch of the space shuttle Challenger on January 20, 1986. (Challenger was the 25th shuttle. One engine was lost at sea and could not be examined.) Each space shuttle contains 6 primary O-rings.

Note these are counts. We can analyze this data using a Poisson distribution or binomial. Make sure you understand why each one is possible, which one is better, and carry out the analysis. Data is available @

http://www.statsci.org/data/general/challenger.txt

3

Returning to the whelk length-mass relationship from class, try fitting an exponential curve to the data. As a hint, try

nls(Mass ~ exp(b0 + b1 * Shell.Length), whelk, 
                   start = list(b0 =1, b1=0), na.action = na.omit)

Compare this model to those that assume a linear and power relationship. Data is available @

https://raw.githubusercontent.com/jsgosnell/CUNY-BioStats/master/datasets/whelk.csv

4

Going back to the TEAM dataset, remember we found that elevation had no impact on carbon storage. But that was a linear fit. Use a gam (generalized additive model) to see if elevation can be related to carbon storage in an additive model. Note we can use the gamm (generalized additive mixed model) function in the mgcv package to denote mixed effects. For example (from help file)

b2 <- gamm(y~s(x0)+s(x1)+s(x2),family=poisson,
           data=dat,random=list(fac=~1))

Team data is available @

https://github.com/jsgosnell/CUNY-BioStats/blob/master/datasets/team_data_no_spaces.csv